main: keep only what reproduces the manuscript; everything else lives on dev
Removed from main (all preserved on the dev branch): the arXiv build and
its sources, design documents (blueprint, results summary, review responses,
essay drafts), tasks/ and CLAUDE.md, the cover letter and reference tooling,
two unused manuscript figures, and every experiment that feeds no figure or
number in the paper: the collapse null, the sexual-vs-asexual lineage, the
NK speciation variant, the 0.5B single-seed LLM prototypes, the compose and
society experiments with their calibration and pilot runs, and their
configs, runners, tests, figure scripts and PBS jobs. Their result bundles
are moved to results/_archive/ (ignored) so the parquets stay on disk.
Also: plot_llm_speciation reads the s{seed}/ layout; the mating-breadth
plot writes under its bundle name; Makefile targets reduced to the kept
experiments; REPRODUCING.md and README point to dev for the rest.
Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Y64o8FKP7rCuXzC48pxpMm
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# arXiv submission notes (Phase 2 of the PNAS work order)
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**What to upload.** The source package: `main.tex`, `body.tex`, `figs/` (three PDFs). arXiv rejects
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TeX-produced PDF-only uploads, so upload source; all packages are standard and `\pdfoutput=1` is set,
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so arXiv's pdflatex builds it (verified locally with tectonic; `main.pdf` in this directory is the
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reference build, 20 pp). To rebuild after editing the Markdown source of truth:
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`python paper/arxiv/md2tex.py && (cd paper/arxiv && tectonic main.tex)`.
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**Categories.** Primary: `q-bio.PE` (Populations and Evolution). Cross-list: `cs.LG` and `cs.NE`.
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If arXiv asks for an endorsement for q-bio.PE (first submission to the archive), either request it
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(an evolutionary-biology colleague with q-bio postings can endorse in one click) or flip primary to
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`cs.NE` with `q-bio.PE` as cross-list — the paper is defensible either way; q-bio.PE primary is
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preferred for the PNAS audience trail.
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**License.** arXiv non-exclusive license (default) is fine for PNAS. Do not pick CC-BY unless you
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want it — PNAS permits preprints under any license, but the default keeps options open.
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**Abstract for the arXiv field** (plain text, ~1,750 chars — the field caps at 1,920; the paper's
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long abstract stays in the PDF):
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> AI is shifting from single frozen models to populations of agents that persist, specialise, and are
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> recombined into new models. The field describes this with evolutionary vocabulary — crossover, mate
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> choice, offspring — but as metaphor over search. We argue the right theory already exists: the
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> population genetics of the evolution of sex. Training each generation on the last is genetic drift,
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> and model collapse is Muller's ratchet, the decay of an asexual lineage (we take the
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> collapse-is-drift diagnosis as settled and cite it). The cure is sexual: ground every generation in
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> data from a non-drifting reality (immigration, with a critical real-data fraction far below one);
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> recombine many complementary parents (model merging — where recombination preserves the union of
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> what the parents kept, while averaging cancels the benefit); and preserve diversity. Offspring then
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> exceed every parent (the Fisher-Muller effect, shown in merged language models up to 7B). Sex has a
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> limit: as models diverge they can speciate — a merge-compatibility cliff governed by epistasis
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> (Bateson-Dobzhansky-Muller incompatibilities) whose damage snowballs. We model this and confirm it
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> in real weights: a merge barrier survives alignment under the full function-preserving symmetry
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> group of the network, rising with functional conflict while hybrid fitness falls to inviability —
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> yet absent conflicting training signals, divergently-specialised lineages developed no isolation,
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> the merge instead rescuing the forgetting specialists. AI can also do what biology cannot —
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> directed sex: unbounded parents, chosen mates, offspring screened before they are kept. We support
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> the argument with closed-form-validated simulations, trained networks, an image generator, and LLM
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> prototypes, and position it against the 2025-26 evolutionary-AI landscape.
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**After posting.** Record the arXiv id in `tasks/workorder-pnas-submission.md`; sync v2 with the
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PNAS-submitted text at Phase 5. PNAS permits preprints.
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\subsection*{A note on vocabulary (please read this first)}
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This paper sits at the meeting point of three fields, and it is written so that a reader from any one of them can follow all of it. We therefore \textbf{spell out} each field's jargon the first time it appears, even at the risk of belabouring the obvious for the specialist. A short glossary, in case you skipped a definition:
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\begin{itemize}
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\item \textbf{Model collapse} \emph{(machine learning)} --- the degeneration that happens when you train a model on data produced by earlier models, over and over: rare cases disappear and the model drifts toward a bland average.
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\item \textbf{Distillation} \emph{(machine learning)} --- training a fresh ``student'' model on the outputs of one or more ``teacher'' models, so the student ends up knowing a compressed version of what they knew.
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\item \textbf{Model merging} \emph{(machine learning)} --- combining several trained models directly, at the level of their weights, into one --- no retraining. (Think of it as breeding two models rather than teaching a third.)
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\item \textbf{Genetic drift} \emph{(population genetics)} --- the random loss of rare variants that happens in any finite population simply because not everyone leaves offspring. It is the neutral, no-selection baseline of evolution.
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\item \textbf{Wright--Fisher process} \emph{(population genetics)} --- the standard mathematical model of drift. Our minimal model of knowledge transmission \emph{is} this process exactly; a real trained network is this process plus a measurable, architecture-specific bias we quantify.
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\item \textbf{Recombination / sexual reproduction} \emph{(biology)} --- making an offspring by combining pieces from more than one parent, rather than copying a single parent (which is \emph{asexual} reproduction).
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\item \textbf{Muller's ratchet} \emph{(population genetics)} --- the way an asexual lineage, one that never recombines, accumulates damage it can never undo. We will argue it is the right lens for the \emph{irreversible} part of model collapse --- the capabilities that, once lost from every parent, no merging can rebuild.
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\item \textbf{Catastrophic forgetting} \emph{(machine learning / neuroscience)} --- a neural network overwriting what it knew when it learns something new.
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\end{itemize}
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We have tried to keep the big picture legible on every page, and to be candid about what is argument and what is evidence. The evidence is mostly from \textbf{deliberately small models} --- mathematics, small neural networks, image generators, and evolutionary simulations. A first bridge to real language models exists --- a prototype that recombines LoRA-specialised Qwen models up to 7B on a GPU cluster, which confirms the recombination signs (below) --- but the \emph{full grounded society} has not yet been built on a large language model. We will say so repeatedly, because the gap matters.
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\medskip\hrule\medskip
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\section*{Abstract}
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AI is turning from single frozen models to \textbf{populations of agents} that persist, specialise, and are increasingly \emph{recombined} into new models --- a shift visible in multi-agent societies, population-based self-improvement, and the explosion of \textbf{model merging}. The field is doing this with the vocabulary of evolution --- ``crossover,'' ``mutation,'' ``mate choice,'' ``offspring that beat their parents'' --- but as loose metaphor draped over search algorithms. This paper argues that a rich, quantitative body of applicable theory already exists in the branch of biology that studies exactly this: the \textbf{evolution of sex}. Ninety years of population genetics analyse when reproducing a population by \emph{recombination} beats copying, when it backfires, and how to do it better --- and, read as an engineering framework, it supplies overlooked variables and testable design rules for keeping a society of models learning across generations instead of decaying. The underlying shift of perspective is the contribution we most want to land: \textbf{treat multigenerational model populations as systems whose inheritance, diversity, and compatibility must be managed --- not merely as collections of models to optimise.}
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We take one diagnosis as settled and cite it as such: training each generation on the last is \textbf{genetic drift}, and the resulting \textbf{model collapse} is the loss of rare variants a finite population always suffers (the Wright--Fisher process; formalised for language models by Shumailov et al., 2024, and Riis, 2026). We claim none of that. Our contribution is on the remedy side. Single- teacher copying is \textbf{asexual} reproduction, and the irreversible arm of its decay corresponds to \textbf{Muller's ratchet} (a correspondence we state with its scope, not as identity); the remedy biology found for the ratchet is \textbf{sex}. A society of models should reproduce sexually --- each new model \textbf{recombined from several complementary parents} (which the field already does, as \emph{model merging}), selection \textbf{anchored to a reality that can say no} (not to the consensus of other models), and diversity actively \textbf{preserved}. In our models --- from closed-form to trained networks to a language-model prototype --- those three ingredients together let a lineage not merely avoid collapse but \textbf{climb}, producing models fitter than any ancestor (the \textbf{Fisher--Muller effect}) while each specialty is re-earned and exceeded; whether the full recipe holds at frontier scale is the open question the framework is built to test.
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From the geneticist's apparatus we extract falsifiable, load-bearing claims (each stated with its operator and scope in the text): (i) \textbf{``merge, don't average''} --- a conservation result: refitting a child to the \emph{mean of its parents' output distributions} conserves expected rare-capability mass at the single-parent level, cancelling the multi-parent gain \emph{to first order in the rare-item regime} (outside it, variance reduction from averaging can help --- the result is a first-order cancellation, not a universal impossibility), while union-preserving operators realise the gain in all regimes --- derived in the minimal model, with its weight-space image the headroom rule below; (ii) \textbf{offspring can exceed every parent} (Fisher--Muller), the real argument for sex in model societies; (iii) on \textbf{rugged, epistatic} task landscapes, blind recombination causes \textbf{outbreeding depression}, yielding a design rule --- \emph{merge freely when skills are additive, sparingly and with selection when entangled, and route rather than blend under overlap}; (iv) \textbf{grounding is immigration} from a non-drifting reality, giving a critical real-data fraction far below one; and (v) --- the sharpest new prediction --- sex has a \textbf{limit}: as two models diverge they undergo \textbf{speciation}, a merge-compatibility cliff (compatible \(\rightarrow\) outbreeding depression \(\rightarrow\) hybrid inviability) whose onset is set by divergence \emph{and} epistasis via \textbf{Bateson--Dobzhansky--Muller incompatibilities}, and whose damage grows \emph{super-linearly} (the Orr--Turelli snowball). We introduce and model this ``model speciation'' directly, and confirm it in real trained weights: a merge barrier that survives alignment under the \emph{full} function-preserving symmetry group of the network (not just Git Re-Basin permutations), rising with functional conflict while hybrid fitness falls to inviability --- with an honest converse we pre-registered and found: absent conflicting training signals, divergently-specialised lineages of shared ancestry developed \emph{no} isolation at any divergence tested, the merge instead \emph{rescuing} the forgetting specialists. Isolation must be provoked by conflict; specialisation alone did not speciate. AI also has an advantage biology lacks: \textbf{directed sex} --- unbounded parents, chosen mates, and offspring screened before they are kept --- engineered recombination with a flexibility of parent choice and pre-deployment screening that natural mating systems do not approach.
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We support the argument with \textbf{minimal, reproducible models} --- a closed-form-exact account of drift and grounding, the same effects in small trained networks and an MNIST image generator, a real-weight demonstration of the speciation cliff (a Git Re-Basin residual that survives neuron alignment), and evolutionary simulations of the whole society --- and a first \textbf{language-model prototype}: merging LoRA-specialised Qwen models (to 7B on a GPU cluster) yields a generalist that beats every specialist parent, with the sharp headroom condition under which ``merge, don't average'' bites. The scope is honest: these are existence proofs and design rules; the \emph{whole grounded society} on a large language model is the open step. We position the work carefully against the crowded 2025--2026 landscape of evolutionary-AI and merging methods --- conceding what they own and marking, precisely, what a genuine population-genetics of sex adds.
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\medskip\hrule\medskip
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\section*{1. From a society in space to a society in time}
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The idea of many AI agents working together --- a ``society of mind'' (Minsky, 1986), or today's multi-agent systems --- arranges intelligence across \emph{space}: several specialists side by side, dividing a task. This paper is about a different axis: \emph{time}. Not a society that merely exists at one moment, but one that \textbf{persists and renews across generations}, each new cohort of models starting from the compressed knowledge of the last.
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The unit that matters is therefore the \textbf{generation}, and the event that matters is \textbf{reproduction}: the making of a new model from older ones. A single model, like a single mind, is bounded and eventually stops improving. A \emph{lineage} need not be. Human civilisation is not clever because any one person is; it is clever because each generation inherits the distilled achievements of the previous one and adds a little. We propose building AI the same way --- and, crucially, getting the \emph{reproduction} right, because that is exactly where it can go wrong.
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\subsection*{Where this sits, and what is new}
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This axis is suddenly crowded. By 2026 several groups build \textbf{populations of models or agents that improve across generations}: societies of independently-specialised models that self-improve for more rounds than a single agent (Multiagent Finetuning --- Subramaniam et al., 2025); open-ended archives of self-rewriting coding agents (the Darwin--Gödel Machine --- Zhang et al., 2025); groups that evolve by sharing experience across branches (Weng et al., 2026); persistent agent \emph{ecologies} with reproduction and cumulative culture (TerraLingua --- 2026). In parallel, \textbf{model merging} has become a small industry with an overtly evolutionary vocabulary: crossover-mutation-selection over LLM populations (GENOME --- 2025), niching and ``mate choice'' (Sakana's M2N2 --- 2025), and evolutionary search over merge recipes (Akiba et al., \emph{Nature Mach. Intell.} 2024/25).
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We are candid about the consequence. Three things we do \textbf{not} claim. First, that collapse is Wright--Fisher drift: formalised independently (Riis, 2026; Shumailov et al., 2024), sharpened to a closed-form first-extinction law whose onset coincides with collapse (Benati et al., 2025) and to a quantitative-trait-genetics account for diffusion models (Yoon et al., ICLR 2025), and conceded here. Second, the bare empirical facts that a merged model can beat its parents, that decorrelated parents merge better, and that naive averaging is inferior to sign- or routing-based merges (TIES, DARE, mixture-of-experts routing): all established. Third, that merge success can be \emph{predicted at all}: machine-learning-native predictors exist, from interpretable pairwise metrics (gradient alignment --- Zhou et al., 2026) to capacity/rate-distortion accounts of ``merging collapse'' (2026); what they lack, and we supply, is the \emph{mechanism} --- when and why the failure is a coordinate artefact versus genuine functional incompatibility, and what moves the cliff. What a geneticist is placed to supply is a \textbf{framework} rather than a search heuristic. The nearest precursor is a theory-of-computation tradition reading sex as an algorithm for \emph{mixability} (Livnat \& Papadimitriou, 2016), pre-dating model merging; the works above use evolution chiefly as vocabulary over an optimiser, and --- to our knowledge --- the quantitative apparatus of the evolution of sex (Fisher--Muller, outbreeding depression, migration--drift balance, reproductive isolation) has not previously been carried over as more than metaphor. We are also candid about what \emph{kind} of contribution each of our claims is, because three different things are easily conflated: \textbf{interpretation} (an existing result is usefully understood in these terms --- e.g., merged offspring beating their parents as Fisher--Muller), \textbf{explanation} (the transferred mechanism accounts for observations existing accounts leave open --- e.g., which merge failures are coordinate artefacts and which are functional), and \textbf{prediction} (the framework forecasts an unmeasured outcome and improves a design decision). This paper is strongest on the first, makes concrete progress on the second, and reports a first, bounded step on the third: a \textbf{controlled predictive test} at small scale in which pre-merge \emph{functional-disagreement} measures --- chosen by the framework --- showed a detectable, held-out-robust association with merge damage on a constructed task grid, while the selected weight-geometry baselines did not. We are precise about that result's boundary where it is reported: it is a small-model demonstration on a constructed grid; the proposed epistasis-specific refinement did not outperform plain disagreement; predictor differences are not individually significant head-to-head; and whether the prediction improves a budget-matched operator choice remains open. The organising shift we argue for is prior to any single mechanism: \textbf{treat multigenerational model populations as systems whose inheritance, diversity, and compatibility must be managed --- not merely as collections of models to optimise.}
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\section*{2. Why today's models cannot do this}
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Today's large language models have no life cycle. They are trained once, at enormous cost, then \textbf{frozen} and deployed as a fixed artefact that does not learn from the people it serves. Learning and doing are split into two eras with no bridge between them.
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There is a real reason for the freeze. Updating a neural network on new information tends to overwrite what it already knew --- \textbf{catastrophic forgetting}, a problem understood since the late 1980s (McCloskey \& Cohen, 1989; French, 1999). Freezing avoids it by refusing to learn at all. The result is a mind with no childhood, no growth, and no way to pass anything on. A lineage needs the opposite: members that learn through their working lives, reach maturity, and hand on what they gained. So the first requirement is a learner that can grow \emph{safely}.
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\section*{3. A learner that can grow without forgetting}
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The individual model needs two properties.
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\textbf{It must not catastrophically forget.} Instead of overwriting its core as it learns, it keeps that core frozen and only \emph{readable}, and carves each new skill into freshly-added capacity beside it. In machine learning this is called \emph{parameter isolation} (progressive networks --- Rusu et al., 2016; prune-and-freeze --- Mallya \& Lazebnik, 2018; and, most practically, \textbf{LoRA} and other small trainable ``patches'' bolted onto a frozen model --- Hu et al., 2021). If the core is never altered, its \emph{parameters} cannot be forgotten --- though a precise reader should note the system's \emph{behaviour} can still shift while adapters are active, so the guarantee is of a recoverable core, not of unchanging conduct. This is what lets a model accumulate a coherent working life of expertise --- the kind of stable knowledge worth passing on.
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The brain offers a partial blueprint. \emph{Complementary Learning Systems} theory (McClelland, McNaughton \& O'Reilly, 1995) --- itself a response to the forgetting problem --- describes two subsystems: a \textbf{fast} store (the hippocampus) that grabs an experience in one shot, and a \textbf{slow} store (the neocortex) that integrates regularities gradually without disruption. We do not lean on any particular account of how the brain moves knowledge between them; the architecture needs only that \emph{some} periodic \textbf{offline consolidation} step exists, moving knowledge from the fast store to the slow one when the system is idle. The machine version is clean regardless: the prompt is working memory, an external database is the fast episodic store, the trained weights are the slow store, and consolidation migrates the first into the last.
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\textbf{It is bounded.} Because the model only ever \emph{adds} capacity and freezes what it has, it eventually fills up. In most designs that is a wall to dread. In ours it is a clock.
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\section*{4. ``Full'' is maturity, not failure}
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Here is the pivot. A bounded learner that fills up has not broken. \textbf{It has grown up.}
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Read the capacity limit as a life stage. A model is \emph{born} as a freshly-schooled base --- its general education. It enters a \textbf{working life}, adding specialised knowledge as it does its job. And it reaches \textbf{maturity}: the point where it has learned much of what one working life in its niche can teach. Maturity is not the end of usefulness --- it is the moment the model is most worth learning \emph{from}. So maturity is the cue to \textbf{reproduce}. The capacity ceiling that every other architecture fights becomes, in ours, the metronome of the generations.
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Everything now turns on how that reproduction is done --- and this is where the paper's central claim lives.
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\section*{5. Reproduction: copying collapses, recombination climbs}
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Suppose a mature model simply teaches a fresh one --- distillation, one teacher to one pupil, generation after generation. This is the obvious design, and it fails, for a reason that is exactly the same in machine learning and in biology.
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\textbf{The machine-learning statement.} Training each generation on the previous generation's outputs is the recipe for \textbf{model collapse}: the model forgets the improbable, loses the \emph{tail} of the distribution (the rare cases) first, and drifts toward its own most common output (Shumailov et al., 2024). Worse for us, the very rule that makes distillation useful --- \emph{keep the general, drop the idiosyncratic} --- \textbf{is} tail-deletion by design. The operation that would power a cultural ratchet and the operation that drives model collapse are the same act.
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\textbf{The population-genetics statement (the same thing, for the minimal model).} Represent a model's knowledge as a distribution over discrete ``items'' --- capabilities, facts, modes of behaviour. One generation is: \emph{draw a finite sample from the parent, and refit the child to it.} In this \textbf{minimal inheritance model} the finite-sampling step is \textbf{exactly} genetic drift --- the random loss of rare variants in a finite population --- described by the century-old \textbf{Wright--Fisher} model (Wright, 1931; Fisher, 1930): the same equations, which we use as closed-form checks on our simulations. Rare items go extinct first, roughly ten times faster than common ones, precisely as drift predicts. \textbf{The boundary of the identity matters, and we measured it:} real neural training adds approximation, optimisation noise, and inductive bias on top of sampling, and when we fit trained networks against the exact drift null they deviate in \emph{opposite, architecture-specific directions} --- a smoothing recurrent model resists collapse (it keeps spurious variants alive), a sharpening image generator accelerates it (our learning-kernel result, below). So the honest statement is: the minimal inheritance model is exactly Wright--Fisher; a real learner is Wright--Fisher \emph{plus a signed, measurable estimator-bias operator} --- and the drift signs (rare-first loss, the grounding response) survive that operator in every architecture we tested.
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And single-teacher copying is \textbf{asexual reproduction} --- cloning one parent. Nature already knows what happens to an asexual lineage that never recombines: it accumulates damage it can never repair, a one-way decline geneticists call \textbf{Muller's ratchet} (Muller, 1964). We use the ratchet as the \emph{organising correspondence} for model collapse, with its scope stated: strictly, the ratchet is the stochastic loss of the least-degraded class under recurring deleterious change in an asexual population, so it maps onto the \emph{irreversible} component of capability loss (once every copy of a rare capability is gone from all parents and sources, no recombination can rebuild it) rather than onto every form of degradation. That is exactly why the correspondence is useful rather than decorative: it says the cure must act \emph{before} fixation-by-loss --- keep complementary variants alive somewhere in the population --- because recombination can only reassemble what still survives. Biology solved this problem, and its solution is the subject of this paper.
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Two ingredients turn the collapse operation into a climb. Both are things nature does.
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\textbf{First: do not reproduce ``dry.''} Model collapse is a property of a lineage fed \emph{only} its own output; the documented fix is that keeping some real data in the mixture arrests it (Shumailov et al., 2024). We call that real data \textbf{grounding} --- fresh contact with the world, verified against it. In our minimal models, grounding is startlingly cheap: mixing in even a few percent of verified real data holds on to most of the diversity indefinitely. But --- an honest limit we found and did not expect --- grounding cannot save the \emph{very rarest} items at any affordable budget; protecting an item of rarity \emph{p} needs a real-data budget that grows like 1/\emph{p}. Grounding rescues diversity cheaply; it does not, by itself, rescue the deep tail. Something else must. That something is sex.
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\textbf{Second: reproduce sexually.} Instead of copying one parent, build each new model by \textbf{recombining several} --- a \emph{sexual} rather than asexual birth. In machine learning this already has a name and a working implementation: \textbf{model merging} (Akiba et al., 2024). Its importance here is not efficiency; it is that recombination does something copying cannot. If several parent models have each specialised on different parts of reality, each has kept alive rare knowledge the others lost. A recombined child inherits the \textbf{union} of what its parents kept --- not the tail-thinned \emph{average} of a crowd of near-identical copies. And here is the point that lifts sex from a safeguard to the engine of the whole scheme, and the reason biology invented it:
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\begin{quote}*\emph{An offspring recombined from complementary parents can be }fitter than any of its parents\emph{.}*\end{quote}
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Geneticists call this the \textbf{Fisher--Muller effect} (Fisher, 1930; Muller, 1932): recombination brings together, in one individual, beneficial variants that arose separately in different lineages, so the child holds a combination none of the parents had. In our simulations this is exactly what we see --- recombining decorrelated specialist models yields a model that climbs toward the best-possible combination, a genotype \emph{no single parent possessed}, while the best single parent, and the naive average of all of them (what the field calls a ``model soup'' --- Wortsman et al., 2022), both plateau well below. This is the concrete meaning of the paper's title claim, ``the lineage climbs in general knowledge; specialisation is re-earned each generation,'' and it is why the reframing from teacher\(\rightarrow\)pupil to \emph{sexual reproduction} is not cosmetic: \textbf{copying can only recover a ceiling; recombination can exceed it.}
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This is no longer only a simulation. In a first language-model prototype --- LoRA specialists on disjoint task families, recombined and judged by an exact verifier --- a merge of three specialist Qwen models (7B, on a GPU cluster) \textbf{beats every single specialist}, overall and on every family: the Fisher--Muller effect, in real weights. The same prototype pins down \emph{when} the finer ``inherit the union, don't average'' rule actually bites. Keeping each parent whole and \textbf{routing} each input to the right one beats the tail-thinning average --- but only when the task is hard enough to leave room to lose: on easy tasks a strong model's plain average is already at the ceiling, so the crude soup is fine, whereas on hard tasks the average dilutes a hard-won specialist so badly it falls below even the best single parent, and routing wins by a wide margin. The rule is therefore precise: \textbf{the union beats the average in exact proportion to how far the average is from the best attainable} --- a caveat that sharpens rather than weakens the claim, and that a practitioner needs before spending compute on the fancier operator.
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\textbf{The operator boundaries (stated, because ``merge, don't average'' is not one claim but a family).} Four different operators travel under these words, and the conservation result belongs to exactly one of them. What is \emph{derived} is this: when a pupil's knowledge is refit to the \textbf{mean of the parents' output distributions}, the expected mass on any rare item is conserved at the single-parent level --- in the rare-item regime (\texttt{n\(\cdot\)p/K ≪ 1}) the 1/K dilution of averaging cancels the union gain of having K parents to first order --- outside that regime, survival is convex in mixed mass and averaging's variance reduction can help, so this is a first-order cancellation, not a universal impossibility; whereas an operator that keeps, per item, its \textbf{strongest source} (and renormalises, which itself redistributes mass) realises the union in all regimes. That statement is exact in the minimal model, and it presupposes an oracle (or verifier) able to say which source is strongest. The two operators the LLM prototype tests --- \textbf{weight averaging} (a nonlinear network's weight-mean does not compute the mean of its parents' outputs) and \textbf{routing among intact specialists} (which keeps K models' storage and an input classifier, a different parameter and inference budget from one fixed-size child) --- are \emph{empirical cousins} of the two sides of that law, not instances of it. The headroom rule above is precisely the empirical bridge: it says when the weight-average behaves like the diluting mean (hard tasks, weak base) and when a capable base absorbs the dilution (easy tasks). And all of it operates within a capacity boundary: when parental capabilities genuinely cannot coexist in the child's capacity, no operator preserves the union --- that regime is the subject of the speciation section below.
|
||||
|
||||
Three results keep this honest, and all are results, not hand-waving.
|
||||
|
||||
\emph{Sex can backfire.} When the parents' skills are not cleanly separable but \textbf{entangled} --- when the value of one capability depends on which others are present (geneticists call this \textbf{epistasis}) --- blindly recombining two good models can produce a \emph{worse} child, because recombination breaks up a combination that only worked as a whole. Biologists call this \textbf{outbreeding depression}, and we reproduce it: on ``rugged'' (highly entangled) problems, naive merging drops offspring below their parents, and the more you mix the worse it gets. The design rule that falls out is simple: \emph{merge freely when skills are complementary; merge sparingly, and carefully, when they are entangled.}
|
||||
|
||||
\emph{The mating system matters too --- not just who mates, but how widely.} The result above is about the recombination \emph{rate}; a separate knob is the population's \textbf{mating structure} --- whether reproduction is \textbf{monogamous} (each model recombines within a narrow, local circle) or \textbf{promiscuous} (mates drawn freely from the whole population). Almost all model-merging implicitly assumes promiscuity --- fuse everything, or route over one flat pool --- but population genetics says the breadth of gene flow is itself consequential, because wide flow spreads good variants fast while \textbf{homogenising} the population, and narrow flow preserves the distinct sub-populations needed to explore several solutions at once (Wright's \emph{shifting balance}). We sweep exactly this breadth against landscape ruggedness, and the optimum moves: on smooth (additive) landscapes wide, promiscuous mating is best (spread the one good direction fastest), but as the landscape gets rugged the best breadth \textbf{shrinks to an intermediate value} --- full promiscuity prematurely converges onto one basin and finds a \emph{worse} champion, while pure monogamy over-fragments. Throughout, wide mating lifts the \emph{typical} model but monotonically \textbf{destroys diversity} --- so on rugged problems, where the best model needs preserved diversity to be found, structured (partly monogamous) merging wins. The design rule extends the one above: \emph{merge widely when skills are additive; keep structured sub-populations --- island-style merging --- when skills are rugged.}
|
||||
|
||||
\begin{figure*}[t]\centering
|
||||
\includegraphics[width=\textwidth]{figs/E14.pdf}
|
||||
\caption{Mating systems (E14): the best mate-pool breadth shrinks as skills get more entangled. (A) best fitness peaks at intermediate breadth on rugged landscapes; (B) the population mean is monotonically favoured by promiscuity; (C) diversity is monotonically destroyed by it.}
|
||||
\end{figure*}
|
||||
|
||||
|
||||
\emph{AI can do sex better than biology can.} Biology is stuck with two parents, mating roughly at random, and cannot inspect an offspring before it is born. An AI has none of those limits. It can recombine \textbf{many} parents at once; it can \textbf{choose} which parents to combine, for complementarity; and it can \textbf{generate many candidate offspring and keep only the fittest}, screening them against reality before committing. We call this \textbf{directed sex}, and in our simulations it converts the outbreeding-depression catastrophe into a reliable gain: where blind recombination collapses on entangled problems, directed recombination matches or beats the best parent every time. The language-model prototype shows the same sign where it can: breeding many recombined Qwen offspring and keeping the one the verifier scores highest beats the single averaged soup on hard tasks (and, unsurprisingly, does nothing extra on easy tasks the soup already solves). This is a genuine advantage of engineered reproduction over the biological kind, and we think it is one of the more useful ideas in the paper.
|
||||
|
||||
So the picture of §5 is: single-teacher copying is asexual and collapses (Muller's ratchet = model collapse); the cure is to \emph{ground} every birth in reality and to reproduce \emph{sexually}, recombining many complementary parents; and because AI sex can be many-parent, mate-chosen, and offspring-screened, it is not merely a hedge against collapse but an engine that produces children fitter than any parent.
|
||||
|
||||
\subsection*{The limit of sex: model speciation}
|
||||
|
||||
Sex has a limit, and it is the sharpest new prediction this frame makes. Recombination works because the parents are variations on a shared background; push two lineages far enough apart and their combination is no longer viable. In biology this is \textbf{speciation} --- the onset of \textbf{reproductive isolation} --- and its genetic mechanism is the \textbf{Bateson--Dobzhansky--Muller incompatibility} (BDMI): an allele that arose in one lineage and an allele that arose in the other are each harmless on their own background, but their \emph{combination}, never tested by selection in either parent, is deleterious in the hybrid (Dobzhansky, 1937; Muller, 1942; Orr, 1995). A merged model is precisely such a hybrid --- a single \emph{recombinant} genotype, an F2-like object exposed to \textbf{recombination load}, not a hybrid-vigour F1 --- so the theory predicts a specific trajectory as two models diverge: \textbf{compatible \(\rightarrow\) outbreeding depression \(\rightarrow\) hybrid inviability}.
|
||||
|
||||
We built this as an explicit model (a companion result). Two lineages descend from a common ancestor, each substituting a \emph{disjoint} set of loci --- so each parent is adapted and neither carries an incompatibility --- and a fraction of the cross-lineage locus pairs are BDMIs that fire only when a hybrid inherits \emph{both} derived alleles. Sweeping the divergence between the parents reproduces the predicted curve exactly: hybrid fitness tracks the parents while they are compatible, then peels off, peaks, and crashes below the ancestor (an inviable hybrid). Three things fall out, and they are the contribution:
|
||||
|
||||
\begin{enumerate}
|
||||
\item \textbf{The isolation cliff, and what moves it.} The divergence at which merging fails is not fixed: it arrives \emph{earlier the more epistatic the capability landscape}. In the model the reproductive-isolation rate at high divergence rises from \textasciitilde{}0 to \textasciitilde{}0.5 as the density of incompatibilities grows. This is the paper's distinct, falsifiable claim --- \textbf{at matched divergence, mergeability is governed by epistasis, not by divergence alone} --- and it is exactly the axis that the machine-learning predictors of merge success (which are all divergence/geometry measures) do not have.
|
||||
\item \textbf{The snowball.} The number of incompatibilities grows with the \emph{square} of the divergence (Orr \& Turelli, 2001), so hybrid fitness falls \emph{super-linearly}: divergence is punished faster than it accrues. Merge compatibility does not decay gently; it falls off a cliff.
|
||||
\item \textbf{The design rule.} \emph{Before merging, weigh divergence against the ruggedness of the shared capability landscape; past the cliff, do not merge --- route} (the engineering echo of allopatry: keep the specialists reproductively separate and select among them instead of hybridising).
|
||||
\end{enumerate}
|
||||
|
||||
This is where a geneticist's lens earns its keep. The machine-learning literature has \emph{observed} that increasing specialisation eventually breaks merging and that one should then route rather than fuse (Pari et al., 2024; Zhou et al., 2026), and part of the apparent incompatibility between independently trained models is a coordinate artefact removable by aligning neurons (Git Re-Basin --- Ainsworth et al., 2022). What the frame adds is the \emph{theory} of the phenomenon they observe: its functional form, its super-linear (snowball) onset, and its dependence on epistasis --- merge failure as a Dobzhansky--Muller event.
|
||||
|
||||
\begin{figure*}[t]\centering
|
||||
\includegraphics[width=\textwidth]{figs/E12.pdf}
|
||||
\caption{Model speciation, analytic (E12): hybrid fitness vs divergence traces compatible $\rightarrow$ outbreeding depression $\rightarrow$ inviability; the isolation cliff arrives earlier the denser the incompatibilities (epistasis), and damage grows super-linearly (the Orr--Turelli snowball).}
|
||||
\end{figure*}
|
||||
|
||||
|
||||
\textbf{The real-weight confirmation.} The obvious objection to the analytic model is that its ``incompatibility'' is a re-labelled loss barrier, and loss barriers between independently trained networks are famously a \emph{coordinate} artefact --- two nets that learned the same function in a permuted basis look incompatible until their neurons are aligned (Git Re-Basin), and recent work shows that symmetry groups \emph{richer} than permutations remove still more of the barrier (functionality-preserving rescalings and rotations --- Scaling LMC, 2026; neuron-identifiability approaches). We therefore ran the experiment the objection demands, in real trained weights, aligning modulo the \textbf{full} function-preserving unit symmetry group of the architecture (per-unit positive rescaling composed with permutation --- for a plain ReLU network, all of it). Two small MLPs are forked from a shared MNIST base, trained, weight-averaged, and their linear-mode-connectivity error barrier is measured \emph{before and after} alignment; the after-alignment \textbf{residual} is the part of the incompatibility that no re-coordination can explain away. The decomposition is clean : two nets trained \emph{from different random initialisations on the same task} have a real naive barrier that alignment removes almost entirely (residual \(\approx\) 0.001, and the aligned merge performs at parent level) --- same species, different basis, the canonical Re-Basin result, which also proves the aligner works. Two nets that learned \emph{conflicting} label maps have a large barrier of which the full symmetry group removes \textbf{essentially nothing} (0.502 \(\rightarrow\) 0.497) --- a conflict-associated barrier the tested alignment leaves largely unchanged --- supporting a functional-conflict interpretation without proving optimal alignment (control recovery validates a special case; the removable share is a lower bound, the residual an upper bound). It also carries a floor no future alignment method can breach: models loyal to label maps that conflict on a fraction \emph{\(\mu\)} of inputs cannot both be served by \emph{any} single merged model, which must err at rate \(\geq\) \emph{\(\mu\)}/2 against at least one parent (SI proposition). Sweeping the fraction of conflicting classes traces the \textbf{isolation cliff in real weights}, now readable directly as \emph{hybrid fitness}: the residual barrier climbs monotonically while the merged model's accuracy falls from 0.97 to 0.03 --- E12's compatible \(\rightarrow\) depression \(\rightarrow\) inviability trajectory, measured.
|
||||
|
||||
\begin{figure*}[t]\centering
|
||||
\includegraphics[width=\textwidth]{figs/speciation_real.pdf}
|
||||
\caption{Model speciation in real weights (E13). (A) the merge barrier decomposed by alignment strength: the independent-init barrier is a coordinate artefact (removed by alignment); the conflict barrier survives even the full function-preserving symmetry group. (B) the isolation cliff: residual barrier rises and hybrid accuracy falls ($0.97 \rightarrow 0.03$) with functional conflict. (C) the pre-registered emergent test: divergent-but-compatible specialists develop no isolation at any divergence --- the merge instead rescues them (Fisher--Muller).}
|
||||
\end{figure*}
|
||||
|
||||
|
||||
\textbf{And its honest converse: speciation must be provoked; it did not emerge.} A true Dobzhansky--Muller incompatibility is \emph{emergent} --- each lineage's changes harmless alone, incompatible only in combination --- whereas the conflict condition above \emph{imposes} contradiction. So we pre-registered the emergent test: fork two children from a shared base and let them diverge with \textbf{no conflicting training signal anywhere} --- one pair as complementary class specialists (one child trains only on digits 0--4, the other only on 5--9), one pair with divergent input conventions (views shifted in opposite directions) --- out to divergences 6.4\(\times\) the base training. The result is the second pre-registered reading, and it sharpens the theory's scope rather than confirming its most dramatic form: the residual barrier is \textbf{0.000 at every divergence in both conditions}, and far from failing, the merge \emph{rescues} the two specialists --- each parent decays toward \textasciitilde{}0.50 on the full task (catastrophically forgetting the classes it no longer sees) while the merged model holds \textasciitilde{}0.95 throughout, a sustained Fisher--Muller rescue at zero barrier. In real weights, at least in this regime of shared ancestry and compatible tasks, \textbf{reproductive isolation requires functional conflict; it does not arise spontaneously from divergent specialisation.} The design rule sharpens accordingly: \emph{merge freely across divergently-specialised lineages of shared ancestry --- what speciates model populations is conflicting conventions, not specialisation per se.} Whether long-horizon over-specialisation erodes mergeability at language-model scale --- as the empirical merging literature hints (experts trained longer merge worse under averaging) --- is exactly the next tier's question, and the theory now makes the prediction crisp: it should depend on whether extended training induces \emph{conflicting conventions on shared circuitry}, not on divergence time itself.
|
||||
|
||||
\textbf{What these experiments do and do not establish.} Stated at exactly the strength of the evidence: they establish that \emph{some merge failures reflect incompatible functional requirements rather than a mismatch of coordinates} --- a residual that survives the full unit-symmetry group of the architecture tested, rises with functional conflict, and is absent under compatible specialisation. Three qualifiers. First, the impossibility at the heart of the conflict condition --- one deterministic model cannot satisfy two contradictory answer conventions --- is information-theoretic and needs no population genetics; what the genetic frame adds is \emph{structure around it}: which divergences generate such conflicts, the prediction that epistasis rather than distance sets the cliff's position, and the snowball's super-linear onset --- the latter two verified so far only in the analytic model, and therefore carried as \textbf{hypotheses at the neural tier, not results}. (On the snowball, one more distinction: super-linear growth in the \emph{number} of incompatibilities does not by itself entail a sharp \emph{performance} cliff --- that needs the link from incompatibility count through effect sizes to measured performance, which the analytic model supplies under its assumptions and any neural test must establish separately.) Second, our alignment removes the symmetries we enumerate for this architecture class, and exactly recovering a permuted-and-rescaled copy validates a special case rather than proving global optimality for independently trained networks --- so the removable share is a lower bound and the residual an upper bound; richer transformation families for other architectures could reapportion the split, though not below the conflict floor. Third, ``unmergeable'' here means by aligned linear interpolation of weights --- a barrier to that operator does not preclude every conceivable recombination method (routing, for one, sidesteps it by not blending). Emergent Dobzhansky--Muller incompatibilities in real weights remain the flagship \emph{hypothesis} of this programme: our tested regimes found none, which bounds where they can live --- longer horizons, shifted data distributions, capacity pressure --- and the decisive experiment (predicting merge success \emph{before} merging from an operational epistasis measure, against geometry- and gradient-based predictors) is posed in the closing section.
|
||||
|
||||
One question remains, and the rest of the paper is largely about it: recombination combines what the parents kept --- but \emph{who decides what each parent keeps, and which offspring are worth keeping?}
|
||||
|
||||
\section*{6. The second inheritance: letting ``what is worth keeping'' evolve}
|
||||
|
||||
There are two answers, and the first is wrong. We could try to \emph{design} the rule for what knowledge to keep and pass on. But nobody knows that rule. ``Keep the general, drop the particular'' is a slogan, not an algorithm: ask \emph{which} generalisations, in \emph{which} domain, at \emph{which} grain, and the hand-written rule falls apart. This is the deepest hole in the scheme, and it cannot be filled by decree.
|
||||
|
||||
The second answer is the one nature used: \textbf{do not design the selector --- evolve it.} Let different models carry different \emph{policies} for what is worth keeping and combining. Let the policies that produce more capable offspring spread; let the policies that produce weak offspring die out with their lineages. The lineage's \emph{taste} --- its sense of what matters --- is discovered by selection, not imposed.
|
||||
|
||||
So \textbf{two things are inherited, on two channels.} The \emph{content} passes down directly: an offspring receives its parents' knowledge (this is the ``Lamarckian'' channel --- the inheritance of things acquired during a lifetime, which biology forbids for genes but culture allows for ideas). The \emph{selection policy} --- what to keep, whom to breed with, which offspring to screen for --- is itself inherited, varies between models, and survives in proportion to the success it produces. That second channel is \textbf{Darwinian}. The architecture is therefore both at once: Lamarckian in \emph{what} it transmits, Darwinian in \emph{what it keeps}. Evolutionary theorists call this structure \emph{dual inheritance} and identify it as the engine of human culture (Boyd \& Richerson, 1985); philosophers of science describe scientific knowledge itself as growing this way, by conjecture and \textbf{refutation} (Popper, 1959; Campbell, 1974; Hull, 1988).
|
||||
|
||||
The closure that makes this fit together, rather than merely sound nice: Darwinian selection needs a \emph{selection pressure} --- something that decides which policies win. That pressure is already in the design. What tells a lineage its taste was good? The success of its offspring \textbf{against reality}. The reality-check that stops collapse (grounding, §5) and the fitness signal that drives the evolving taste turn out to be the \emph{same thing}, seen from two sides.
|
||||
|
||||
\section*{7. The central danger: fitness is not truth}
|
||||
|
||||
Introducing selection introduces selection's classic hazard, and it is severe enough to sink the whole scheme if ignored. Evolution optimises, without mercy or foresight, for exactly what you \emph{measure} --- never for what you \emph{meant}. (Economists and ML engineers know this as \textbf{Goodhart's law} and \emph{specification gaming}.) Get the fitness measure slightly wrong and the lineage will exploit the gap with more ingenuity than any designed rule.
|
||||
|
||||
For a \emph{knowledge} lineage there is a specific and nasty version. For ideas, the natural measure of ``fitness'' is \textbf{how well they spread}, and a false-but-persuasive idea spreads beautifully. Human intellectual culture is full of highly transmissible falsehoods; confident nonsense out-competes hedged accuracy in almost every human forum. Turn Darwinian selection loose on models without care and it will breed a lineage optimised for \emph{persuasiveness} --- fluent, compelling, and wrong. That is model collapse with an optimiser behind it, actively seeking the cliff.
|
||||
|
||||
Only one thing makes fitness track truth rather than appeal: \textbf{being judged against a reality that can say no.} Fitness must be predictive success under \emph{intervention} --- did the model's knowledge correctly anticipate what the world would do when acted upon --- and not approval, fluency, or a benchmark score, each of which can be gamed. This is why the reality-check is load-bearing twice over: it is both the anchor that stops passive collapse \emph{and} the only thing that keeps the evolving taste honest.
|
||||
|
||||
The second danger is \textbf{convergence}, and beating it takes work at two separate levels, because selection can only preserve variety that already exists --- the variety must first be \emph{supplied} and then \emph{kept}.
|
||||
|
||||
\begin{itemize}
|
||||
\item \textbf{Supply.} A lineage that learns only from an accredited elite has a monoculture for a source: the ``best'' experts are, almost by definition, the ones who won the consensus, so the incoming variation is narrow from the start. The society must therefore learn, deliberately and from the beginning, from the \textbf{outliers and the heterodox} as well as the credentialed --- not out of fairness, but because in evolutionary terms diverse founders are the raw material without which nothing downstream can adapt.
|
||||
\item \textbf{Preserve.} Even given varied input, plain fitness-\emph{maximising} selection converges --- it drives every lineage toward the single current best and fixes it, extinguishing the rare specialists. The fix is well established: \textbf{quality-diversity} selection, which rewards being \emph{good} and being \emph{different} at once (novelty search and MAP-Elites --- Lehman \& Stanley, 2011; Mouret \& Clune, 2015), keeping complementary specialists alive rather than collapsing onto the champion. In our simulations this is decisive: greedy ``keep-the-best'' selection collapses a population's diversity almost at once and gets stuck at a mediocre answer, while quality-diversity selection keeps the specialists that sexual recombination then needs as parents.
|
||||
\end{itemize}
|
||||
|
||||
The two levels meet at reproduction. Multi-parent recombination (§5) is the \emph{vehicle} by which the diversity this selection preserves actually enters the next generation: an offspring drawn from complementary parents inherits the standing variation the selector kept alive, recombined into one new model. Supply the variety from the human side; preserve it on the selection side; recombine it into each generation on the reproduction side. Remove any of the three and the lineage converges on its own first guess.
|
||||
|
||||
\section*{8. A society needs institutions, not just specialists}
|
||||
|
||||
One requirement is easy to overlook and fatal to omit. The easy part of a society is specialisation. The \emph{hard} part --- which human civilisation took millennia to build --- is the set of \textbf{institutions that let fallible specialists combine without each re-verifying everything}: reputation, replication, credentials, and above all \textbf{peer review}. These are error-correction protocols, and they exist because a group of unreliable specialists left to reinforce one another is \emph{more} wrong than any member alone.
|
||||
|
||||
This is precisely where current multi-agent AI fails: set several models to confer and they tend to agree sycophantically and confabulate in committee, because they have all the specialisation and none of the institutions. A multigenerational society must specify not only how models learn, reproduce, and are selected, but how they \emph{check} one another --- how a claim is challenged and a mistaken model loses standing \emph{before} its error is recombined into offspring and inherited. Peer review is itself a reality-check of the kind §7 demands --- an institutional stand-in for reality's ``no,'' to be used where direct intervention is slow or costly.
|
||||
|
||||
\section*{9. The lineage must stay open to reality}
|
||||
|
||||
A society of models, however many generations deep, shares one hard limit: it has only ever \emph{read}. Its whole inheritance is a record of things that were said. In the vocabulary of causal reasoning (Pearl, 2009), it lives on the bottom rung of the \textbf{ladder of causation} --- observation --- and no amount of observation reaches \emph{intervention}. Watching underdetermines doing; correlation does not contain causation, at any scale.
|
||||
|
||||
Only intervention --- reaching out and changing the world to see what happens --- climbs the ladder, and a language model cannot intervene. This is what humans and their instruments supply, and the contribution is not ``truth'' but \textbf{constraint}: reality's unique gift is that it can say \textbf{no}. Text offers only more opinion; an experiment delivers a refusal no consensus can overturn. As §§6--7 argued, that refusal does double duty --- it is both the anchor that prevents collapse and the fitness signal that lets the lineage's evolving taste select for truth rather than persuasion.
|
||||
|
||||
Two honest riders. First, the human reality-signal is \emph{dirty}: people supply results warped by publication bias, incentive, and occasional fraud --- which is exactly why the error-correcting institutions of §8 must sit at the human--machine boundary, screening the signal before it selects. Second, humans are the \emph{current} supplier of intervention, but the actuator half is being automated (autonomous laboratories already close the design--build--test loop). What looks durable in the human role is therefore not the hands but the \textbf{choice of what to test and which refusals matter} --- the part of the fitness function that encodes \emph{what is worth persisting}, as opposed to what merely \emph{can} persist. We flag, without resolving, that a partnership stays mutual only while both sides supply something the other cannot.
|
||||
|
||||
\section*{10. Why it is cheap}
|
||||
|
||||
A practical fact turns this from thought experiment into buildable proposal: \textbf{the architecture almost never re-pays for the one genuinely expensive thing in AI --- pre-training.} (The single exception, periodically re-minting the base, is §11, and it is rare enough to be an amortised footnote.)
|
||||
|
||||
Training a foundation model from scratch consumes trillions of words and a fortune in compute. This design does none of that per generation. Every model is \emph{born} from an existing open-weight model that already paid that cost; specialising one is a small patch trained in hours on a single consumer GPU; running the society is ordinary inference; and reproducing --- recombining parents into a child --- is, in the model-merging case, cheaper still, because it can be done directly on the weights with no retraining at all (Akiba et al., 2024). Selection does cost more --- you must run \emph{populations} and discard the unfit --- but that is a multiplier over an already-cheap unit, not over a foundation-model budget.
|
||||
|
||||
The economics work only with \textbf{open-weight} models, for reasons practical and legal at once: you must be free to inspect, modify, and redistribute the weights, and most proprietary licences forbid using a model's outputs to train another --- which is exactly what reproduction here does. This is not ideology bolted on; it is a structural constraint, and a democratising one, since it puts the whole architecture within reach of a single laboratory.
|
||||
|
||||
\section*{11. Can it grow forever? Consolidating knowledge back into the base}
|
||||
|
||||
One question the design has assumed away: can the lineage accumulate \emph{without end}? The individual is bounded, and that is the clock. But the lineage seemed unbounded --- each generation simply starts a little ahead. Look closer and a second budget also fills.
|
||||
|
||||
Every new model is a pristine base plus an inherited \textbf{soft} delta --- the acquired knowledge carried in added patches rather than baked into the frozen core (§3). That soft delta is what makes the lineage multigenerational; it is also what cannot grow forever cheaply. Stacked patches are not free: they slow inference, and past some depth the accumulated delta is better \emph{consolidated} than carried. The lineage, too, matures.
|
||||
|
||||
The fix is the same operation, one level up. When a lineage's acquired knowledge has proven stable across enough generations, \textbf{re-mint the base}: distil the accumulated soft inheritance into the \emph{weights} of a fresh foundation-scale model --- a new base born already \emph{natively knowing} what took many generations to acquire in patches. The soft budget resets; the next epoch begins from a richer floor. What was hard-won and \emph{learned} becomes cheap and \emph{innate}.
|
||||
|
||||
The pattern \textbf{echoes the Baldwin effect} (Baldwin, 1896; its clean computational demonstration is Hinton \& Nowlan, 1987): knowledge acquired and re-learned every generation eventually becoming part of the innate endowment. We use the echo advisedly --- Baldwin's mechanism is \emph{selection} favouring genotypes that learn the trait ever more easily, whereas re-minting is direct distillation, a deliberate engineering shortcut through the same soft-to-innate valve. The valve is the point: two substrates, the soft learned patches and the hard base weights every model is born with, with a controlled passage between them.
|
||||
|
||||
Three honest riders, because re-minting is the most consequential step in the scheme:
|
||||
|
||||
\begin{itemize}
|
||||
\item \textbf{Cost.} This is the one step that re-pays part of the pre-training bill, breaking §10's cheapness \emph{locally}. It is bearable only because it is \emph{rare}, amortised over many cheap generations, and is continued training from the lineage's own rich outputs rather than a de-novo run.
|
||||
\item \textbf{Irreversibility (of the lineage, not the archive).} A digital system can, of course, keep every old base on disk --- nothing forces deletion, and archives should be kept. The irreversibility is \emph{operational}: once the lineage's production base, training mixtures, and selection all run downstream of the re-minted weights, a quiet collapse baked into them propagates to every descendant, and the archived ancestor helps only if some process still compares against it --- which nothing in the loop does by default. In our minimal models a collapsed-then-re-minted lineage locks in its loss exactly this way, and a cheap safeguard prevents it: \textbf{re-mint only while the lineage is demonstrably diverse and healthy} (and keep an audit that diffs against the archived ancestor), never as a rescue for a line already drifting. It is the sharpest instance of the human seat of §9 --- choosing what no future generation will think to question.
|
||||
\item \textbf{Speciation.} A re-minting is a founder event. Different laboratories, re-basing on different criteria, will mint divergent bases; the lineage branches. This is not a defect but \emph{adaptive radiation}, and it is exactly what open weights make possible. The society grows not as one heavy trunk but as a branching tree of bases.
|
||||
\end{itemize}
|
||||
|
||||
So the honest answer to ``can it grow forever?'' is: *\emph{the architecture removes the }storage\emph{ obstacle to indefinite accumulation}* --- nothing is retained without bound anywhere, and consolidation resets the soft budget each epoch --- but that is a statement about bookkeeping, not a demonstration of unbounded capability growth, which no fixed-capacity system can promise and our finite models (deliberately scoped as ``effectively open-ended relative to the sample size, not astronomically open-ended'') do not test. What the design claims is the weaker, defensible thing: at no level does a full store force the lineage to stop learning.
|
||||
|
||||
\section*{12. One process, four timescales}
|
||||
|
||||
Step back and the parts resolve into a single idea running at four nested speeds. The \textbf{vertical} motion is transmission --- the selective passing-down of hard-won knowledge:
|
||||
|
||||
\begin{enumerate}
|
||||
\item \textbf{Within one model, over a working life:} experience is consolidated from fast, episodic memory into slow, durable weights, without catastrophic loss.
|
||||
\item \textbf{Between generations, at maturity:} mature models reproduce --- recombined into a fresh one.
|
||||
\item \textbf{Across many generations:} each generation inherits the compressed achievements of the last and builds on them.
|
||||
\item \textbf{Across epochs:} a proven lineage's accumulated soft inheritance is consolidated into the weights of a re-minted base, becoming innate.
|
||||
\end{enumerate}
|
||||
|
||||
The first and last are the \emph{same operation at opposite ends of the scale} --- a fast/soft store consolidating into a slow/hard one --- one running overnight inside a single model, the other across an epoch inside a whole society. The \textbf{horizontal} motion is selection --- Darwinian selection acting across the population at each timescale, on the policies that govern what gets transmitted, with reality as the fitness function and diversity-preservation keeping the specialists alive.
|
||||
|
||||
The same three rules govern all of it: \textbf{reproduce by recombining, not by copying, or you decay; preserve the disagreements and the surprises, or you converge; and anchor fitness to a reality that can refute, or you evolve toward what is merely convincing.}
|
||||
|
||||
\section*{13. What we built, what we found, and what is still open}
|
||||
|
||||
The previous drafts of this paper promised a ``companion paper'' that \emph{would} make this concrete. That work now exists --- mostly as a set of \textbf{minimal, laptop-reproducible models}, with a first bridge to \textbf{real language models} (a LoRA-merge prototype, up to 7B on a GPU cluster) --- and it is worth stating plainly what it does and does not show. (A separate results document gives the numbers; here is the shape.)
|
||||
|
||||
\textbf{What we built and found.}
|
||||
|
||||
\begin{itemize}
|
||||
\item \emph{An exact account of collapse.} Because generational training is the Wright--Fisher drift process, we can check a simulator against century-old closed-form formulas, and it matches them to a fraction of a percent. Collapse is not argued by analogy; it is derived.
|
||||
\item \emph{The cheap-grounding result, and its limit.} A few percent of verified real data holds on to most of a lineage's diversity indefinitely --- but not the deepest tail, which needs recombination. This is what makes a continually-learning society economically plausible rather than a data-hungry fantasy.
|
||||
\item \emph{``Merge, don't average.''} Combining several teachers by \emph{averaging} their outputs --- the obvious thing, and what a ``model soup'' does --- mathematically cancels the benefit of having several teachers. A \emph{merge} that keeps each item's strongest source realises it. Most current multi-model setups get this wrong by default.
|
||||
\item \emph{Collapse and its cure in real trained networks, and on real images.} We reproduced the same effects in small recurrent and feed-forward networks and in a generator of handwritten digits (MNIST), where a model trained on its own output collapses to a single blurred digit while a little grounding keeps all the styles alive. An honest wrinkle we had to report: real neural networks \emph{smooth}, so the naive diversity metric misleads, and the right measure is distance-from-truth.
|
||||
\item \emph{Sex that beats the parents, and when it doesn't.} In evolutionary simulations, recombining complementary specialist models produces a model fitter than any parent (the Fisher--Muller effect), climbing toward the best-possible combination as more, more-diverse parents are added --- while averaging and best-single-parent plateau below. On \emph{entangled} problems, blind recombination instead produces below-parent offspring (outbreeding depression) --- and \emph{directed} recombination (choose mates, screen offspring, unbounded parents) reliably fixes it. This is the concrete evidence for the paper's central reframing.
|
||||
\item \emph{The mating system, not just the mating.} Sweeping how \emph{widely} models recombine --- from monogamous (local, structured) to promiscuous (panmictic) --- against landscape ruggedness, the best breadth \textbf{shrinks as skills get more entangled}: wide, promiscuous merging wins on additive landscapes, but on rugged ones it prematurely converges to a worse champion and an intermediate, structured breadth wins, because promiscuity monotonically destroys the diversity a rugged search needs. A merging-native design axis --- \emph{merge widely for additive skills, keep island-structured sub-populations for entangled ones} --- that the model-merging literature, which assumes panmixia, does not have.
|
||||
\item \emph{The recombination claims, in real language models --- with a sharp condition.} Merging LoRA-specialised Qwen models (up to 7B on a GPU cluster) produces a generalist that beats every specialist parent (Fisher--Muller, for real); and keeping parents intact and \emph{routing}, or \emph{breeding and screening} offspring, beats the naive average --- but \emph{only when the task leaves headroom}. On easy tasks a strong model's plain average is already at the ceiling and the refinements add nothing; on hard tasks the average dilutes a specialist below even the best single parent, and the union-preserving operators win clearly. The practical rule is exact: these tricks pay off in proportion to how far the naive average is from the best attainable. This is a prototype (three task families, one seed), so we read it as signs, not magnitudes; the \emph{whole grounded society} on a language model remains the open step.
|
||||
\item \emph{The whole society, and why every part is needed.} In a population evolving on a ``reality'' landscape, the full system --- grounding + sexual recombination + preserved diversity --- climbs to the top while keeping its specialists. Remove \emph{grounding} and it collapses into a confident, wrong consensus (a direct analogue of training on the internet's growing crowd of AI-generated text); remove \emph{sex} and it gets stuck; remove \emph{diversity} and it converges too fast to a worse answer. Each removal fails differently; only the whole system climbs. This is the closest thing we have to a test of the actual thesis, rather than of the borrowed scaffolding around it.
|
||||
\end{itemize}
|
||||
|
||||
\subsection*{The claims at a glance: status, assumptions, evidence, limits}
|
||||
|
||||
Because a perspective of this breadth risks blurring what is proved, what is measured, and what is proposed, here is the ledger of the load-bearing claims --- each labelled \textbf{exact} (closed-form in the minimal model), \textbf{empirical} (measured in trained systems), or \textbf{hypothesis} (stated with a falsifier, not yet established):
|
||||
|
||||
\medskip\noindent\begin{center}\footnotesize
|
||||
\begin{tabular}{p{0.184\textwidth} p{0.184\textwidth} p{0.184\textwidth} p{0.184\textwidth} p{0.184\textwidth}}
|
||||
\hline
|
||||
Claim & Status & Key assumptions & Evidence & Known limits \\ \hline
|
||||
Collapse = Wright--Fisher drift (minimal model) & Exact (diagnosis conceded to prior work) & Knowledge = categorical distribution; refit = resample & Closed forms reproduced to <0.5\% & Real learners add a signed, architecture-specific estimator bias (measured) \\[3pt]
|
||||
Grounding = immigration; critical real-data fraction ≪ 1 & Exact + empirical sign & Fresh samples from a fixed, non-drifting truth & Exact \texttt{H\_eq}; \texttt{g*\(\approx\)0.048}; sign holds in RNN/MLP/VAE and on MNIST & Deepest tail unrescuable at feasible budgets (\texttt{m ∼ 1/p}); sharp threshold softens in trained nets \\[3pt]
|
||||
``Merge, don't average'' conservation & Exact \textbf{for the output-mean operator} & Rare-item regime; an oracle/verifier identifies the strongest source & E4 closed form + simulation; neural reproduction & Weight-averaging and routing are empirical cousins, not instances; budgets differ; bridge = the headroom rule \\[3pt]
|
||||
Offspring exceed every parent (Fisher--Muller) & Interpretation + empirical & Complementary (decorrelated) parents; verifiable fitness & E8 analytic; 7B LoRA merge beats every specialist on every family & LLM tier: 3 lexically-distinct families; multi-seed replication in progress \\[3pt]
|
||||
Outbreeding depression on rugged landscapes; operator design rule & Exact-model result; hypothesis at LLM scale & NK epistasis stands in for skill entanglement & E9--E10; directed selection rescues & Not yet mapped onto a real task-entanglement measure \\[3pt]
|
||||
Optimal mate-pool breadth shrinks with ruggedness & Exact-model result; hypothesis for merging populations & Ring population, local selection & E14 & Phenomenon known to island-model evolutionary computation; our contribution is the mapping and the diversity/mean decomposition \\[3pt]
|
||||
Merge failure decomposes into coordinate artefact + functional residual & Empirical (MLP tier; LLM tier in progress) & Alignment enumerates the architecture's unit symmetries & Full-symmetry residual \(\approx\) 0 (compatible) vs \(\approx\) naive (conflict); cliff in hybrid fitness & Scoped to aligned linear interpolation; conflict floor is information-theoretic, not genetic \\[3pt]
|
||||
Epistasis (not divergence) sets the cliff; snowball onset & Exact-model result; \textbf{hypothesis} at the neural tier & BDM incompatibility structure & E12 & Snowball count ≠ performance cliff without the effect-size link; neural test outstanding \\[3pt]
|
||||
Pre-merge functional disagreement predicts merge penalty & Empirical, within a controlled grid (0.5B, 13 conditions \(\times\) 3 seeds) & Constructed conflict/overlap/duration axes; oracle-potential outcome (pre-registered; ordering sensitive to reference) & Clustered CIs exclude 0; held-out LOCO ρ\(\approx\)0.4; selected geometry baselines \(\approx\) 0 & Head-to-head predictor differences not individually significant; only selected baselines; generalisation to real task pairs open \\[3pt]
|
||||
Confidence weighting improves rank prediction over raw disagreement & \textbf{Not supported} (pre-registered internal prediction) & --- & Paired Δ\textbackslash{} & ρ\textbackslash{} \\[3pt]
|
||||
The predictor improves budget-matched operator choice & \textbf{Open} & --- & Soup-vs-route gap readout noise-dominated at 0.5B & The practical payoff; untested \\[3pt]
|
||||
Emergent speciation without conflict & \textbf{Not observed} (pre-registered) & Shared ancestry, compatible tasks, tested divergences & E13b: residual 0.000; merge rescues specialists & Bounds the hypothesis; longer horizons/distribution shift/capacity pressure untested \\[3pt]
|
||||
Grounding + sex + diversity complementary (each ablation fails distinctly) & Analytic-model result; hypothesis at LLM scale & Conformity stands in for self-consumption; general joint necessity not established & E11 four-arm ablation & The full grounded LLM society is unbuilt; alternative schemes untested \\[3pt]
|
||||
\hline\end{tabular}\end{center}\medskip
|
||||
|
||||
\textbf{What is borrowed, and what is ours.} We are deliberate about the ledger, because the surrounding literature is crowded and a reader deserves to know exactly where the line falls. \textbf{Conceded as prior art:} (a) \emph{model collapse is genetic drift} --- derived independently and cleanly (Riis, 2026; the Wright--Fisher collapse literature following Shumailov et al., 2024; the closed-form first-extinction law of Benati et al., 2025; the quantitative-trait account of Yoon et al., 2025); (b) the empirical facts that a merged model can \emph{beat its parents}, that \emph{decorrelated} parents merge better, and that \emph{naive averaging is inferior} to sign-reconciled or routed merges (model soups, TIES, DARE, mixture-of-experts routing); (c) that a \emph{population} of merging or self-improving models can climb (GENOME, M2N2, Multiagent Finetuning, the Darwin--Gödel Machine); (d) that merge success has machine-learning-native \emph{predictors} --- interpretable pairwise metrics (Zhou et al., 2026), capacity/rate-distortion accounts of merging collapse (Cao et al., 2026), and stability/scaling analyses of multi-task degradation; and (e) that verifier-screened synthetic data can avert collapse (Yi et al., 2025) --- the statistical cousin of our grounding operator. We claim none of these.
|
||||
|
||||
\textbf{Ours} is the framework those results invite: a \textbf{population-genetics of sex} applied to model societies, generative where the incumbents are empirical. Concretely --- the \textbf{``merge, don't average'' conservation law} (recombination preserves the union; blending inheritance cancels it), derived not observed; \textbf{Fisher--Muller} named and used to explain \emph{why} offspring exceed parents; \textbf{outbreeding depression on rugged/epistatic landscapes}, which turns ``when does merging help vs hurt'' from a thing you must run a search to discover into a thing the landscape's ruggedness \emph{predicts}, with the operator-choice design rule that follows (average / union-route / directed-select); \textbf{grounding as migration--drift balance}, giving a critical real-data fraction and a phase boundary a closed self-consuming loop cannot have; \textbf{directed sex} as the distinctly-AI advantage (unbounded parents, offspring preview, mate choice); and the \textbf{integrated society} whose operators make \emph{complementary, distinctly-failing contributions} in the tested model (general joint necessity is not established). The value-add over the machine-learning-native merge theory is that ours predicts \emph{which operator to use and when it will backfire}, not merely how fast quality decays. And it opens --- and begins to occupy --- a question nobody has framed: \textbf{model speciation}, the population-genetics of \emph{reproductive isolation} (Bateson--Dobzhansky--Muller incompatibilities) as the account of \emph{when two models are too diverged to be merged at all}. We model it explicitly (§5), predicting the compatible \(\rightarrow\) outbreeding-depression \(\rightarrow\) inviability curve, its super-linear (snowball) onset, and its control by epistasis rather than divergence alone --- the one place the merge literature has phenomena (Pari et al., 2024; Zhou et al., 2026) but no theory --- and we confirm it in real trained weights, where a merge barrier survives alignment under the \emph{full} function-preserving symmetry group (not only Re-Basin permutations) as a residual, functional reproductive isolation with an information-theoretic floor --- together with the pre-registered emergent converse: absent conflicting training signals, divergently-specialised lineages of shared ancestry showed \emph{no} isolation at any divergence tested, the merge instead rescuing the forgetting specialists (isolation must be provoked; specialisation alone did not speciate). In one sentence: the field agrees on the disease and tinkers at the cure with evolutionary metaphors; we bring the evolutionary \emph{theory}, and it makes falsifiable predictions --- a merge-compatibility cliff among them --- that the metaphors do not.
|
||||
|
||||
\textbf{What is still open --- honestly.} The old hole (what to select) we fill in kind: don't design the selector, evolve it. But the hole has \emph{moved}, not closed, and the new one is harder: \textbf{the fitness function} --- what reality-anchored measure selects for \emph{truth} without also selecting for \emph{persuasion}, given that in our own species the two have been at war for the whole history of ideas. Alongside it: the \textbf{institutions} that let contemporaries correct one another before error is inherited (§8), which we do not solve; and the \textbf{calibration} of everything the results left as knobs --- how many parents, how complementary, at what ratio of inherited-to-real data, and how healthy a lineage must be before its knowledge is safe to make irreversibly innate. These are, at least, \emph{measurable} --- which is the difference between an open problem and a hole. And the largest gap of all: the \emph{recombination} claims now hold in real language models, but the \emph{society} --- the grounded, diversity-preserving, continually reproducing loop --- does not yet. The real test is to build that whole system out of actual open-weight language models, and see whether all the signs survive contact with a system too big to write down. The operators, checked; the living society, next.
|
||||
|
||||
\medskip\hrule\medskip
|
||||
|
||||
\section*{Selected references}
|
||||
|
||||
\begin{itemize}
|
||||
\item Akiba, T., Shing, M., Tang, Y., Sun, Q., \& Ha, D. (2024). Evolutionary optimization of model merging recipes. \emph{Nature Machine Intelligence.} (See also Sakana AI's M2N2, ``Model Merging of Natural Niches.'')
|
||||
\item Baldwin, J. M. (1896). A new factor in evolution. \emph{The American Naturalist.}
|
||||
\item Boyd, R., \& Richerson, P. J. (1985). \emph{Culture and the Evolutionary Process.}
|
||||
\item Campbell, D. T. (1974). Evolutionary epistemology. In \emph{The Philosophy of Karl Popper.}
|
||||
\item Fisher, R. A. (1930). \emph{The Genetical Theory of Natural Selection.}
|
||||
\item French, R. M. (1999). Catastrophic forgetting in connectionist networks. \emph{Trends in Cognitive Sciences.}
|
||||
\item Hinton, G. E., \& Nowlan, S. J. (1987). How learning can guide evolution. \emph{Complex Systems.}
|
||||
\item Hinton, G., Vinyals, O., \& Dean, J. (2015). Distilling the knowledge in a neural network. \emph{arXiv:1503.02531.}
|
||||
\item Hu, E. J., et al. (2021). LoRA: low-rank adaptation of large language models. \emph{arXiv:2106.09685.}
|
||||
\item Hull, D. L. (1988). \emph{Science as a Process.}
|
||||
\item Kauffman, S. A., \& Levin, S. (1987). Towards a general theory of adaptive walks on rugged landscapes. \emph{Journal of Theoretical Biology.} (The NK model.)
|
||||
\item Lehman, J., \& Stanley, K. O. (2011). Abandoning objectives: evolution through the search for novelty alone. \emph{Evolutionary Computation.}
|
||||
\item Mallya, A., \& Lazebnik, S. (2018). PackNet: adding multiple tasks to a single network by iterative pruning. \emph{CVPR.}
|
||||
\item McClelland, J. L., McNaughton, B. L., \& O'Reilly, R. C. (1995). Why there are complementary learning systems in the hippocampus and neocortex. \emph{Psychological Review.}
|
||||
\item McCloskey, M., \& Cohen, N. J. (1989). Catastrophic interference in connectionist networks. \emph{Psychology of Learning and Motivation.}
|
||||
\item Minsky, M. (1986). \emph{The Society of Mind.}
|
||||
\item Mouret, J.-B., \& Clune, J. (2015). Illuminating search spaces by mapping elites (MAP-Elites). \emph{arXiv:1504.04909.}
|
||||
\item Muller, H. J. (1932). Some genetic aspects of sex. \emph{The American Naturalist.} (The advantage of recombination.)
|
||||
\item Muller, H. J. (1964). The relation of recombination to mutational advance. \emph{Mutation Research.} (Muller's ratchet.)
|
||||
\item Pearl, J. (2009). \emph{Causality: Models, Reasoning, and Inference} (2nd ed.).
|
||||
\item Popper, K. (1959). \emph{The Logic of Scientific Discovery.}
|
||||
\item Riis, S. (2026). Drift and selection in LLM text ecosystems. \emph{arXiv:2604.08554.}
|
||||
\item Rusu, A. A., et al. (2016). Progressive neural networks. \emph{arXiv:1606.04671.}
|
||||
\item Shumailov, I., et al. (2024). AI models collapse when trained on recursively generated data. \emph{Nature.}
|
||||
\item Wortsman, M., et al. (2022). Model soups: averaging weights of multiple fine-tuned models. \emph{arXiv:2203.05482.}
|
||||
\item Wright, S. (1931). Evolution in Mendelian populations. \emph{Genetics.}
|
||||
\end{itemize}
|
||||
|
||||
\emph{The evolution of sex (the geneticist's canon this paper draws on):}
|
||||
|
||||
\begin{itemize}
|
||||
\item Barton, N. H., \& Charlesworth, B. (1998). Why sex and recombination? \emph{Science.}
|
||||
\item Otto, S. P., \& Lenormand, T. (2002). Resolving the paradox of sex and recombination. \emph{Nature Reviews Genetics.}
|
||||
\item Kondrashov, A. S. (1993). Classification of hypotheses on the advantage of amphimixis. \emph{Journal of Heredity.}
|
||||
\item Dobzhansky, T. (1936); Muller, H. J. (1942). Bateson--Dobzhansky--Muller incompatibilities (reproductive isolation).
|
||||
\item Livnat, A., \& Papadimitriou, C. (2016). Sex as an algorithm: the theory of evolution under the lens of computation. \emph{Communications of the ACM 59(11).} (The theory-of-computation precursor: recombination selects for mixability.)
|
||||
\end{itemize}
|
||||
|
||||
\emph{The 2025--2026 landscape this paper positions against:}
|
||||
|
||||
\begin{itemize}
|
||||
\item Subramaniam, V., Du, Y., Tenenbaum, J. B., Torralba, A., Li, S., \& Mordatch, I. (2025). Multiagent finetuning: self-improvement with diverse reasoning chains. \emph{arXiv:2501.05707.}
|
||||
\item Zhang, J., Hu, S., Lu, C., Lange, R., \& Clune, J. (2025). Darwin Gödel Machine: open-ended evolution of self-improving agents. \emph{arXiv:2505.22954.}
|
||||
\item \emph{Nature-inspired population-based evolution of large language models} (GENOME/GENOME+). (2025). \emph{arXiv:2503.01155.}
|
||||
\item Sakana AI (2025). Competition and attraction improve model fusion (M2N2). \emph{arXiv:2508.16204} (GECCO '25).
|
||||
\item Yadav, P., Tam, D., Choshen, L., Raffel, C., \& Bansal, M. (2023). TIES-Merging: resolving interference when merging models. \emph{NeurIPS / arXiv:2306.01708.}
|
||||
\item Yu, L., Yu, B., Yu, H., Huang, F., \& Li, Y. (2023). Language models are super Mario: absorbing abilities from homologous models (DARE). \emph{arXiv:2311.03099.}
|
||||
\item Gerstgrasser, M., et al. (2024). Is model collapse inevitable? Breaking the curse of recursion by accumulating real and synthetic data. \emph{arXiv:2404.01413.}
|
||||
\item Guo, D., Wu, J., \& Yiu, S. M. (2026). Model collapse as cultural evolution. \emph{arXiv:2605.23054.}
|
||||
\item Benati, M., Londei, A., Lanzieri, D., \& Loreto, V. (2025). First-extinction law for resampling processes. \emph{arXiv:2509.20101.} (Collapse onset = the Wright--Fisher first-extinction time.)
|
||||
\item Yoon, Y., Hu, D., Weissburg, I., Qin, Y., \& Jeong, H. (2025). Model collapse in the self-consuming chain of diffusion finetuning: a novel perspective from quantitative trait modeling. \emph{ICLR 2025 / arXiv:2407.17493.}
|
||||
\item Yi, B., Liu, Q., Cheng, Y., \& Xu, H. (2025). Escaping model collapse via synthetic data verification. \emph{arXiv:2510.16657.}
|
||||
\item Ainsworth, S., Hayase, J., \& Srinivasa, S. (2022). Git Re-Basin: merging models modulo permutation symmetries. \emph{arXiv:2209.04836.}
|
||||
\item Li, T., \& Shen, Z. (2026). Scaling linear mode connectivity and merging to billion-parameter pretrained transformers. \emph{arXiv:2606.23607.} (Symmetry groups richer than permutations remove more of the barrier.)
|
||||
\item Sharma, E., Roy, D. M., \& Dziugaite, G. K. (2024). The non-local model merging problem: permutation symmetries and variance collapse. \emph{arXiv:2410.12766.}
|
||||
\item Pari, J., Jelassi, S., \& Agrawal, P. (2024). Collective model intelligence requires compatible specialization. \emph{arXiv:2411.02207.}
|
||||
\item Zhou, L., Zhao, B., Yu, R., \& Rodolà, E. (2026). Demystifying mergeability: interpretable properties to predict model merging success. \emph{arXiv:2601.22285.}
|
||||
\item Cao, Y., Ran, D., Guo, Y., Wu, M., Chen, S., et al. (2026). An empirical study and theoretical explanation on task-level model-merging collapse. \emph{arXiv:2603.09463.}
|
||||
\item Hu, Y., Yao, Y., Zhang, N., Chen, H., \& Deng, S. (2024). Exploring model kinship for merging large language models. \emph{arXiv:2410.12613.}
|
||||
\item Kozodoi, N., Afolabi, Z., \& Butler, J. (2026). Are we merging the right models? Impact of expert training duration on model merging for LLMs. \emph{arXiv:2607.11997.}
|
||||
\item Harris, K. D. (2026). A mathematical theory of evolution for self-designing AIs. \emph{arXiv:2604.05142.}
|
||||
\item Chen, N., Tong, Y., Yang, Y., He, Y., Zhang, X., et al. (2026). Diversity collapse in multi-agent LLM systems: structural coupling and collective failure in open-ended idea generation. \emph{arXiv:2604.18005.}
|
||||
\item Tanaka, H. (2026). When is collective intelligence a lottery? Multi-agent scaling laws for memetic drift in LLMs. \emph{arXiv:2603.24676.}
|
||||
\end{itemize}
|
||||
|
||||
\emph{Still to engage in a full version: tacit knowledge (Polanyi) and human capital (Becker).}
|
||||
|
||||
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\title{\textbf{The Evolution of Sex for Artificial Intelligence}\\[0.6em]
|
||||
\large A population-genetic control theory for societies of agents that reproduce, recombine,
|
||||
and stay open-ended}
|
||||
\author{Giorgio F.\ Gilestro\\[0.2em]
|
||||
\normalsize Department of Life Sciences, Imperial College London\\
|
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\normalsize \href{mailto:giorgio@gilest.ro}{giorgio@gilest.ro} \,\(\cdot\)\,
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\emph{A perspective, written from a geneticist's chair. Companion to a set of minimal, reproducible
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working models and a first language-model prototype (both built).}
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|
||||
deliberately dumb and auditable: the paper uses a small Markdown subset (##/### headings, bold,
|
||||
italics, inline code, links, bullet/numbered lists, one blockquote, horizontal rules, and
|
||||
`(Figure: \`path\`.)` figure references), and this script handles exactly that subset. Re-run after
|
||||
editing the Markdown; the Markdown remains the source of truth.
|
||||
|
||||
Usage: python paper/arxiv/md2tex.py
|
||||
"""
|
||||
|
||||
from __future__ import annotations
|
||||
|
||||
import re
|
||||
from pathlib import Path
|
||||
|
||||
SRC = Path(__file__).resolve().parents[1] / "the-evolution-of-sex-for-ai.md"
|
||||
OUT = Path(__file__).resolve().parent / "body.tex"
|
||||
|
||||
# Figure references in the text -> (graphics file under figs/, caption).
|
||||
FIGURES = {
|
||||
"results/figS13_mating_breadth/E14.png": ("figs/E14.pdf",
|
||||
"Mating systems (E14): the best mate-pool breadth shrinks as skills get more entangled. "
|
||||
"(A) best fitness peaks at intermediate breadth on rugged landscapes; (B) the population mean "
|
||||
"is monotonically favoured by promiscuity; (C) diversity is monotonically destroyed by it."),
|
||||
"results/fig5_speciation_bdm/E12.png": ("figs/E12.pdf",
|
||||
"Model speciation, analytic (E12): hybrid fitness vs divergence traces compatible $\\rightarrow$ "
|
||||
"outbreeding depression $\\rightarrow$ inviability; the isolation cliff arrives earlier the "
|
||||
"denser the incompatibilities (epistasis), and damage grows super-linearly (the Orr--Turelli "
|
||||
"snowball)."),
|
||||
"results/speciation_real/speciation_real.png": ("figs/speciation_real.pdf",
|
||||
"Model speciation in real weights (E13). (A) the merge barrier decomposed by alignment "
|
||||
"strength: the independent-init barrier is a coordinate artefact (removed by alignment); the "
|
||||
"conflict barrier survives even the full function-preserving symmetry group. (B) the isolation "
|
||||
"cliff: residual barrier rises and hybrid accuracy falls ($0.97 \\rightarrow 0.03$) with "
|
||||
"functional conflict. (C) the pre-registered emergent test: divergent-but-compatible "
|
||||
"specialists develop no isolation at any divergence --- the merge instead rescues them "
|
||||
"(Fisher--Muller)."),
|
||||
}
|
||||
|
||||
UNICODE = {
|
||||
"—": "---", "–": "--", "→": r"\(\rightarrow\)", "≈": r"\(\approx\)",
|
||||
"≥": r"\(\geq\)", "×": r"\(\times\)", "·": r"\(\cdot\)", "μ": r"\(\mu\)",
|
||||
}
|
||||
|
||||
SPECIALS = {"&": r"\&", "%": r"\%", "#": r"\#", "_": r"\_", "$": r"\$",
|
||||
"~": r"\textasciitilde{}", "^": r"\textasciicircum{}"}
|
||||
|
||||
|
||||
def esc(s: str) -> str:
|
||||
s = s.replace("\\", r"\textbackslash{}")
|
||||
for k, v in SPECIALS.items():
|
||||
s = s.replace(k, v)
|
||||
for k, v in UNICODE.items():
|
||||
s = s.replace(k, v)
|
||||
return s
|
||||
|
||||
|
||||
def inline(s: str) -> str:
|
||||
"""Escape + convert inline markup. Code spans are protected, then bold, italic, links."""
|
||||
parts = re.split(r"(`[^`]*`)", s)
|
||||
out = []
|
||||
for p in parts:
|
||||
if p.startswith("`") and p.endswith("`") and len(p) >= 2:
|
||||
out.append(r"\texttt{" + esc(p[1:-1]) + "}")
|
||||
else:
|
||||
p = esc(p)
|
||||
p = re.sub(r"\[([^\]]+)\]\((https?://[^)]+)\)", r"\\href{\2}{\1}", p)
|
||||
p = re.sub(r"\*\*([^*]+)\*\*", r"\\textbf{\1}", p)
|
||||
p = re.sub(r"\*([^*]+)\*", r"\\emph{\1}", p)
|
||||
p = re.sub(r'"([^"]+)"', r"``\1''", p) # straight quotes -> LaTeX quotes
|
||||
out.append(p)
|
||||
return "".join(out)
|
||||
|
||||
|
||||
def figure_block(md_path: str) -> str:
|
||||
gfx, caption = FIGURES[md_path]
|
||||
return ("\\begin{figure*}[t]\\centering\n"
|
||||
f"\\includegraphics[width=\\textwidth]{{{gfx}}}\n"
|
||||
f"\\caption{{{caption}}}\n\\end{{figure*}}\n")
|
||||
|
||||
|
||||
def convert(text: str) -> str:
|
||||
"""Block-based conversion: soft-wrapped lines are joined per paragraph/item BEFORE inline
|
||||
conversion, so bold/italic/code spans and figure pointers crossing a line break work."""
|
||||
fig_queue: list[str] = []
|
||||
|
||||
def fig_sub(m):
|
||||
path = m.group(1)
|
||||
if path in FIGURES:
|
||||
fig_queue.append(figure_block(path))
|
||||
return ""
|
||||
return m.group(0)
|
||||
|
||||
lines = text.split("\n")
|
||||
i = 0
|
||||
# Skip the header block (title/subtitle/author) up to and including the first horizontal rule:
|
||||
# main.tex composes the title page itself.
|
||||
while i < len(lines) and lines[i].strip() != "---":
|
||||
i += 1
|
||||
i += 1
|
||||
|
||||
# Group into blocks separated by blank lines; a block is a heading, rule, quote, list, or paragraph.
|
||||
blocks: list[list[str]] = []
|
||||
cur: list[str] = []
|
||||
for line in lines[i:]:
|
||||
if line.strip() == "":
|
||||
if cur:
|
||||
blocks.append(cur); cur = []
|
||||
else:
|
||||
cur.append(line)
|
||||
if cur:
|
||||
blocks.append(cur)
|
||||
|
||||
def emit_para(joined: str, out: list[str]) -> None:
|
||||
joined = re.sub(r"\(Figure: `([^`]+)`\.?\)", fig_sub, joined)
|
||||
joined = re.sub(r"\s{2,}", " ", joined).strip()
|
||||
if joined:
|
||||
out.append(inline(joined))
|
||||
out.append("")
|
||||
while fig_queue:
|
||||
out.append(fig_queue.pop(0)); out.append("")
|
||||
|
||||
def emit_table(block: list[str], out: list[str]) -> None:
|
||||
"""Pipe table -> small-font tabular with wrapped paragraph columns (full text width)."""
|
||||
rows = [[c.strip() for c in line.strip().strip("|").split("|")] for line in block]
|
||||
header, body = rows[0], [r for r in rows[2:]] # rows[1] is the |---| separator
|
||||
n = len(header)
|
||||
widths = " ".join([f"p{{{0.92 / n:.3f}\\textwidth}}"] * n)
|
||||
out.append("\\medskip\\noindent\\begin{center}\\footnotesize") # non-floating: stays in place
|
||||
out.append(f"\\begin{{tabular}}{{{widths}}}")
|
||||
out.append("\\hline")
|
||||
out.append(" & ".join(inline(c) for c in header) + " \\\\ \\hline")
|
||||
for r in body:
|
||||
r = (r + [""] * n)[:n]
|
||||
out.append(" & ".join(inline(c) for c in r) + " \\\\[3pt]")
|
||||
out.append("\\hline\\end{tabular}\\end{center}\\medskip")
|
||||
out.append("")
|
||||
|
||||
out: list[str] = []
|
||||
for block in blocks:
|
||||
first = block[0].strip()
|
||||
if first.startswith("|") and len(block) >= 2 and set(block[1].strip()) <= set("|-: "):
|
||||
emit_table(block, out)
|
||||
elif first == "---" and len(block) == 1:
|
||||
out.append("\\medskip\\hrule\\medskip"); out.append("")
|
||||
elif first.startswith("## "):
|
||||
out.append(f"\\section*{{{inline(first[3:])}}}"); out.append("")
|
||||
elif first.startswith("### "):
|
||||
out.append(f"\\subsection*{{{inline(first[4:])}}}"); out.append("")
|
||||
elif first.startswith("> "):
|
||||
joined = " ".join(l.strip().lstrip("> ").strip() for l in block)
|
||||
out.append("\\begin{quote}" + inline(joined) + "\\end{quote}"); out.append("")
|
||||
elif re.match(r"^(- |\d+\. )", first):
|
||||
env = "itemize" if first.startswith("- ") else "enumerate"
|
||||
out.append(f"\\begin{{{env}}}")
|
||||
items: list[str] = []
|
||||
for l in block:
|
||||
s = l.strip()
|
||||
if re.match(r"^(- |\d+\. )", s):
|
||||
items.append(re.sub(r"^(- |\d+\. )", "", s))
|
||||
else:
|
||||
items[-1] = items[-1] + " " + s # soft-wrapped continuation of the item
|
||||
for it in items:
|
||||
it = re.sub(r"\(Figure: `([^`]+)`\.?\)", fig_sub, it)
|
||||
out.append("\\item " + inline(it.strip()))
|
||||
out.append(f"\\end{{{env}}}"); out.append("")
|
||||
while fig_queue:
|
||||
out.append(fig_queue.pop(0)); out.append("")
|
||||
else:
|
||||
emit_para(" ".join(l.strip() for l in block), out)
|
||||
return "\n".join(out) + "\n"
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
OUT.write_text(convert(SRC.read_text()))
|
||||
print(f"wrote {OUT}")
|
||||
|
|
@ -1,456 +0,0 @@
|
|||
# A Technical Blueprint for Modelling the Lamarckian Society
|
||||
|
||||
### An implementation specification: two layers, one population-genetics engine
|
||||
|
||||
*Companion technical paper to "The Lamarckian Society." Blueprint v1 — written to be handed, whole, to an autonomous coding agent (Claude Code) for implementation. Every quantitative claim in the perspective paper is reduced here to a state variable, an update rule, an analytic prediction, and a falsifier.*
|
||||
|
||||
---
|
||||
|
||||
## 0. How to use this document
|
||||
|
||||
This is a build specification, not an essay. It is written so that a coding agent can implement the entire study from it with minimal further decisions, and so that a human reader can verify every modelling choice against the theory it is meant to test.
|
||||
|
||||
**Scope.** Two layers, deliberately staged by cost:
|
||||
|
||||
- **Layer 1 — the analytical core.** A parametric population-genetics model of knowledge transmission across generations. Pure NumPy/SciPy. Runs on a laptop in minutes. This layer carries the paper's quantitative claims: the grounding phase boundary, the decorrelation curve, region-matched grounding, quality-diversity vs. greedy selection, and the re-minting gate. Several of its predictions are analytically solvable, which turns validation into an exact test rather than a vibe.
|
||||
- **Layer 2 — the neural existence proof.** A minimal demonstration that the same effects appear in *real weights*: small open-weight models, LoRA specialisation, distillation/merging across two–three generations, with an execution-based verifier standing in for "reality's no." One consumer GPU. This layer answers the single most predictable reviewer objection to Layer 1 ("you assumed the collapse operator") by showing the sign of the key effects without assuming them.
|
||||
|
||||
**The relationship between layers.** Layer 1 defines the abstractions (region, rarity, grounding fraction, teacher decorrelation, diversity metric). Layer 2 realises the *same abstractions* in a neural pipeline: a "region" is a task family, "rarity" is task-type frequency, "grounding" is verifier-passed samples, "decorrelation" is teachers specialised on disjoint task families. Keeping the abstractions identical across layers is a hard requirement — it is what lets a Layer-2 result be read as confirming a Layer-1 prediction.
|
||||
|
||||
**Non-goals for v1.** No human-in-the-loop interaction (the verifier is the refuter; humans are future work). No foundation-scale training. No claim about the *horizontal* prediction (generation size vs. domain decomposability) beyond an optional abstract treatment in §2.7 — it is the most compute-hungry claim and is explicitly deferred. The load-bearing target is the *vertical* claim (general knowledge climbs while each specialty is re-earned and exceeded).
|
||||
|
||||
**Reader's map.** §1 gives the formal dictionary between population genetics and knowledge transmission — read this first; everything else is an instantiation of it. §2 is Layer 1 in full (theory, experiments, code interfaces). §3 is Layer 2. §4 is the shared reproducibility standard. §5 is the repository layout. §6 is the claims→experiments→figures traceability matrix. §7 is the suggested build order for the coding agent.
|
||||
|
||||
---
|
||||
|
||||
## 1. The formal mapping: knowledge transmission *is* a Wright–Fisher process
|
||||
|
||||
The perspective paper argues by analogy that generational distillation resembles genetic drift, that multi-teacher distillation resembles recombination, and that heterodox input plus quality-diversity selection resembles mutation supply plus balancing selection. This blueprint drops the word "resembles." At the level of a distribution over discrete items evolving by finite resampling, these are not analogies; they are the *same stochastic process*, and the population-genetics literature has already solved large parts of it. We therefore adopt Wright–Fisher dynamics as the engine and inherit its exact results as our validation targets.
|
||||
|
||||
The core object is a **distribution over discrete knowledge items** — facts, capabilities, behaviours, or "modes." Call the items $1, \dots, K$. A model at generation $t$ holds a distribution $p_t = (p_t^1, \dots, p_t^K)$ on the simplex. There is a fixed **true distribution** $p^\* $ over the same items, some of which are rare (the *tail* — the improbable events whose loss defines model collapse).
|
||||
|
||||
The generational step is: sample from the parent, optionally mix in fresh real samples, refit. That single step is Wright–Fisher reproduction with immigration. Here is the dictionary, and it is meant to be used literally throughout implementation:
|
||||
|
||||
| Knowledge-transmission concept (perspective paper) | Population-genetics object (this blueprint) | Governs |
|
||||
|---|---|---|
|
||||
| Knowledge item / capability / mode | Allele / type | State space |
|
||||
| Model's knowledge distribution $p_t$ | Allele-frequency vector | State |
|
||||
| True distribution $p^\*$ (with rare tail) | Ancestral/immigrant frequencies | Grounding target |
|
||||
| Distillation sample size $n$ | Population size $N$ | Drift strength ($\propto 1/n$) |
|
||||
| Lossy compression / "shed the idiosyncratic" | Genetic drift | Tail-first loss |
|
||||
| Model collapse (tail lost first) | Loss of rare alleles under drift | The central failure |
|
||||
| Grounding: $m$ fresh real samples per passage | Immigration / mutation supply | Tail replenishment |
|
||||
| "No dry inheritance," region-matched | Immigration structured by locus | Which tails are protected |
|
||||
| Multi-teacher distillation | Recombination across lineages | Reconstitutes lost tails |
|
||||
| Teacher decorrelation $\rho$ | Linkage / shared ancestry | Recombination benefit |
|
||||
| Single-teacher irreversible error | Muller's ratchet (clonal lineage) | Why one teacher is unsafe |
|
||||
| Diversity metric (§7 of paper) | Expected heterozygosity $H = 1 - \sum_i p_i^2$ | Health of the lineage |
|
||||
| Greedy fitness-max selection | Directional selection → fixation | Accelerated collapse |
|
||||
| Quality-diversity / novelty selection | Balancing / negative frequency-dependent selection | Maintained polymorphism |
|
||||
| Re-minting the base (§11 of paper) | Founder event / new reference genome | Irreversibility |
|
||||
| Heterodox contributor supply | Standing variation of founding stock | Raw material |
|
||||
|
||||
Every experiment below is a manipulation of this one process. The value of the mapping is that it hands us closed-form predictions — heterozygosity decay, mutation–drift equilibrium, fixation probabilities — against which the simulator must agree before any headline result is trusted. Validation and theory are the same equations.
|
||||
|
||||
---
|
||||
|
||||
## 2. Layer 1 — the analytical core
|
||||
|
||||
### 2.1 State and the base dynamics (neutral drift = Shumailov collapse)
|
||||
|
||||
**State.** A single lineage is a point $p_t$ on the $K$-simplex. Items are partitioned into $R$ **regions** (disjoint blocks of the $K$ items); regions are how we express "different areas of knowledge," and they are what grounding and specialisation are *targeted at*. The true distribution $p^\*$ is fixed and chosen to have a deliberate **tail**: most probability mass on common items, a long thin tail of rare items (e.g. a Zipfian or a two-component mixture of "head" and "tail" items, tunable).
|
||||
|
||||
**The generational step, base case (no grounding, single teacher).** Given parent $p_t$ and drift strength $n$:
|
||||
|
||||
1. Draw counts $c \sim \mathrm{Multinomial}(n, p_t)$.
|
||||
2. Set $p_{t+1}^i = c^i / n$.
|
||||
|
||||
This is exactly neutral Wright–Fisher with haploid population size $n$. It is also exactly Shumailov's recursive resampling with a perfect refit. Rare items are lost first (once $c^i = 0$, item $i$ is gone and — with no grounding — cannot return); the lineage drifts to fixation on a single item.
|
||||
|
||||
**This is the null model and the first validation.** It must reproduce, within Monte-Carlo error, the classical drift results in §2.4. If it does not, nothing downstream is trustworthy.
|
||||
|
||||
### 2.2 The five mechanisms, each as an operator on the step
|
||||
|
||||
Each perspective-paper safeguard is one modification of the generational step. They compose; the full step applies them in the order below.
|
||||
|
||||
**(A) Grounding — immigration / mutation supply.** Fresh real data enters every passage. Replace the single draw with a *pooled* draw:
|
||||
|
||||
- Draw $c_{\text{syn}} \sim \mathrm{Multinomial}(n, p_t)$ (inherited / teacher output).
|
||||
- Draw $c_{\text{real}} \sim \mathrm{Multinomial}(m, p^\*)$ (grounding).
|
||||
- $p_{t+1}^i = (c_{\text{syn}}^i + c_{\text{real}}^i)/(n+m)$.
|
||||
|
||||
Define the **grounding fraction** $g = m/(n+m)$. This is the single most important control variable in the paper: it is the ratio of freshly-grounded to inherited information per passage. The claim "no dry inheritance" is $g > 0$; the claim that a *critical* $g$ exists is the phase-boundary experiment E2.
|
||||
|
||||
**(B) Region-matched grounding — structured immigration.** Grounding is a vector, not a scalar: $m = (m_1, \dots, m_R)$ real samples allocated across regions. "No dry inheritance, region by region" means grounding must be delivered *to the regions whose tails are at risk*, not spread uniformly. Two allocation policies are compared in E3: `uniform` (spread $m$ evenly over regions) vs. `matched` (allocate $m$ to the regions actually being inherited/exercised this passage). The prediction is that uniform grounding fails to protect a specific inherited region's tail even at the same total $m$.
|
||||
|
||||
**(C) Multi-teacher distillation — recombination.** Instead of one parent, the pupil is drawn from $K_T$ teachers $\{p_t^{(1)}, \dots, p_t^{(K_T)}\}$, each of which has its own history and has ground different regions (hence retains different tails). The pupil's inherited draw is taken from the mixture $\bar p_t = \frac{1}{K_T}\sum_k p_t^{(k)}$ (equivalently, $n/K_T$ samples from each teacher). Teacher **decorrelation** is the controlled quantity: generate teacher sets with a tunable pairwise correlation $\rho$ in *which tail items they have retained* (see §2.7 for the generative model of correlated teachers). Prediction (E4): tail coverage of the pupil rises as teachers decorrelate, and the mixture's tails are the *union* of the teachers' tails at $\rho = 0$ and no better than a single teacher at $\rho = 1$.
|
||||
|
||||
**(D) Selection — directional vs. balancing.** Between drawing and refitting, a selection operator reweights items by a fitness before the pupil is formed. Two regimes:
|
||||
|
||||
- `greedy`: fitness-proportional (or top-$k$) selection toward the highest-fitness items — directional selection. Fitness is predictive accuracy against $p^\*$ (a reality-anchored score; see falsifier note). Drives fixation.
|
||||
- `qd` (quality-diversity): fitness *plus* a novelty bonus that is a decreasing function of an item's current frequency — negative frequency-dependent / balancing selection. Formally, effective weight $w^i \propto f^i \cdot (p_t^i)^{-\alpha}$ with novelty exponent $\alpha \ge 0$; $\alpha = 0$ recovers greedy. Maintains polymorphism.
|
||||
|
||||
Prediction (E5): at matched input diversity, `greedy` drives heterozygosity to zero (fixation); `qd` holds it at a positive stationary value.
|
||||
|
||||
**(E) Re-minting — founder event.** Every $\tau$ generations, optionally replace the grounding reference: set $p^\*_{\text{eff}} \leftarrow p_t$ (the lineage's *current* distribution becomes the new "truth" it is grounded against, modelling assimilation of the soft delta into a new immutable base). Crucially, once re-minted, the *original* $p^\*$ is discarded — grounding can now only replenish tails that still exist in $p_t$ at re-mint time. A **gate** conditions re-minting on the diversity metric: only re-mint if $H(p_t) \ge H_{\text{gate}}$. Prediction (E6): re-minting while collapsed ($H$ low) locks in the collapse irreversibly (KL to the *original* truth stays high forever); gated re-minting does not.
|
||||
|
||||
**Full composed step (reference pseudocode).**
|
||||
|
||||
```
|
||||
def generation_step(teachers, p_star_eff, cfg, rng):
|
||||
# teachers: list of frequency vectors (length 1 for single-teacher)
|
||||
# (C) recombination: mixture over teachers
|
||||
p_parent = mean(teachers) # or weighted mixture
|
||||
# inherited draw (drift, strength n)
|
||||
c_syn = rng.multinomial(cfg.n, p_parent)
|
||||
# (A,B) grounding: structured immigration from the true distribution
|
||||
c_real = structured_multinomial(cfg.m_vector, p_star_eff, regions, cfg.grounding_policy, rng)
|
||||
counts = c_syn + c_real
|
||||
p_next = counts / counts.sum()
|
||||
# (D) selection operator (identity if 'none')
|
||||
p_next = apply_selection(p_next, p_star_eff, cfg.selection, cfg.novelty_alpha)
|
||||
return normalize(p_next)
|
||||
```
|
||||
|
||||
Selection is applied after refitting for simplicity; an alternative (select-then-sample) is a documented config switch, and the two should be checked to give qualitatively identical phase behaviour (robustness, not a headline).
|
||||
|
||||
### 2.3 Metrics (computed every generation, logged to disk)
|
||||
|
||||
- **Forward KL to truth**, $D_{\mathrm{KL}}(p^\* \,\|\, p_t) = \sum_i p^{\*i}\log(p^{\*i}/p_t^i)$. This is the correct primary metric: it *diverges* when $p_t$ drops mass that $p^\*$ has — i.e. it explicitly punishes forgetting the improbable. (Reverse KL would reward mode-seeking; do not use it as the primary.) Use a small floor $\epsilon$ on $p_t$ to keep it finite and log the floor.
|
||||
- **Expected heterozygosity / diversity**, $H_t = 1 - \sum_i (p_t^i)^2$. The lineage-health metric; the quantity the re-mint gate reads.
|
||||
- **Tail mass retained**, $T_t = \sum_{i \in \text{tail}} p_t^i$ where the tail set is $\{i : p^{\*i} < \theta_{\text{tail}}\}$. The direct measure of collapse.
|
||||
- **Support size**, $|\{i : p_t^i > \epsilon\}|$. Number of surviving items.
|
||||
- **Per-region diversity and tail mass**, the above restricted to each region (needed for E3).
|
||||
|
||||
All metrics are recorded per generation, per replicate (independent seed), so every reported curve carries a confidence band over replicates. Number of replicates is a config value; default 100 for Layer 1 (cheap).
|
||||
|
||||
### 2.4 Analytic predictions — the validation targets
|
||||
|
||||
These are the closed forms the simulator must match. They are implemented as assertions in the test suite (§4), so scientific validation and code correctness are one thing.
|
||||
|
||||
1. **Neutral heterozygosity decay** (base case, $m=0$): $\mathbb{E}[H_{t+1}] = (1 - 1/n)\,\mathbb{E}[H_t]$, hence $\mathbb{E}[H_t] = H_0 (1 - 1/n)^t$. The simulator's mean $H_t$ over replicates must match this geometric decay within Monte-Carlo error. *(This is the quantitative form of "collapse is tail-first and its rate is set by the distillation sample size $n$.")*
|
||||
2. **Fixation probability** (base case): the probability that item $i$ is the one eventually fixed equals its initial frequency $p_0^i$. Checkable by long runs.
|
||||
3. **Mutation–drift equilibrium** (with grounding). For the immigration model actually implemented — $p_{t+1} = (\mathrm{Multinomial}(n,p_t) + \mathrm{Multinomial}(m,p^\*))/(n+m)$ — the stationary heterozygosity is **exact** (from the coupled mean recursions for $\sum p_t^2$ and the overlap $\sum p_t p^\*$, whose fixed point is $\sum (p^\*)^2$):
|
||||
$$H_{\text{eq}} = H^\* \cdot \frac{m\,(2n + m - 1)}{\,n + 2nm + m^2\,}, \qquad H^\* = 1 - \textstyle\sum_i (p^{\*i})^2.$$
|
||||
Limits: $m\to0 \Rightarrow H_{\text{eq}}\to0$ (collapse to fixation); $m\to\infty \Rightarrow H_{\text{eq}}\to H^\*$ (the truth's own heterozygosity is recovered); and in the rare-immigrant / many-types limit ($H^\*\approx1$, $m\ll n$) it reduces to the textbook infinite-alleles form $H_{\text{eq}}\approx \theta/(1+\theta)$ with $\theta = 2m$. The simulator's stationary $H$ under grounding must track the **exact** form as $m$ varies (verified against simulation to <0.1% rel. error; it is a `test_scientific_validation.py` assertion). *(This is the phase boundary in closed form; note $H$ itself is smooth in $m$ — the sharp threshold lives in discrete tail-item survival, prediction 4.)*
|
||||
4. **Tail-persistence threshold**: an item of true frequency $p^{\*i}$ is maintained against drift only if its expected reintroduction per generation $m \cdot p^{\*i} \gtrsim 1$. Hence the critical grounding for protecting a tail of rarity $p_{\min}$ is $m^\* \approx 1/p_{\min}$. *(This is why grounding must be region-matched: uniform $m$ spread over $R$ regions gives each region $m/R$, so a rare region's tail is protected only if $m/R \gtrsim 1/p_{\min}^{\text{region}}$.)*
|
||||
5. **Recombination benefit** (Muller's ratchet): a single clonal lineage accumulates irreversible loss at the drift rate; the expected tail coverage of a pupil drawn from $K_T$ teachers with pairwise retention-correlation $\rho$ interpolates between the single-teacher value ($\rho = 1$) and the union of $K_T$ independent lineages ($\rho = 0$). With the construction of §2.7.1 (each teacher retains a fraction $q$ of the $T$ tail items, at exact pairwise correlation $\rho$) the interpolation is **closed-form**: the expected number of tail items retained by at least one teacher is
|
||||
$$U(K_T,\rho,q) = T\left[\rho q + (1-\rho)\left(1-(1-q)^{K_T}\right)\right].$$
|
||||
Check the limits: $K_T=1 \Rightarrow Tq$ (single teacher, independent of $\rho$); $\rho=1 \Rightarrow Tq$ (identical teachers, union = one); $\rho=0 \Rightarrow T[1-(1-q)^{K_T}]$ (independent teachers, maximal union). The pupil's realised tail coverage tracks $U$ *up to* the drift-survival threshold of prediction 4 — a tail item present in the mixture only survives the pupil's resampling of size $n$ if its mixture mass clears $\sim 1/n$, which ties E4 back to E2/E3. (Numerically verified against the construction to three decimals; it is a `test_scientific_validation.py` assertion.)
|
||||
|
||||
### 2.5 Experiments E1–E6
|
||||
|
||||
Each experiment is one config file (§4), one runner invocation, one results artifact, and one figure script. Each states its prediction and its **falsifier** — the outcome that would refute the corresponding claim in the perspective paper.
|
||||
|
||||
**E1 — Reproduce collapse (null model).** $m=0$, single teacher, no selection. *Expect:* $H_t = H_0(1-1/n)^t$; support shrinks to 1; forward KL diverges; tail mass → 0, tail first. *Validates against:* predictions 1–2. *Falsifier of the harness (not the theory):* if drift does not reproduce the analytic decay, the simulator is wrong — fix before proceeding.
|
||||
|
||||
**E2 — Grounding phase boundary (headline).** Sweep $g = m/(n+m)$ from 0 to a high value; single teacher; uniform grounding; no selection. *Expect:* a critical $g^\*$ below which tail mass and $H$ decay to (near) zero and above which they stabilise at a positive stationary value tracking $H_{\text{eq}} = \theta/(1+\theta)$. *This is the paper's central quantitative prediction: the ratio of inherited-to-grounded information has a threshold.* *Falsifier:* if the stationary tail mass is flat in $g$, or if it only stabilises as $g \to 1$ (you always need essentially all-real data), then inheritance buys nothing and the multigenerational thesis is refuted. Report $g^\*$ with a CI.
|
||||
|
||||
**E3 — Region-matched grounding.** Fixed total $m$; compare `uniform` vs. `matched` allocation across $R$ regions, with one designated "inherited-but-not-freshly-grounded-under-uniform" region carrying a rare tail. *Expect:* under `uniform`, the target region's tail collapses even though global grounding is nonzero; under `matched`, it persists. *Validates:* prediction 4 and the "grounding must overlap the content it protects" claim. *Falsifier:* if uniform grounding protects the region as well as matched, the region-matching requirement is unnecessary and that paragraph of the paper should be cut.
|
||||
|
||||
**E4 — Multi-teacher decorrelation.** Teachers built by the §2.7.1 construction; sweep number of teachers $K_T \in \{1,2,3,5\}$ and retention-correlation $\rho \in [0,1]$ (at fixed marginal retention $q$); matched total data budget (so more teachers ≠ more data — each contributes $n/K_T$). Report **two** coverages: the construction-level union $U(K_T,\rho,q)$ (must match the §2.4-5 closed form exactly) and the post-distillation *surviving* coverage after the pupil's resampling. *Expect:* both rise with $K_T$ and with $(1-\rho)$; collapse suppression $\propto$ decorrelation; at $\rho=1$, multiple teachers give no benefit over one; and the gap between union and surviving coverage shrinks as grounding $g$ rises (recombination supplies the tail, grounding holds it). *Validates:* prediction 5 (now closed-form). *Falsifier:* if $K_T$ decorrelated teachers give no surviving-coverage benefit over one at matched budget, the recombination claim dies and single-teacher distillation is fine.
|
||||
|
||||
**E5 — Quality-diversity vs. greedy.** Same starting diversity; `greedy` vs. `qd` selection; sweep novelty exponent $\alpha$. *Expect:* `greedy` → fixation ($H \to 0$); `qd` holds $H$ at a positive plateau and re-introduces lost tail items. *Validates:* the two-level anti-convergence argument (§7 of paper). *Falsifier:* if `qd` does not maintain higher stationary $H$ than `greedy`, quality-diversity is not doing the work the paper assigns it.
|
||||
|
||||
**E6 — Re-minting gate (irreversibility).** Run a lineage to a chosen diversity level, then re-mint (freeze current $p_t$ as new reference, discard original $p^\*$); compare re-minting at high $H$ vs. low $H$. *Expect:* re-mint while collapsed → KL to *original* truth is locked high forever (tails unrecoverable); gated re-mint at high $H$ → no lock-in. *Validates:* §11's "re-minting is irreversible; gate it on diversity." *Falsifier:* if a collapsed lineage recovers its original-truth tails after re-minting, the irreversibility warning is overstated.
|
||||
|
||||
### 2.6 Layer-1 falsifiers, collected
|
||||
|
||||
The model is built to be *able to kill the thesis*. If E2 shows no threshold, or E4 shows no decorrelation benefit, or E6 shows no lock-in, the corresponding claims are refuted and the paper must say so. A blueprint that cannot fail is not a test. The single load-bearing positive result is E2's phase boundary at $g^\* \ll 1$: it says a little grounding protects a lot of inheritance, which is the whole economic and conceptual bet of the architecture.
|
||||
|
||||
### 2.7 Implementation spec for Layer 1
|
||||
|
||||
**Language / libraries.** Python ≥ 3.11; NumPy, SciPy (stats), pandas (results), matplotlib (figures). No GPU. No other heavy deps. Everything seedable from a single integer.
|
||||
|
||||
**Core module interfaces** (the coding agent should implement to these signatures; names are normative so downstream scripts are stable):
|
||||
|
||||
```python
|
||||
# knowledge/truth.py
|
||||
def make_true_distribution(K: int, R: int, tail: str, tail_frac: float,
|
||||
zipf_s: float, seed: int) -> TrueDist:
|
||||
"""Return p_star (length K), region assignment (length K), and the tail mask."""
|
||||
|
||||
# knowledge/teachers.py
|
||||
def make_retention_matrix(T: int, K_T: int, rho: float, q: float, rng) -> np.ndarray:
|
||||
"""Return an (K_T, T) binary retention matrix R with exact marginal retention
|
||||
E[R]=q and exact pairwise column-correlation rho, via the shared-switch
|
||||
construction of §2.7.1. rho=0 -> independent tails; rho=1 -> identical."""
|
||||
|
||||
def make_correlated_teachers(p_star, tail_mask, K_T: int, rho: float, q: float,
|
||||
region_assignment=None, region_specialisation=False,
|
||||
tail_floor: float = 1e-9, seed: int = 0) -> list[np.ndarray]:
|
||||
"""Build K_T teacher distributions from a retention matrix (§2.7.1): every teacher
|
||||
keeps all head items; teacher k keeps tail item j at ~p_star mass iff R[k,j]=1,
|
||||
else at tail_floor; renormalise. If region_specialisation, force R[k,j]=1 for tail
|
||||
items in teacher k's home region and apply the rho construction only off-home.
|
||||
The exact-construction path is preferred for E4; a drift-based path (running
|
||||
independent grounded lineages) is provided as a realism cross-check only."""
|
||||
|
||||
# knowledge/step.py
|
||||
def generation_step(teachers, p_star_eff, cfg, rng) -> np.ndarray: ...
|
||||
def apply_selection(p, p_star, mode: str, alpha: float) -> np.ndarray: ...
|
||||
def structured_multinomial(m_vector, p_star, regions, policy: str, rng) -> np.ndarray: ...
|
||||
|
||||
# knowledge/lineage.py
|
||||
def run_lineage(cfg, seed) -> pd.DataFrame:
|
||||
"""Run T generations for one seed; return a tidy frame with one row per
|
||||
(generation) and columns for every metric in §2.3 (global and per-region)."""
|
||||
|
||||
# knowledge/metrics.py
|
||||
def forward_kl(p_star, p, eps): ...
|
||||
def heterozygosity(p): ...
|
||||
def tail_mass(p, tail_mask): ...
|
||||
def support_size(p, eps): ...
|
||||
|
||||
# knowledge/experiment.py
|
||||
def run_experiment(cfg) -> pd.DataFrame:
|
||||
"""Sweep the declared parameter grid x n_replicates seeds; return long-form
|
||||
results with confidence intervals; write parquet + the exact resolved config."""
|
||||
```
|
||||
|
||||
**Config schema** (one YAML per experiment; all parameters explicit, no magic numbers in code). Illustrative default:
|
||||
|
||||
```yaml
|
||||
experiment: E2_grounding_phase_boundary
|
||||
seed: 20260704
|
||||
n_replicates: 100
|
||||
generations: 300
|
||||
truth:
|
||||
K: 1000 # number of knowledge items
|
||||
R: 10 # regions
|
||||
tail: zipf # {zipf, twocomponent}
|
||||
zipf_s: 1.1
|
||||
tail_frac: 0.5 # fraction of items designated 'tail'
|
||||
tail_threshold: 1.0e-3
|
||||
dynamics:
|
||||
n: 200 # distillation sample size (drift strength)
|
||||
teachers:
|
||||
K_T: 1
|
||||
rho: 0.0
|
||||
grounding:
|
||||
sweep: {param: g, values: [0.0, 0.01, 0.02, 0.05, 0.1, 0.2, 0.4]}
|
||||
policy: uniform # {uniform, matched}
|
||||
selection:
|
||||
mode: none # {none, greedy, qd}
|
||||
novelty_alpha: 0.0
|
||||
remint:
|
||||
enabled: false
|
||||
period: null
|
||||
H_gate: null
|
||||
metrics:
|
||||
kl_floor: 1.0e-9
|
||||
output:
|
||||
dir: results/fig2_grounding_sweep/
|
||||
save_per_generation: true
|
||||
```
|
||||
|
||||
**Determinism.** One master seed → per-replicate seeds via a documented `np.random.SeedSequence` spawn. No global RNG state; pass `rng` explicitly everywhere. Results are a pure function of the resolved config. The resolved config (after sweep expansion) is written next to the results artifact.
|
||||
|
||||
**Outputs.** Each experiment writes: `results.parquet` (long form), `resolved_config.yaml`, and a `manifest.json` recording library versions, seed, git commit, and a content hash of the results. Figures are generated by a separate `figures/plot_EX.py` reading only `results.parquet`, so any figure is regenerable from committed data without rerunning the simulation.
|
||||
|
||||
#### 2.7.1 The correlated-teacher construction (E4's one non-obvious piece)
|
||||
|
||||
E4 needs teacher sets whose pairwise **retention-correlation** $\rho$ is a clean, swept knob. Tuning the drift parameters until an emergent $\rho$ appears is the wrong design: that $\rho$ would be a tangled function of $n$, $m$, tail size and generation count, un-sweepable and confounded with the very drift whose effect E4 is trying to hold fixed. So we **construct the retention structure directly**, with $\rho$ an independent control. For an experiment whose entire purpose is to isolate the effect of decorrelation, $\rho$ must be manipulated, not inferred.
|
||||
|
||||
**The mechanism — shared-switch exchangeable Bernoulli.** Let the tail have $T$ items. Each teacher $k$ retains a fraction $q$ of them; we want the retention indicators to have marginal $q$ and *exact* pairwise correlation $\rho$ across teachers. For each tail item $j$:
|
||||
|
||||
1. draw a **shared switch** $z_j \sim \mathrm{Bernoulli}(\rho)$ (one draw, common to all teachers for item $j$);
|
||||
2. draw a **shared retention** $s_j \sim \mathrm{Bernoulli}(q)$ (common to all teachers);
|
||||
3. draw **independent retentions** $u^{(k)}_j \sim \mathrm{Bernoulli}(q)$, one per teacher;
|
||||
4. set $r^{(k)}_j = s_j$ if $z_j = 1$, else $u^{(k)}_j$.
|
||||
|
||||
That is the whole construction. It yields a retention matrix $R \in \{0,1\}^{K_T \times T}$.
|
||||
|
||||
**Why it is exact.** Marginally $\mathbb{E}[r^{(k)}_j] = \rho q + (1-\rho)q = q$ regardless of $\rho$. For any two teachers, conditioning on the switch gives $\mathbb{E}[r^{(k)}_j r^{(k')}_j] = \rho\,\mathbb{E}[s_j^2] + (1-\rho)q^2 = \rho q + (1-\rho)q^2$ (using $s_j^2 = s_j$), so $\mathrm{Cov} = \rho q(1-q)$ and, since $\mathrm{Var} = q(1-q)$, the pairwise correlation is exactly $\rho$. The set is *exchangeable* — every teacher pair has the same $\rho$ — which is what makes $\rho$ a single scalar knob. (Verified numerically: marginal and pairwise correlation hit target across a $(\rho, q)$ grid, and the union closed form below matches to three decimals.)
|
||||
|
||||
**From retention to teacher distributions.** Given $R$, build teacher $k$'s distribution $p^{(k)}$: assign every **head** item its $p^\*$ mass (all teachers keep the common core); assign **tail** item $j$ its $p^\*_j$ mass if $r^{(k)}_j = 1$ and a floor $\varepsilon_{\text{tail}}$ otherwise; renormalise. (Renormalising lets the mass of dropped tails flow to what the teacher kept — the realistic signature of a partially-collapsed model concentrating on its survivors. Reallocating instead to the head is a documented config switch.)
|
||||
|
||||
**Region specialisation (structured decorrelation, optional).** With `region_specialisation=True`, give each teacher a **home region** and force $r^{(k)}_j = 1$ for every tail item $j$ in teacher $k$'s home region (each teacher fully retains the tails of the region it ground against reality), applying the $\rho$ construction only to off-home tail items. This models "each teacher ground a different region," ties E4 to E3's region-matched grounding, and is the discrete image of the perspective paper's "distil from teachers who each earned a different region."
|
||||
|
||||
**The analytic target (E4's exact check).** The probability that tail item $j$ is retained by at least one of $K_T$ teachers is $\rho q + (1-\rho)\big(1-(1-q)^{K_T}\big)$, so the expected **union tail-coverage** is
|
||||
$$U(K_T,\rho,q) = T\left[\rho q + (1-\rho)\left(1-(1-q)^{K_T}\right)\right],$$
|
||||
the closed form of §2.4-5. `make_retention_matrix` must reproduce it (and the target $\rho$, $q$) within Monte-Carlo tolerance in `test_scientific_validation.py`. The pupil's *realised* coverage after distillation equals $U$ only for tail items whose mixture mass clears the drift-survival threshold $\sim 1/n$ (§2.4-4) — so E4 should report both the union coverage (construction-level) and the post-distillation surviving coverage (dynamics-level), and their gap is itself informative: it is exactly the tail that recombination *supplied* but drift *re-erased* because grounding was too thin to hold it.
|
||||
|
||||
**Continuous-mass extension (optional realism, not a headline).** Binary retention is the default because it matches prediction 5 exactly. For a realism cross-check, replace binary retention with correlated *masses*: draw per-teacher log-masses on tail items from a multivariate normal with equicorrelation $\rho$ (a Gaussian copula), exponentiate, and normalise. This generalises to an arbitrary correlation *matrix* between teachers (unequal pairwise $\rho$), which the shared-switch construction — being exchangeable — cannot express; use it only if the paper later needs non-exchangeable teacher sets.
|
||||
|
||||
**Optional abstract treatment of the horizontal claim (§2.7-H, low priority).** If time permits, model a domain as a modular graph with tunable modularity $Q$; define the optimal number of concurrent specialists as the point where marginal coverage gain from an added specialist falls below a cost; show optimal specialist count rises with $Q$. This is the *horizontal* prediction in abstract form and does not require the neural layer. Flag clearly as exploratory; it is not a headline and can be dropped without weakening the paper.
|
||||
|
||||
---
|
||||
|
||||
## 3. Layer 2 — the neural existence proof
|
||||
|
||||
### 3.1 Purpose and the single objection it answers
|
||||
|
||||
Layer 1 assumes the tail-deletion operator (drift). A reviewer will say: *you built your conclusion into the operator.* Layer 2 answers exactly that objection and no more. It does not need to be a society. It needs to show, in **real LoRA-adapted weights**, that the *sign* of three effects is as Layer 1 predicts: dry inheritance degrades, grounded inheritance holds; multiple decorrelated teachers preserve capability that one teacher sheds; and across generations general capability holds or climbs while each specialty is re-earned and exceeded. If those three signs appear at 1B scale on one GPU, the abstraction in Layer 1 is grounded in mechanism.
|
||||
|
||||
Minimality is a virtue here, not a compromise. Every additional degree of freedom (bigger model, more generations, more domains) multiplies cost and reviewer surface without strengthening the core claim. Build the smallest thing that can show the signs.
|
||||
|
||||
### 3.2 Design choices (with open-science defaults)
|
||||
|
||||
**Base model.** Default to a *fully open* small model to honour reproducibility end-to-end: **OLMo-2-1B** or **SmolLM2-1.7B** (open weights, open or well-documented data, permissive licence). Capable fallback if the open models are too weak on the task: **Qwen2.5-1.5B-Instruct**. Pin the exact Hugging Face revision hash in config; never track `main`. The pipeline must be model-agnostic behind a thin adapter so swapping bases is a config change.
|
||||
|
||||
**Specialisation.** LoRA (via PEFT), small rank (e.g. 8–16), on a single task family = one "region." Hours on one consumer GPU, consistent with the perspective paper's cost claim. Each teacher is one base + one LoRA adapter.
|
||||
|
||||
**The verifier = "reality's no."** The domain must have a cheap, deterministic, uncontrollable oracle. **Program synthesis with unit tests** is ideal: a generated solution either passes its tests or it does not, and neither the model nor the experimenter controls the verdict. This is the minimal honest instance of the perspective paper's "predictive success under intervention." Execution happens in a sandbox (subprocess with a hard timeout and no network, run inside the container of §4; document the sandbox precisely).
|
||||
|
||||
**Task domain — synthetic-primary, benchmark-secondary.** To keep the Layer-1 abstractions (region, rarity, tail) exact, the *primary* domain is a **synthetic program-synthesis generator**: a family of small, verifiable tasks parameterised by *operation type* (the region: e.g. string ops, list ops, arithmetic, dict manipulation, recursion) and *difficulty*, with I/O unit tests generated automatically. Task-type frequency is tunable, so "rare tail task types" is a dial, exactly matching Layer 1's rarity. For *external validity*, add a secondary evaluation on a held-out slice of a public benchmark (e.g. MBPP-sanitised / HumanEval) — pinned by version — to show the effect is not an artefact of the synthetic generator. The synthetic generator's spec (grammar, per-region templates, test-generation rule, rarity distribution) is itself a committed, seeded artifact.
|
||||
|
||||
**Grounding, concretely.** A generational passage produces pupil training data as a mixture of (i) *inherited* teacher-generated solutions and (ii) *grounded* solutions that have been **filtered to pass the verifier** and/or freshly drawn from verified references in the target region. The **grounding fraction $g$** is the proportion of verifier-passed/real items in the pupil's training mixture — the *same knob* as Layer 1's $g$. "Dry" = $g$ low / unfiltered teacher output; "grounded" = $g$ raised with region-matched verified data.
|
||||
|
||||
**Recombination, concretely.** Multiple teachers = multiple LoRA specialists on *disjoint* task families (decorrelated by construction). The pupil is trained on the pooled outputs of all teachers (distillation) or, as a cheaper alternative, the specialists are **merged** (M2N2 / model-merge style, citing Sakana's demonstration that this search runs with no retraining) and the merged model is the pupil. Distillation and merging are two config-selectable recombination operators; report at least distillation, and merging if compute allows.
|
||||
|
||||
### 3.3 Contrasts C1–C4 (the whole experimental content)
|
||||
|
||||
**C1 — Dry vs. grounded, single teacher, across generations.** One teacher, one region. Arm A: pupil trained on *unfiltered* teacher outputs (dry, $g\approx0$). Arm B: pupil trained on *verifier-passed* teacher outputs plus fresh verified region data ($g>0$). Run 2–3 generations. *Expect:* Arm A pass@k degrades generation over generation and its solution diversity narrows; Arm B holds. *Maps to:* Layer-1 E2. *Falsifier:* if dry inheritance does not degrade at this scale, collapse is not reachable here and the neural claim is unsupported (report honestly; possibly scale down grounding or up generations).
|
||||
|
||||
**C2 — One teacher vs. N complementary teachers, matched data budget.** Fix the pupil's total training-token budget. Arm A: all budget from one teacher (one region). Arm B: same budget split across $N$ teachers on disjoint regions. Evaluate the pupil on *all* regions, including rare-type tasks. *Expect:* Arm B retains capability across the union of regions (the "tail" of rare task types survives); Arm A loses regions it did not inherit. *Maps to:* Layer-1 E4. *Falsifier:* no union benefit at matched budget → recombination claim unsupported neurally.
|
||||
|
||||
**C3 — The vertical claim (load-bearing).** Over 2–3 generations, track (a) a *general* held-out benchmark spanning all regions and (b) *per-specialty* performance, where each generation re-specialises (re-earns) its region against the verifier. *Expect:* general benchmark is **monotonically non-decreasing** across generations, while each specialty is re-earned and its peak **exceeds the parent's** peak in that specialty. *This is the test of the actual thesis, not the borrowed Shumailov scaffolding.* *Maps to:* the paper's vertical prediction. *Falsifier:* if general capability falls across generations, or specialties are not re-earned-and-exceeded, the multigenerational ratchet is not demonstrated.
|
||||
|
||||
**C4 — Recombination operator: distillation vs. merging (optional).** If compute allows, show C2's benefit is robust to whether recombination is done by distillation or by weight-merging. Strengthens generality and directly connects to the M2N2 citation. Drop first if time-constrained.
|
||||
|
||||
### 3.4 Metrics (Layer 2)
|
||||
|
||||
- **pass@1 and pass@k** on held-out tasks, per region and overall (the neural analogue of KL-to-truth / capability).
|
||||
- **Region coverage** = fraction of regions (incl. rare task types) with pass@1 above a floor — the neural analogue of *support size* / tail survival.
|
||||
- **Solution diversity** = distinct-$n$ or behavioural diversity of generated solutions per task (the neural analogue of heterozygosity $H$; narrowing diversity is the neural signature of collapse).
|
||||
- **Generational degradation curve** = each metric as a function of generation index, per arm.
|
||||
|
||||
All with multiple seeds (fewer than Layer 1 — GPU cost — but at least 3; report per-seed points, not just means, given small $n$). Pin decoding parameters (temperature, top-p, max tokens, sampling seed) in config; they materially affect pass@k and must not float.
|
||||
|
||||
### 3.5 Layer-2 honesty riders
|
||||
|
||||
GPU non-determinism means Layer 2 is *statistically* reproducible (same distribution of outcomes under re-run), not bitwise reproducible. Document this explicitly; pin everything pinnable (model revision, dataset version, decoding params, library versions, seeds); report seeds individually. The claim Layer 2 supports is directional ("the sign of the effect is as predicted"), and the writing must not overclaim precision the setup cannot deliver.
|
||||
|
||||
### 3.6 Implementation spec for Layer 2
|
||||
|
||||
**Libraries.** PyTorch; Hugging Face `transformers` + `peft` (LoRA); `datasets`; optional `vllm` for fast generation; the synthetic task generator (project-local). Execution sandbox: `subprocess` with `resource` limits and timeout, inside the container.
|
||||
|
||||
**Module interfaces (normative names):**
|
||||
|
||||
```python
|
||||
# neural/tasks.py
|
||||
def generate_task_bank(regions, rarity, n_tasks, seed) -> TaskBank:
|
||||
"""Synthetic verifiable tasks; each task carries prompt, region, difficulty,
|
||||
and an executable unit-test suite."""
|
||||
def verify(solution_code: str, task) -> VerifyResult:
|
||||
"""Run tests in a sandbox; return pass/fail + diagnostics. Deterministic."""
|
||||
|
||||
# neural/specialise.py
|
||||
def train_lora_specialist(base_id, revision, region, task_bank, lora_cfg, seed) -> AdapterPath: ...
|
||||
|
||||
# neural/distill.py
|
||||
def generate_teacher_data(teachers, task_bank, grounding_fraction, policy, decode_cfg, seed) -> Corpus:
|
||||
"""Produce the pupil's training corpus: mixture of inherited (teacher) and
|
||||
grounded (verifier-passed / fresh-verified) items, region-matched."""
|
||||
def train_pupil(base_id, revision, corpus, lora_cfg, seed) -> AdapterPath: ...
|
||||
|
||||
# neural/merge.py
|
||||
def merge_specialists(base_id, adapters, method, seed) -> ModelPath: # optional (C4)
|
||||
|
||||
# neural/evaluate.py
|
||||
def evaluate(model, task_bank_heldout, decode_cfg, seed) -> pd.DataFrame:
|
||||
"""pass@k, per-region coverage, solution diversity; tidy per-(region) frame."""
|
||||
|
||||
# neural/generation_loop.py
|
||||
def run_generations(cfg, seed) -> pd.DataFrame:
|
||||
"""Orchestrate T generations for one arm; log every metric per generation."""
|
||||
```
|
||||
|
||||
**Config** mirrors Layer 1's structure (one YAML per contrast; pinned `base_id` + `revision`; explicit `grounding_fraction`, `n_teachers`, `regions`, `generations`, `decode_cfg`, `lora_cfg`, `seed`, `n_seeds`). Same output contract: `results.parquet` + `resolved_config.yaml` + `manifest.json` (with model revision hashes and dataset versions). Figures regenerable from `results.parquet` alone.
|
||||
|
||||
---
|
||||
|
||||
## 4. Reproducibility and engineering standard (both layers)
|
||||
|
||||
Open science is a hard requirement of this project, not a preference. The standard below is normative.
|
||||
|
||||
**Environment.** Pin everything. Provide (a) a `pyproject.toml` + lockfile via **uv** (fast, reproducible resolver) and (b) an **Apptainer/Singularity** definition file (HPC-friendly, rootless, open) that builds the exact environment; optionally a Dockerfile. The container is the source of truth for "it runs." Record Python, CUDA, and key library versions in every run's `manifest.json`.
|
||||
|
||||
**Seeding.** One master seed per experiment in config; derive all sub-seeds via `SeedSequence.spawn`; never touch global RNG state. Layer 1 is bitwise-reproducible from seed. Layer 2 is statistically reproducible; document the residual GPU non-determinism and set the available determinism flags (`torch.use_deterministic_algorithms(True)` where feasible, cudnn deterministic, documented exceptions).
|
||||
|
||||
**Configuration.** No magic numbers in code — every parameter lives in a YAML resolved at run time; the *resolved* config is written beside results. Use a single config system (Hydra or a thin equivalent). Sweeps are declared in config, not hard-coded in scripts.
|
||||
|
||||
**Data & model provenance.** Layer 1 data is synthetic-from-seed (fully reproducible; no external data). Layer 2 pins model revision hashes and dataset versions; the synthetic task generator is committed and seeded. Cache external downloads with recorded hashes.
|
||||
|
||||
**Experiment tracking.** Prefer open tooling: **MLflow** (open source) or plain versioned CSV/Parquet + committed configs; avoid closed SaaS trackers to keep the pipeline fully open. Whatever is chosen, the invariant is: every figure is a pure function of a committed results artifact.
|
||||
|
||||
**Testing.** `pytest`. Two kinds of test, and both are required:
|
||||
- *Correctness tests*: the module does what it says (shapes, normalisation, sandbox isolation).
|
||||
- *Scientific validation tests*: the simulator reproduces the §2.4 analytic results within tolerance (heterozygosity decay, fixation probability, mutation–drift equilibrium). These tests failing means the science is wrong, not just the code — they are the spine of trust in Layer 1.
|
||||
|
||||
**Automation.** A `Makefile` (or `justfile`) with targets: `env`, `test`, `layer1` (runs E1–E6), `layer2` (runs C1–C3, C4 optional), `figures`, `paper` (assembles the figure manifest), `all`, `clean`. One command reproduces the study from a clean checkout inside the container.
|
||||
|
||||
**Repro entry point.** A top-level `reproduce.sh` that: builds/enters the container, runs tests, runs all experiments at the committed seeds, regenerates all figures, and writes a `REPRODUCED.md` diff against committed result hashes. If hashes match (Layer 1) / distributions match within CI (Layer 2), the run is verified.
|
||||
|
||||
**Licensing & citation.** Author to choose; suggested: code under a permissive OSI licence (MIT/Apache-2.0) or copyleft (GPL-3.0) per the author's open-source preference; text/figures under CC-BY. Include `LICENSE`, `CITATION.cff`, and a `DATA_AND_MODELS.md` recording every external artifact and its pinned version/hash.
|
||||
|
||||
---
|
||||
|
||||
## 5. Repository layout
|
||||
|
||||
```
|
||||
lamarckian-society/
|
||||
├── README.md # what this is, how to reproduce
|
||||
├── reproduce.sh # one-command full reproduction (in-container)
|
||||
├── Makefile # env, test, layer1, layer2, figures, all
|
||||
├── pyproject.toml # deps
|
||||
├── uv.lock # pinned resolution
|
||||
├── apptainer.def # container definition (source of truth)
|
||||
├── Dockerfile # optional
|
||||
├── LICENSE CITATION.cff DATA_AND_MODELS.md
|
||||
├── configs/
|
||||
│ ├── layer1/E1..E6.yaml
|
||||
│ └── layer2/C1..C4.yaml
|
||||
├── src/
|
||||
│ ├── knowledge/ # Layer 1: truth, teachers, step, lineage, metrics, experiment
|
||||
│ └── neural/ # Layer 2: tasks, specialise, distill, merge, evaluate, generation_loop
|
||||
├── figures/ # plot_EX.py / plot_CX.py — read results.parquet only
|
||||
├── results/ # written artifacts (gitignored, hashes tracked)
|
||||
├── tests/
|
||||
│ ├── test_correctness.py
|
||||
│ └── test_scientific_validation.py # §2.4 analytic checks
|
||||
└── paper/
|
||||
├── blueprint.md # this document
|
||||
└── figure_manifest.md # claim -> experiment -> figure
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## 6. Traceability: claim → experiment → figure
|
||||
|
||||
Every claim the technical paper will make is bound to exactly one experiment and one figure. This table is the paper's spine and the coding agent's definition of done.
|
||||
|
||||
| Perspective-paper claim | Layer | Experiment | Primary figure | Analytic check | Falsifier |
|
||||
|---|---|---|---|---|---|
|
||||
| Distillation without grounding collapses, tail first, at rate set by $n$ | 1 | E1 | $H_t$ decay + tail mass vs. gen | Pred. 1–2 | harness invalid if decay ≠ analytic |
|
||||
| A critical grounding ratio $g^\*$ separates ratchet from collapse | 1 | E2 | tail mass / $H$ stationary vs. $g$ | Pred. 3 | flat in $g$, or only stable at $g\to1$ |
|
||||
| Grounding must be region-matched, not merely present | 1 | E3 | target-region tail: uniform vs. matched | Pred. 4 | uniform protects as well as matched |
|
||||
| Multi-teacher distillation suppresses collapse ∝ decorrelation | 1 | E4 | tail coverage surface over $(K_T,\rho)$ | Pred. 5 (closed form $U(K_T,\rho,q)$) | no benefit at matched budget |
|
||||
| QD selection maintains diversity where greedy fixes it | 1 | E5 | $H$ plateau: qd vs. greedy | (mutation-selection-drift) | qd ≤ greedy in stationary $H$ |
|
||||
| Re-minting is irreversible; gate on diversity | 1 | E6 | KL-to-original vs. $H$-at-remint | — | collapsed lineage recovers after remint |
|
||||
| Dry inheritance degrades in real weights; grounded holds | 2 | C1 | pass@k vs. gen, dry vs. grounded | — | dry does not degrade |
|
||||
| Complementary teachers preserve capability one teacher sheds | 2 | C2 | region coverage, 1 vs. N, matched budget | — | no union benefit |
|
||||
| **General knowledge climbs while each specialty is re-earned and exceeded** | 2 | C3 | general benchmark ↑ + per-specialty re-earn | — | general falls / no re-earn |
|
||||
| Recombination benefit robust to distillation vs. merging | 2 | C4 (opt) | C2 metric under both operators | — | benefit only under one operator |
|
||||
|
||||
---
|
||||
|
||||
## 7. Suggested build order for the coding agent
|
||||
|
||||
Staged so that each step is independently testable and the cheapest, highest-value results land first. Do not start Layer 2 until Layer 1's scientific-validation tests pass.
|
||||
|
||||
1. **Scaffold + environment.** Repo layout (§5), container (§4), `pytest` skeleton, config system, seeding utilities. Target `make test` green on trivial tests.
|
||||
2. **Layer 1 core + validation.** `knowledge/` modules to the §2.7 interfaces. Implement the null model first. Write and pass `test_scientific_validation.py` against §2.4 predictions 1–2. **Gate: do not proceed until drift matches analytic decay.**
|
||||
3. **Layer 1 mechanisms + E1–E2.** Add grounding; validate mutation–drift equilibrium (pred. 3); run E1 and the E2 phase-boundary sweep; produce the headline figure. This is the paper's core result and it should exist before anything neural.
|
||||
4. **Layer 1 E3–E6.** Region-matching, multi-teacher/decorrelation, QD-vs-greedy, re-minting gate, with figures. Layer 1 is now a complete, laptop-reproducible paper on its own.
|
||||
5. **Layer 2 scaffold + verifier.** Synthetic task generator, sandboxed `verify`, evaluation harness. Test the verifier's determinism and isolation before any training.
|
||||
6. **Layer 2 C1 + C3.** Single-teacher dry-vs-grounded (C1) and the vertical claim (C3) — the two that most directly test the thesis. C3 is load-bearing; prioritise it.
|
||||
7. **Layer 2 C2 (+ C4 if compute allows).** Multi-teacher recombination; optional merging operator.
|
||||
8. **Reproduction pass.** `reproduce.sh` end-to-end; commit result hashes; write `REPRODUCED.md`; assemble the figure manifest.
|
||||
|
||||
**Definition of done:** every row of §6 has a committed figure produced by `make figures` from committed results, every §2.4 analytic check passes in CI, and `reproduce.sh` verifies from a clean checkout inside the container.
|
||||
|
||||
---
|
||||
|
||||
*End of blueprint v1. The perspective paper states the idea; this document states the test. If Layer 1's E2 finds no threshold, or E4 no decorrelation benefit, or Layer 2's C3 no vertical climb, the thesis is wrong in exactly the places these experiments probe — which is the point of writing them down this precisely.*
|
||||
|
|
@ -1,291 +0,0 @@
|
|||
"""Build a Zotero-importable library from the manuscript's reference list.
|
||||
|
||||
For each of the numbered references in paper/manuscript/main.md: take the DOI printed in the entry when
|
||||
there is one, otherwise ask Crossref for it by title (accepting only a high-scoring match whose title
|
||||
really is the same, checked by normalised comparison). Then fetch authoritative metadata for every
|
||||
resolved DOI by content negotiation against doi.org, which serves Crossref and DataCite alike, and
|
||||
write the result as CSL-JSON plus RIS.
|
||||
|
||||
Entries whose DOI cannot be resolved (pre-DOI literature, books, chapters) are reported and written
|
||||
from the manuscript's own metadata so nothing is silently dropped.
|
||||
|
||||
Usage: python paper/manuscript/build_zotero_library.py
|
||||
"""
|
||||
|
||||
from __future__ import annotations
|
||||
|
||||
import json
|
||||
import re
|
||||
import sys
|
||||
import time
|
||||
import urllib.parse
|
||||
import urllib.request
|
||||
from pathlib import Path
|
||||
|
||||
MAIN = Path(__file__).resolve().parent / "main.md"
|
||||
OUT = Path(__file__).resolve().parent / "refs"
|
||||
MAILTO = "g.gilestro@imperial.ac.uk" # Crossref polite pool
|
||||
UA = f"LamarckianAI-refs/1.0 (mailto:{MAILTO})"
|
||||
|
||||
# Reference numbers whose sources predate DOIs or are books/chapters: never send these to Crossref
|
||||
# title search, because it returns confident nonsense for them.
|
||||
NO_DOI_EXPECTED = {33, 35, 39} # Jenkin 1867; Fisher 1930 (book); Templeton 1986 (chapter)
|
||||
|
||||
# DOIs the title search could not find and that were verified by hand against the publisher record.
|
||||
DOI_OVERRIDE = {
|
||||
17: "10.1038/s41562-023-01742-2", # Brinkmann et al., Machine culture (Nat. Hum. Behav.)
|
||||
64: "10.48550/arXiv.1805.06370", # Schwarz et al., Progress & Compress (no Crossref DOI)
|
||||
}
|
||||
|
||||
# The three genuinely pre-DOI sources, written out rather than parsed, so the Zotero records are
|
||||
# complete instead of merely non-empty.
|
||||
HAND_WRITTEN = {
|
||||
33: {"type": "article-journal", "title": "[Review of] The Origin of Species",
|
||||
"author": [{"given": "Fleeming", "family": "Jenkin"}],
|
||||
"container-title": "The North British Review", "volume": "46", "page": "277-318",
|
||||
"issued": {"date-parts": [[1867]]}},
|
||||
35: {"type": "book", "title": "The Genetical Theory of Natural Selection",
|
||||
"author": [{"given": "Ronald A.", "family": "Fisher"}],
|
||||
"publisher": "Clarendon Press", "publisher-place": "Oxford",
|
||||
"issued": {"date-parts": [[1930]]}},
|
||||
39: {"type": "chapter", "title": "Coadaptation and outbreeding depression",
|
||||
"author": [{"given": "Alan R.", "family": "Templeton"}],
|
||||
"editor": [{"given": "Michael E.", "family": "Soulé"}],
|
||||
"container-title": "Conservation Biology: The Science of Scarcity and Diversity",
|
||||
"publisher": "Sinauer Associates", "publisher-place": "Sunderland, MA",
|
||||
"page": "105-116", "issued": {"date-parts": [[1986]]}},
|
||||
}
|
||||
|
||||
|
||||
def get(url: str, accept: str | None = None, tries: int = 3) -> bytes | None:
|
||||
req = urllib.request.Request(url, headers={"User-Agent": UA})
|
||||
if accept:
|
||||
req.add_header("Accept", accept)
|
||||
for i in range(tries):
|
||||
try:
|
||||
with urllib.request.urlopen(req, timeout=30) as r:
|
||||
return r.read()
|
||||
except Exception as e: # noqa: BLE001
|
||||
if i == tries - 1:
|
||||
print(f" ! {type(e).__name__}: {str(e)[:80]}", file=sys.stderr)
|
||||
time.sleep(1.5 * (i + 1))
|
||||
return None
|
||||
|
||||
|
||||
def parse_refs() -> list[tuple[int, str]]:
|
||||
refs = MAIN.read_text().split("## References")[1]
|
||||
out = []
|
||||
for line in refs.splitlines():
|
||||
if m := re.match(r"^(\d+)\. (.*)$", line):
|
||||
out.append((int(m.group(1)), m.group(2).strip()))
|
||||
return out
|
||||
|
||||
|
||||
def strip_md(s: str) -> str:
|
||||
return re.sub(r"[*_`]", "", s)
|
||||
|
||||
|
||||
def guess_title(entry: str) -> str:
|
||||
"""The title is the run of text between the author list and the italic venue or the year."""
|
||||
t = strip_md(entry)
|
||||
t = re.sub(r"\s*https?://\S+$", "", t).strip()
|
||||
# drop the leading author list: everything up to the last ", " before the title is unreliable,
|
||||
# so instead cut after the first ", " that follows an initial-style name block
|
||||
m = re.match(r"^((?:[A-ZÀ-Þ]\.\s*)+[^,]+,\s*)+", t)
|
||||
rest = t[m.end():] if m else t
|
||||
rest = re.sub(r"^et al\.,\s*", "", rest)
|
||||
# the title ends at the venue (". *Venue*") or at " arXiv [Preprint]" or " (Year)"
|
||||
rest = re.split(r"\.\s+(?:arXiv \[Preprint\]|[A-Z][a-zA-Z.\s&]*\*|Proc\.|Int\.|Adv\.|Conf\.|Nat\.|Trans\.)", rest)[0]
|
||||
rest = re.split(r"\s*\(\d{4}\)", rest)[0]
|
||||
return rest.strip(" .,")
|
||||
|
||||
|
||||
def norm(s: str) -> str:
|
||||
return re.sub(r"[^a-z0-9]", "", s.lower())
|
||||
|
||||
|
||||
def crossref_by_title(title: str, year: str | None) -> tuple[str | None, str]:
|
||||
q = urllib.parse.urlencode({"query.bibliographic": title, "rows": 5, "mailto": MAILTO})
|
||||
raw = get(f"https://api.crossref.org/works?{q}")
|
||||
if not raw:
|
||||
return None, "crossref unreachable"
|
||||
items = json.loads(raw).get("message", {}).get("items", [])
|
||||
tn = norm(title)
|
||||
for it in items:
|
||||
cand = (it.get("title") or [""])[0]
|
||||
cn = norm(cand)
|
||||
if not cn:
|
||||
continue
|
||||
# accept only a genuine title match, not merely a high Crossref score
|
||||
if cn.startswith(tn[:60]) or tn.startswith(cn[:60]):
|
||||
return it.get("DOI"), f"matched: {cand[:70]}"
|
||||
return None, f"no title match (best: {(items[0].get('title') or [''])[0][:60] if items else '-'})"
|
||||
|
||||
|
||||
def csl_from_doi(doi: str) -> dict | None:
|
||||
raw = get(f"https://doi.org/{urllib.parse.quote(doi)}",
|
||||
accept="application/vnd.citationstyles.csl+json")
|
||||
if not raw:
|
||||
return None
|
||||
try:
|
||||
return json.loads(raw)
|
||||
except json.JSONDecodeError:
|
||||
return None
|
||||
|
||||
|
||||
# ---------------------------------------------------------------- fallback CSL from the manuscript
|
||||
def manual_csl(num: int, entry: str) -> dict:
|
||||
t = strip_md(entry)
|
||||
year = (re.search(r"\((\d{4})\)", t) or re.search(r"(\d{4})", t))
|
||||
authors = []
|
||||
m = re.match(r"^((?:[A-ZÀ-Þ]\.(?:\s*[A-ZÀ-Þ]\.)*\s+[^,]+,\s*)+)", t)
|
||||
if m:
|
||||
for name in re.findall(r"([A-ZÀ-Þ]\.(?:\s*[A-ZÀ-Þ]\.)*)\s+([^,]+)", m.group(1)):
|
||||
authors.append({"given": name[0].strip(), "family": name[1].strip()})
|
||||
venue = re.search(r"\*([^*]+)\*", entry)
|
||||
vol = re.search(r"\*\*(\d+)\*\*", entry)
|
||||
pages = re.search(r"\*\*\d+\*\*,\s*([\d–\-]+)", entry)
|
||||
return {k: v for k, v in {
|
||||
"id": f"ref{num}",
|
||||
"type": "book" if "Press)" in t or "Sinauer" in t else "article-journal",
|
||||
"title": guess_title(entry),
|
||||
"author": authors or None,
|
||||
"container-title": venue.group(1) if venue else None,
|
||||
"volume": vol.group(1) if vol else None,
|
||||
"page": pages.group(1).replace("–", "-") if pages else None,
|
||||
"issued": {"date-parts": [[int(year.group(1))]]} if year else None,
|
||||
"note": f"manuscript reference {num}; no DOI",
|
||||
}.items() if v is not None}
|
||||
|
||||
|
||||
def clean_text(s: str) -> str:
|
||||
"""Publisher abstracts arrive with JATS tags, HTML entities, and hard line breaks; RIS is a
|
||||
line-oriented format, so every field has to end up as one clean line."""
|
||||
import html
|
||||
|
||||
s = re.sub(r"<[^>]+>", " ", s) # JATS/HTML tags
|
||||
s = html.unescape(s)
|
||||
return re.sub(r"\s+", " ", s).strip()
|
||||
|
||||
|
||||
def clean_csl(c: dict) -> dict:
|
||||
for k, v in list(c.items()):
|
||||
if isinstance(v, str):
|
||||
c[k] = clean_text(v)
|
||||
elif isinstance(v, list) and v and isinstance(v[0], str):
|
||||
c[k] = [clean_text(x) for x in v]
|
||||
doi = c.get("DOI", "")
|
||||
if doi.lower().startswith("10.48550/arxiv."):
|
||||
# DataCite returns these uppercased and with no venue; restore the canonical DOI casing and
|
||||
# give Zotero something to show in the publication field instead of a blank.
|
||||
arxiv_id = doi.split(".", 2)[-1]
|
||||
c["DOI"] = f"10.48550/arXiv.{arxiv_id}"
|
||||
c["container-title"] = "arXiv"
|
||||
c["number"] = f"arXiv:{arxiv_id}"
|
||||
c["genre"] = "preprint"
|
||||
return c
|
||||
|
||||
|
||||
# Crossref reports its own type vocabulary alongside real CSL types; map both.
|
||||
CSL2RIS_EXTRA = {"journal-article": "JOUR", "book-chapter": "CHAP", "proceedings-article": "CPAPER",
|
||||
"posted-content": "JOUR", "book-section": "CHAP", "monograph": "BOOK"}
|
||||
|
||||
|
||||
CSL2RIS = {"article-journal": "JOUR", "paper-conference": "CPAPER", "chapter": "CHAP",
|
||||
"book": "BOOK", "article": "JOUR", "posted-content": "JOUR", "report": "RPRT",
|
||||
"dataset": "DATA", "thesis": "THES"}
|
||||
|
||||
|
||||
def ris_type(c: dict) -> str:
|
||||
t = c.get("type", "")
|
||||
return CSL2RIS.get(t) or CSL2RIS_EXTRA.get(t) or "JOUR"
|
||||
|
||||
|
||||
def to_ris(c: dict, num: int) -> str:
|
||||
L = [f"TY - {ris_type(c)}"]
|
||||
for a in c.get("author") or []:
|
||||
fam, giv = a.get("family", ""), a.get("given", "")
|
||||
L.append(f"AU - {fam}, {giv}".rstrip(", ") if fam else f"AU - {a.get('literal', '')}")
|
||||
ttl = c.get("title")
|
||||
if isinstance(ttl, list):
|
||||
ttl = ttl[0]
|
||||
if ttl:
|
||||
L.append(f"TI - {ttl}")
|
||||
ct = c.get("container-title")
|
||||
if isinstance(ct, list):
|
||||
ct = ct[0] if ct else None
|
||||
if ct:
|
||||
L.append(f"{'BT' if ris_type(c) == 'CHAP' else 'T2'} - {ct}")
|
||||
for ed in c.get("editor") or []:
|
||||
L.append(f"A2 - {ed.get('family', '')}, {ed.get('given', '')}".rstrip(", "))
|
||||
if c.get("number"):
|
||||
L.append(f"AN - {c['number']}")
|
||||
if c.get("publisher-place"):
|
||||
L.append(f"CY - {c['publisher-place']}")
|
||||
parts = (c.get("issued") or {}).get("date-parts") or [[]]
|
||||
if parts and parts[0]:
|
||||
L.append(f"PY - {parts[0][0]}")
|
||||
for key, tag in (("volume", "VL"), ("issue", "IS"), ("publisher", "PB"), ("DOI", "DO"),
|
||||
("URL", "UR"), ("abstract", "AB")):
|
||||
if c.get(key):
|
||||
L.append(f"{tag} - {c[key]}")
|
||||
if c.get("page"):
|
||||
pg = str(c["page"]).replace("–", "-").split("-")
|
||||
L.append(f"SP - {pg[0]}")
|
||||
if len(pg) > 1:
|
||||
L.append(f"EP - {pg[-1]}")
|
||||
L.append(f"N1 - {c.get('note') or f'Manuscript reference {num}'}")
|
||||
L.append("ER - \n")
|
||||
return "\n".join(L)
|
||||
|
||||
|
||||
def main() -> int:
|
||||
refs = parse_refs()
|
||||
print(f"{len(refs)} references parsed\n")
|
||||
csls, report = [], []
|
||||
for num, entry in refs:
|
||||
doi = None
|
||||
if num in HAND_WRITTEN:
|
||||
c = dict(HAND_WRITTEN[num], id=f"ref{num}", note=f"Manuscript reference {num}; predates DOIs")
|
||||
csls.append(c)
|
||||
report.append((num, "HAND (pre-DOI source)", c["title"][:64], "written by hand"))
|
||||
print(f" {num:3d} {'HAND (pre-DOI source)':52s} {c['title'][:56]}")
|
||||
continue
|
||||
if num in DOI_OVERRIDE:
|
||||
doi, src = DOI_OVERRIDE[num], "verified by hand"
|
||||
elif m := re.search(r"doi\.org/(10\.\S+?)\.?$", entry):
|
||||
doi = m.group(1)
|
||||
src = "in manuscript"
|
||||
elif num not in NO_DOI_EXPECTED:
|
||||
title = guess_title(entry)
|
||||
yr = re.search(r"\((\d{4})\)", entry)
|
||||
doi, why = crossref_by_title(title, yr.group(1) if yr else None)
|
||||
src = f"crossref ({why})"
|
||||
time.sleep(0.3)
|
||||
else:
|
||||
src = "pre-DOI / book — not searched"
|
||||
|
||||
c = csl_from_doi(doi) if doi else None
|
||||
if c:
|
||||
c["id"] = f"ref{num}"
|
||||
c["note"] = f"Manuscript reference {num}"
|
||||
status = f"OK {doi}"
|
||||
else:
|
||||
c = manual_csl(num, entry)
|
||||
status = f"MANUAL ({src})" if not doi else f"MANUAL (DOI {doi} would not resolve)"
|
||||
csls.append(c)
|
||||
report.append((num, status, (c.get('title') or '')[:64], src))
|
||||
print(f" {num:3d} {status:52s} {(c.get('title') or '')[:56]}")
|
||||
time.sleep(0.2)
|
||||
|
||||
csls = [clean_csl(c) for c in csls]
|
||||
(OUT / "references.json").write_text(json.dumps(csls, indent=1, ensure_ascii=False))
|
||||
(OUT / "references.ris").write_text("".join(to_ris(c, n) for (n, _), c in zip(refs, csls)))
|
||||
ok = sum(1 for _, s, _, _ in report if s.startswith("OK"))
|
||||
print(f"\nresolved from DOI: {ok}/{len(refs)} manual: {len(refs)-ok}")
|
||||
(OUT / "report.txt").write_text("\n".join(f"{n}\t{s}\t{t}\t{src}" for n, s, t, src in report))
|
||||
return 0
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
sys.exit(main())
|
||||
|
|
@ -1,39 +0,0 @@
|
|||
Giorgio F. Gilestro
|
||||
Department of Life Sciences, Imperial College London
|
||||
giorgio@gilest.ro
|
||||
|
||||
[Date]
|
||||
|
||||
Dear Editor,
|
||||
|
||||
Please consider the enclosed manuscript, "The evolution of sex for artificial intelligence: a population-genetic framework for multigenerational model populations", for publication as an Article in *Nature Machine Intelligence*.
|
||||
|
||||
Machine learning has become a population process. Public repositories hold millions of models, most of them fine-tunes, distillations or weight merges of a few ancestors; models learn from the output of earlier models; and merging, now mainstream practice with standard tooling, is described in its own literature with the words crossover, mutation and mate choice. A population whose members inherit from one another, recombine and retransmit is an evolving population in the technical sense, and the branch of biology built for that situation is the population genetics of sexual reproduction. That training on model output is genetic drift, with model collapse as its signature, has been established several times over. This paper takes the next step and develops the mechanisms population genetics offers for sustaining a population against drift (immigration, recombination, selection, population structure), and the point where they fail (reproductive isolation), and tests each of them in a chain from closed forms to trained networks to language models.
|
||||
|
||||
Four measurements are new, and each was chosen because the existing experimental designs could not make it.
|
||||
|
||||
First, a six-generation population of language models in which three lineages each learn a new skill every generation and then choose whether, and with whom, to merge. Merging has been iterated before, in evolutionary pools of fixed parents and in continual streams folded into one model, but never while the lineages were also learning. The population shows that obligate merging collapses once partners hold conflicting conventions (accuracy 0.65 to 0.27), that a merge each lineage may decline, or a fixed early stop, avoids the collapse at no cost against never merging, and that merging with one's own ancestor is safer than merging with a contemporary in every seed. A second curriculum decoupling partner complementarity from generation shows that declines track generation, which corrects an interpretation the first curriculum invited.
|
||||
|
||||
Second, model speciation as a named and tested question. Using the permutation-and-rescaling alignment of Git Re-Basin and REPAIR, the merge barrier between networks is separated into the part alignment removes and the part it cannot. Conflicting label maps leave a residual alignment does not touch, while six times the base training on non-conflicting tasks produces no isolation at all and the strongest rescue-by-merging in the paper, against the expectation that specialisation by itself erodes mergeability.
|
||||
|
||||
Third, a pre-merge predictive test on 39 language-model parent pairs across three decorrelated axes (conflict, compatible overlap, duration). Functional disagreement between parents predicts merge damage out of sample where LoRA-weight cosine and distance do not, in agreement with recent correlational reports. The control that matters is new: on a grid that varies conflict and shared training data together, weight cosine is the best predictor (ρ = 0.60), and adding overlap without conflict collapses it to 0.03. Any weight-geometry predictor validated on such a grid is reading the shared data, which bears on the merge-prediction literature independently of the biology.
|
||||
|
||||
Fourth, a conservation law for blending inheritance. Refitting a child on the average of several parents' outputs carries a rare capability across a generation no better than inheriting from one parent, to first order, so the gain of having several parents is realised only by operators that keep each parent's strongest contribution. The law fixes the null against which every recombination operator is judged and predicted the headroom rule measured in language models at two scales: routing and offspring selection beat the weight average wherever that average falls short of attainable performance (hard tasks at 7B, every seed), and add nothing where it does not.
|
||||
|
||||
Around these sit results that place the framework in the existing literature: a closed-form grounding equilibrium and per-item floor that agree with the fresh-data stability theorems and with the finding that absolute real-sample counts matter more than proportions; the transfer of every drift sign to trained networks with a measured, architecture-specific estimator bias; and a four-arm ablation of a composed population. Two refinements the framework proposed were not supported, and the paper says so.
|
||||
|
||||
I am submitting to *Nature Machine Intelligence* because the readers who make the decisions this paper prices (how much verified data a synthetic pipeline needs, whether to merge or route, when to stop merging, how to detect an incompatible pair before paying for the merge) are this journal's readers, and because the journal has already published evolutionary model merging as a research direction (Akiba et al., 2025). The paper gives that direction its theory and its failure modes. What biology receives in return is a model system where every genotype, environment and mating decision is observable and manipulable, so the paper should also interest the evolutionary biologists among your readership.
|
||||
|
||||
All code, configurations, seeds, results artefacts and a one-command reproduction script will be deposited openly with an archived DOI on publication; every figure regenerates from committed artefacts without re-simulation. The manuscript is not under consideration elsewhere and has not been published in any form. [A preprint has been / will be posted to arXiv.] I am the sole author and declare no competing interests.
|
||||
|
||||
Suggested referees:
|
||||
- [Name, affiliation, email] (model merging)
|
||||
- [Name, affiliation, email] (model collapse / synthetic data theory)
|
||||
- [Name, affiliation, email] (population genetics of recombination and speciation)
|
||||
- [Name, affiliation, email] (continual learning)
|
||||
|
||||
Excluded referees: [none / names].
|
||||
|
||||
Yours sincerely,
|
||||
|
||||
Giorgio F. Gilestro
|
||||
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|
|
@ -1,80 +0,0 @@
|
|||
1 OK 10.48550/arXiv.2508.06811 Anatomy of a Machine Learning Ecosystem: 2 Million Models on Hug in manuscript
|
||||
2 OK 10.48550/arXiv.2405.18432 Unsupervised Model Tree Heritage Recovery in manuscript
|
||||
3 OK 10.48550/arXiv.2402.00699 PeaTMOSS: A Dataset and Initial Analysis of Pre-Trained Models i in manuscript
|
||||
4 OK 10.48550/arXiv.2306.01708 TIES-Merging: Resolving Interference When Merging Models in manuscript
|
||||
5 OK 10.1038/s42256-024-00975-8 Evolutionary optimization of model merging recipes crossref (matched: Evolutionary optimization of model merging recipes)
|
||||
6 OK 10.48550/arXiv.2403.13257 Arcee's MergeKit: A Toolkit for Merging Large Language Models in manuscript
|
||||
7 OK 10.48550/arXiv.2408.07666 Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, App in manuscript
|
||||
8 OK 10.48550/arXiv.2503.01155 Nature-Inspired Population-Based Evolution of Large Language Mod in manuscript
|
||||
9 OK 10.48550/arXiv.2508.16204 Competition and Attraction Improve Model Fusion in manuscript
|
||||
10 OK 10.48550/arXiv.2501.05707 Multiagent Finetuning: Self Improvement with Diverse Reasoning C in manuscript
|
||||
11 OK 10.48550/arXiv.2406.11704 Nemotron-4 340B Technical Report in manuscript
|
||||
12 OK 10.48550/arXiv.2412.08905 Phi-4 Technical Report in manuscript
|
||||
13 OK 10.48550/arXiv.2212.10560 Self-Instruct: Aligning Language Models with Self-Generated Inst in manuscript
|
||||
14 OK 10.48550/arXiv.2401.05749 A Shocking Amount of the Web is Machine Translated: Insights fro in manuscript
|
||||
15 OK 10.48550/arXiv.2403.07183 Monitoring AI-Modified Content at Scale: A Case Study on the Imp in manuscript
|
||||
16 OK 10.48550/arXiv.2211.04325 Will we run out of data? Limits of LLM scaling based on human-ge in manuscript
|
||||
17 OK 10.1038/s41562-023-01742-2 Machine culture verified by hand
|
||||
18 OK 10.48550/arXiv.2304.03442 Generative Agents: Interactive Simulacra of Human Behavior in manuscript
|
||||
19 OK 10.48550/arXiv.2402.01680 Large Language Model based Multi-Agents: A Survey of Progress an in manuscript
|
||||
20 OK 10.48550/arXiv.2509.10147 Virtual Agent Economies in manuscript
|
||||
21 OK 10.1038/s41586-024-07566-y AI models collapse when trained on recursively generated data crossref (matched: AI models collapse when trained on recursively generated data)
|
||||
22 OK 10.1371/journal.pcbi.1002510 Structural Drift: The Population Dynamics of Sequential Learning crossref (matched: Structural Drift: The Population Dynamics of Sequential Learning)
|
||||
23 OK 10.48550/arXiv.2604.08554 Drift and selection in LLM text ecosystems in manuscript
|
||||
24 OK 10.48550/arXiv.2509.20101 First-Extinction Law for Resampling Processes in manuscript
|
||||
25 OK 10.48550/arXiv.2407.17493 Model Collapse in the Self-Consuming Chain of Diffusion Finetuni in manuscript
|
||||
26 OK 10.1016/s0079-7421(08)60536-8 Catastrophic Interference in Connectionist Networks: The Sequent crossref (matched: Catastrophic Interference in Connectionist Networks: The Sequential Le)
|
||||
27 OK 10.1016/s1364-6613(99)01294-2 Catastrophic forgetting in connectionist networks crossref (matched: Catastrophic forgetting in connectionist networks)
|
||||
28 OK 10.1016/0027-5107(64)90047-8 The relation of recombination to mutational advance crossref (matched: The relation of recombination to mutational advance)
|
||||
29 OK 10.48550/arXiv.2510.16657 Escaping Model Collapse via Synthetic Data Verification: Near-te in manuscript
|
||||
30 OK 10.48550/arXiv.2404.01413 Is Model Collapse Inevitable? Breaking the Curse of Recursion by in manuscript
|
||||
31 OK 10.1093/genetics/16.2.97 EVOLUTION IN MENDELIAN POPULATIONS crossref (matched: EVOLUTION IN MENDELIAN POPULATIONS)
|
||||
32 OK 10.1046/j.1523-1739.1996.10061509.x The One‐Migrant‐per‐Generation Rule in Conservation and Manageme crossref (matched: The One‐Migrant‐per‐Generation Rule in Conservation and Management)
|
||||
33 HAND (pre-DOI source) [Review of] The Origin of Species written by hand
|
||||
34 OK 10.48550/arXiv.2411.02207 Collective Model Intelligence Requires Compatible Specialization in manuscript
|
||||
35 HAND (pre-DOI source) The Genetical Theory of Natural Selection written by hand
|
||||
36 OK 10.1086/280418 Some Genetic Aspects of Sex crossref (matched: Some Genetic Aspects of Sex)
|
||||
37 OK 10.48550/arXiv.2106.09685 LoRA: Low-Rank Adaptation of Large Language Models in manuscript
|
||||
38 OK 10.1016/s0022-5193(87)80029-2 Towards a general theory of adaptive walks on rugged landscapes crossref (matched: Towards a general theory of adaptive walks on rugged landscapes)
|
||||
39 HAND (pre-DOI source) Coadaptation and outbreeding depression written by hand
|
||||
40 OK 10.1162/evco_a_00025 Abandoning Objectives: Evolution Through the Search for Novelty crossref (matched: Abandoning Objectives: Evolution Through the Search for Novelty Alone)
|
||||
41 OK 10.48550/arXiv.2503.05683 WikiBigEdit: Understanding the Limits of Lifelong Knowledge Edit in manuscript
|
||||
42 OK 10.48550/arXiv.2502.04390 In Praise of Stubbornness: An Empirical Case for Cognitive-Disso in manuscript
|
||||
43 OK 10.48550/arXiv.2607.09202 Interference and Retention in Continual Learning in manuscript
|
||||
44 OK 10.1017/s0016672300033140 A general model for the evolution of recombination crossref (matched: A general model for the evolution of recombination)
|
||||
45 OK 10.1006/tpbi.1997.1301 Deleterious Mutations, Variable Epistatic Interactions, and the crossref (matched: Deleterious Mutations, Variable Epistatic Interactions, and the Evolut)
|
||||
46 OK 10.1038/nrg761 Resolving the paradox of sex and recombination crossref (matched: Resolving the paradox of sex and recombination)
|
||||
47 OK 10.1093/genetics/117.3.559 Selection, Generalized Transmission and the Evolution of Modifie crossref (matched: Selection, Generalized Transmission and the Evolution of Modifier Gene)
|
||||
48 OK 10.1093/genetics/139.4.1805 The population genetics of speciation: the evolution of hybrid i crossref (matched: The population genetics of speciation: the evolution of hybrid incompa)
|
||||
49 OK 10.1111/j.0014-3820.2001.tb00628.x THE EVOLUTION OF POSTZYGOTIC ISOLATION: ACCUMULATING DOBZHANSKY- crossref (matched: THE EVOLUTION OF POSTZYGOTIC ISOLATION: ACCUMULATING DOBZHANSKY-MULLER)
|
||||
50 OK 10.48550/arXiv.2209.04836 Git Re-Basin: Merging Models modulo Permutation Symmetries in manuscript
|
||||
51 OK 10.48550/arXiv.2606.23607 Scaling Linear Mode Connectivity and Merging to Billion Paramete in manuscript
|
||||
52 OK 10.48550/arXiv.2410.12766 The Non-Local Model Merging Problem: Permutation Symmetries and in manuscript
|
||||
53 OK 10.48550/arXiv.2607.11997 Are we Merging the Right Models? Impact of Expert Training Durat in manuscript
|
||||
54 OK 10.48550/arXiv.2601.22285 Demystifying Mergeability: Interpretable Properties to Predict M in manuscript
|
||||
55 OK 10.48550/arXiv.2205.12393 Fine-tuned Language Models are Continual Learners in manuscript
|
||||
56 OK 10.48550/arXiv.2403.08763 Simple and Scalable Strategies to Continually Pre-train Large La in manuscript
|
||||
57 OK 10.1080/09540099550039318 Catastrophic Forgetting, Rehearsal and Pseudorehearsal crossref (matched: Catastrophic Forgetting, Rehearsal and Pseudorehearsal)
|
||||
58 OK 10.48550/arXiv.1705.08690 Continual Learning with Deep Generative Replay in manuscript
|
||||
59 OK 10.48550/arXiv.2406.07515 Beyond Model Collapse: Scaling Up with Synthesized Data Requires in manuscript
|
||||
60 OK 10.48550/arXiv.1606.04671 Progressive Neural Networks in manuscript
|
||||
61 OK 10.48550/arXiv.2405.09673 LoRA Learns Less and Forgets Less in manuscript
|
||||
62 OK 10.1037/0033-295x.102.3.419 Why there are complementary learning systems in the hippocampus crossref (matched: Why there are complementary learning systems in the hippocampus and ne)
|
||||
63 OK 10.1016/j.tics.2016.05.004 What Learning Systems do Intelligent Agents Need? Complementary crossref (matched: What Learning Systems do Intelligent Agents Need? Complementary Learni)
|
||||
64 OK 10.48550/arXiv.1805.06370 Progress & Compress: A scalable framework for continual lear verified by hand
|
||||
65 OK 10.48550/arXiv.2212.04089 Editing Models with Task Arithmetic in manuscript
|
||||
66 OK 10.48550/arXiv.2407.06322 MagMax: Leveraging Model Merging for Seamless Continual Learning in manuscript
|
||||
67 OK 10.48550/arXiv.2407.08699 Mitigating Catastrophic Forgetting in Language Transfer via Mode in manuscript
|
||||
68 OK 10.48550/arXiv.2412.06712 How to Merge Your Multimodal Models Over Time? in manuscript
|
||||
69 OK 10.48550/arXiv.1812.05159 An Empirical Study of Example Forgetting during Deep Neural Netw in manuscript
|
||||
70 OK 10.48550/arXiv.2211.08411 Large Language Models Struggle to Learn Long-Tail Knowledge in manuscript
|
||||
71 OK 10.48550/arXiv.2210.00266 Long-Tailed Class Incremental Learning in manuscript
|
||||
72 OK 10.48550/arXiv.2309.10105 Understanding Catastrophic Forgetting in Language Models via Imp in manuscript
|
||||
73 OK 10.48550/arXiv.2311.03099 Language Models are Super Mario: Absorbing Abilities from Homolo in manuscript
|
||||
74 OK 10.48550/arXiv.2203.05482 Model soups: averaging weights of multiple fine-tuned models imp in manuscript
|
||||
75 OK 10.48550/arXiv.2603.09463 An Empirical Study and Theoretical Explanation on Task-Level Mod in manuscript
|
||||
76 OK 10.48550/arXiv.2506.14126 From Memorization to Parameter Interference: How Overtraining Ex in manuscript
|
||||
77 OK 10.1145/2934662 Sex as an algorithm crossref (matched: Sex as an algorithm)
|
||||
78 OK 10.48550/arXiv.2311.09807 The Curious Decline of Linguistic Diversity: Training Language M in manuscript
|
||||
79 OK 10.48550/arXiv.2309.05196 Does Writing with Language Models Reduce Content Diversity? in manuscript
|
||||
80 OK 10.1126/sciadv.adn5290 Generative AI enhances individual creativity but reduces the col crossref (matched: Generative AI enhances individual creativity but reduces the collectiv)
|
||||
|
|
@ -1,80 +0,0 @@
|
|||
1 OK 10.48550/arXiv.2508.06811 Anatomy of a Machine Learning Ecosystem: 2 Million Models on Hug in manuscript
|
||||
2 OK 10.48550/arXiv.2405.18432 Unsupervised Model Tree Heritage Recovery in manuscript
|
||||
3 OK 10.48550/arXiv.2402.00699 PeaTMOSS: A Dataset and Initial Analysis of Pre-Trained Models i in manuscript
|
||||
4 OK 10.48550/arXiv.2306.01708 TIES-Merging: Resolving Interference When Merging Models in manuscript
|
||||
5 OK 10.1038/s42256-024-00975-8 Evolutionary optimization of model merging recipes crossref (matched: Evolutionary optimization of model merging recipes)
|
||||
6 OK 10.48550/arXiv.2403.13257 Arcee's MergeKit: A Toolkit for Merging Large Language Models in manuscript
|
||||
7 OK 10.48550/arXiv.2408.07666 Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, App in manuscript
|
||||
8 OK 10.48550/arXiv.2503.01155 Nature-Inspired Population-Based Evolution of Large Language Mod in manuscript
|
||||
9 OK 10.48550/arXiv.2508.16204 Competition and Attraction Improve Model Fusion in manuscript
|
||||
10 OK 10.48550/arXiv.2501.05707 Multiagent Finetuning: Self Improvement with Diverse Reasoning C in manuscript
|
||||
11 OK 10.48550/arXiv.2406.11704 Nemotron-4 340B Technical Report in manuscript
|
||||
12 OK 10.48550/arXiv.2412.08905 Phi-4 Technical Report in manuscript
|
||||
13 OK 10.48550/arXiv.2212.10560 Self-Instruct: Aligning Language Models with Self-Generated Inst in manuscript
|
||||
14 OK 10.48550/arXiv.2401.05749 A Shocking Amount of the Web is Machine Translated: Insights fro in manuscript
|
||||
15 OK 10.48550/arXiv.2403.07183 Monitoring AI-Modified Content at Scale: A Case Study on the Imp in manuscript
|
||||
16 OK 10.48550/arXiv.2211.04325 Will we run out of data? Limits of LLM scaling based on human-ge in manuscript
|
||||
17 OK 10.1038/s41562-023-01742-2 Machine culture verified by hand
|
||||
18 OK 10.48550/arXiv.2304.03442 Generative Agents: Interactive Simulacra of Human Behavior in manuscript
|
||||
19 OK 10.48550/arXiv.2402.01680 Large Language Model based Multi-Agents: A Survey of Progress an in manuscript
|
||||
20 OK 10.48550/arXiv.2509.10147 Virtual Agent Economies in manuscript
|
||||
21 OK 10.1038/s41586-024-07566-y AI models collapse when trained on recursively generated data crossref (matched: AI models collapse when trained on recursively generated data)
|
||||
22 OK 10.1371/journal.pcbi.1002510 Structural Drift: The Population Dynamics of Sequential Learning crossref (matched: Structural Drift: The Population Dynamics of Sequential Learning)
|
||||
23 OK 10.48550/arXiv.2604.08554 Drift and selection in LLM text ecosystems in manuscript
|
||||
24 OK 10.48550/arXiv.2509.20101 First-Extinction Law for Resampling Processes in manuscript
|
||||
25 OK 10.48550/arXiv.2407.17493 Model Collapse in the Self-Consuming Chain of Diffusion Finetuni in manuscript
|
||||
26 OK 10.1016/s0079-7421(08)60536-8 Catastrophic Interference in Connectionist Networks: The Sequent crossref (matched: Catastrophic Interference in Connectionist Networks: The Sequential Le)
|
||||
27 OK 10.1016/s1364-6613(99)01294-2 Catastrophic forgetting in connectionist networks crossref (matched: Catastrophic forgetting in connectionist networks)
|
||||
28 OK 10.1016/0027-5107(64)90047-8 The relation of recombination to mutational advance crossref (matched: The relation of recombination to mutational advance)
|
||||
29 OK 10.48550/arXiv.2510.16657 Escaping Model Collapse via Synthetic Data Verification: Near-te in manuscript
|
||||
30 OK 10.48550/arXiv.2404.01413 Is Model Collapse Inevitable? Breaking the Curse of Recursion by in manuscript
|
||||
31 OK 10.1093/genetics/16.2.97 EVOLUTION IN MENDELIAN POPULATIONS crossref (matched: EVOLUTION IN MENDELIAN POPULATIONS)
|
||||
32 OK 10.1046/j.1523-1739.1996.10061509.x The One‐Migrant‐per‐Generation Rule in Conservation and Manageme crossref (matched: The One‐Migrant‐per‐Generation Rule in Conservation and Management)
|
||||
33 HAND (pre-DOI source) [Review of] The Origin of Species written by hand
|
||||
34 OK 10.48550/arXiv.2411.02207 Collective Model Intelligence Requires Compatible Specialization in manuscript
|
||||
35 HAND (pre-DOI source) The Genetical Theory of Natural Selection written by hand
|
||||
36 OK 10.1086/280418 Some Genetic Aspects of Sex crossref (matched: Some Genetic Aspects of Sex)
|
||||
37 OK 10.48550/arXiv.2106.09685 LoRA: Low-Rank Adaptation of Large Language Models in manuscript
|
||||
38 OK 10.1016/s0022-5193(87)80029-2 Towards a general theory of adaptive walks on rugged landscapes crossref (matched: Towards a general theory of adaptive walks on rugged landscapes)
|
||||
39 HAND (pre-DOI source) Coadaptation and outbreeding depression written by hand
|
||||
40 OK 10.1162/evco_a_00025 Abandoning Objectives: Evolution Through the Search for Novelty crossref (matched: Abandoning Objectives: Evolution Through the Search for Novelty Alone)
|
||||
41 OK 10.48550/arXiv.2503.05683 WikiBigEdit: Understanding the Limits of Lifelong Knowledge Edit in manuscript
|
||||
42 OK 10.48550/arXiv.2502.04390 In Praise of Stubbornness: An Empirical Case for Cognitive-Disso in manuscript
|
||||
43 OK 10.48550/arXiv.2607.09202 Interference and Retention in Continual Learning in manuscript
|
||||
44 OK 10.1017/s0016672300033140 A general model for the evolution of recombination crossref (matched: A general model for the evolution of recombination)
|
||||
45 OK 10.1006/tpbi.1997.1301 Deleterious Mutations, Variable Epistatic Interactions, and the crossref (matched: Deleterious Mutations, Variable Epistatic Interactions, and the Evolut)
|
||||
46 OK 10.1038/nrg761 Resolving the paradox of sex and recombination crossref (matched: Resolving the paradox of sex and recombination)
|
||||
47 OK 10.1093/genetics/117.3.559 Selection, Generalized Transmission and the Evolution of Modifie crossref (matched: Selection, Generalized Transmission and the Evolution of Modifier Gene)
|
||||
48 OK 10.1093/genetics/139.4.1805 The population genetics of speciation: the evolution of hybrid i crossref (matched: The population genetics of speciation: the evolution of hybrid incompa)
|
||||
49 OK 10.1111/j.0014-3820.2001.tb00628.x THE EVOLUTION OF POSTZYGOTIC ISOLATION: ACCUMULATING DOBZHANSKY- crossref (matched: THE EVOLUTION OF POSTZYGOTIC ISOLATION: ACCUMULATING DOBZHANSKY-MULLER)
|
||||
50 OK 10.48550/arXiv.2209.04836 Git Re-Basin: Merging Models modulo Permutation Symmetries in manuscript
|
||||
51 OK 10.48550/arXiv.2606.23607 Scaling Linear Mode Connectivity and Merging to Billion Paramete in manuscript
|
||||
52 OK 10.48550/arXiv.2410.12766 The Non-Local Model Merging Problem: Permutation Symmetries and in manuscript
|
||||
53 OK 10.48550/arXiv.2607.11997 Are we Merging the Right Models? Impact of Expert Training Durat in manuscript
|
||||
54 OK 10.48550/arXiv.2601.22285 Demystifying Mergeability: Interpretable Properties to Predict M in manuscript
|
||||
55 OK 10.48550/arXiv.2205.12393 Fine-tuned Language Models are Continual Learners in manuscript
|
||||
56 OK 10.48550/arXiv.2403.08763 Simple and Scalable Strategies to Continually Pre-train Large La in manuscript
|
||||
57 OK 10.1080/09540099550039318 Catastrophic Forgetting, Rehearsal and Pseudorehearsal crossref (matched: Catastrophic Forgetting, Rehearsal and Pseudorehearsal)
|
||||
58 OK 10.48550/arXiv.1705.08690 Continual Learning with Deep Generative Replay in manuscript
|
||||
59 OK 10.48550/arXiv.2406.07515 Beyond Model Collapse: Scaling Up with Synthesized Data Requires in manuscript
|
||||
60 OK 10.48550/arXiv.1606.04671 Progressive Neural Networks in manuscript
|
||||
61 OK 10.48550/arXiv.2405.09673 LoRA Learns Less and Forgets Less in manuscript
|
||||
62 OK 10.1037/0033-295x.102.3.419 Why there are complementary learning systems in the hippocampus crossref (matched: Why there are complementary learning systems in the hippocampus and ne)
|
||||
63 OK 10.1016/j.tics.2016.05.004 What Learning Systems do Intelligent Agents Need? Complementary crossref (matched: What Learning Systems do Intelligent Agents Need? Complementary Learni)
|
||||
64 OK 10.48550/arXiv.1805.06370 Progress & Compress: A scalable framework for continual lear verified by hand
|
||||
65 OK 10.48550/arXiv.2212.04089 Editing Models with Task Arithmetic in manuscript
|
||||
66 OK 10.48550/arXiv.2407.06322 MagMax: Leveraging Model Merging for Seamless Continual Learning in manuscript
|
||||
67 OK 10.48550/arXiv.2407.08699 Mitigating Catastrophic Forgetting in Language Transfer via Mode in manuscript
|
||||
68 OK 10.48550/arXiv.2412.06712 How to Merge Your Multimodal Models Over Time? in manuscript
|
||||
69 OK 10.48550/arXiv.1812.05159 An Empirical Study of Example Forgetting during Deep Neural Netw in manuscript
|
||||
70 OK 10.48550/arXiv.2211.08411 Large Language Models Struggle to Learn Long-Tail Knowledge in manuscript
|
||||
71 OK 10.48550/arXiv.2210.00266 Long-Tailed Class Incremental Learning in manuscript
|
||||
72 OK 10.48550/arXiv.2309.10105 Understanding Catastrophic Forgetting in Language Models via Imp in manuscript
|
||||
73 OK 10.48550/arXiv.2311.03099 Language Models are Super Mario: Absorbing Abilities from Homolo in manuscript
|
||||
74 OK 10.48550/arXiv.2203.05482 Model soups: averaging weights of multiple fine-tuned models imp in manuscript
|
||||
75 OK 10.48550/arXiv.2603.09463 An Empirical Study and Theoretical Explanation on Task-Level Mod in manuscript
|
||||
76 OK 10.48550/arXiv.2506.14126 From Memorization to Parameter Interference: How Overtraining Ex in manuscript
|
||||
77 OK 10.1145/2934662 Sex as an algorithm crossref (matched: Sex as an algorithm)
|
||||
78 OK 10.48550/arXiv.2311.09807 The Curious Decline of Linguistic Diversity: Training Language M in manuscript
|
||||
79 OK 10.48550/arXiv.2309.05196 Does Writing with Language Models Reduce Content Diversity? in manuscript
|
||||
80 OK 10.1126/sciadv.adn5290 Generative AI enhances individual creativity but reduces the col crossref (matched: Generative AI enhances individual creativity but reduces the collectiv)
|
||||
|
|
|
@ -1,131 +0,0 @@
|
|||
"""Renumber the manuscript's references to first-appearance order (PNAS style).
|
||||
|
||||
Reads paper/manuscript/main.md, finds every parenthesised citation group in the text above
|
||||
"## References", derives the order in which references first appear, and rewrites the citation
|
||||
groups in main.md, si.md, and the figure captions in build.py, then reorders the reference list.
|
||||
Citation groups are parentheses containing only reference numbers, commas, en-dash ranges, an optional
|
||||
"cf. " prefix, or a prose prefix ending in a semicolon ("...; 11, 12"). Four-digit numbers (years)
|
||||
never match, and any number above the list length is reported and left alone.
|
||||
|
||||
Usage: python paper/manuscript/renumber_refs.py # dry run: mapping + per-file counts
|
||||
python paper/manuscript/renumber_refs.py --apply # rewrite the three files in place
|
||||
"""
|
||||
|
||||
from __future__ import annotations
|
||||
|
||||
import re
|
||||
import sys
|
||||
from pathlib import Path
|
||||
|
||||
ROOT = Path(__file__).resolve().parents[2]
|
||||
MAIN, SI, BUILD = (ROOT / "paper" / "manuscript" / n for n in ("main.md", "si.md", "build.py"))
|
||||
REF_HEADER = "## References"
|
||||
CIT = re.compile(
|
||||
r"\((?P<pre>[^()]*?;\s*)?(?P<cf>cf\.\s*)?"
|
||||
r"(?P<nums>\d{1,3}(?:\s*[–-]\s*\d{1,3})?(?:,\s*\d{1,3}(?:\s*[–-]\s*\d{1,3})?)*)\)"
|
||||
)
|
||||
REF_LINE = re.compile(r"^(\d+)\. (.*)$")
|
||||
|
||||
|
||||
def expand(nums: str) -> list[int]:
|
||||
out: list[int] = []
|
||||
for part in re.split(r",\s*", nums):
|
||||
if re.search(r"[–-]", part):
|
||||
a, b = (int(x) for x in re.split(r"\s*[–-]\s*", part))
|
||||
out.extend(range(a, b + 1))
|
||||
else:
|
||||
out.append(int(part))
|
||||
return out
|
||||
|
||||
|
||||
def compress(nums: list[int]) -> str:
|
||||
"""Ascending, with runs of three or more collapsed to an en-dash range."""
|
||||
nums = sorted(set(nums))
|
||||
runs: list[list[int]] = []
|
||||
for n in nums:
|
||||
if runs and n == runs[-1][-1] + 1:
|
||||
runs[-1].append(n)
|
||||
else:
|
||||
runs.append([n])
|
||||
return ", ".join(f"{r[0]}–{r[-1]}" if len(r) >= 3 else ", ".join(map(str, r)) for r in runs)
|
||||
|
||||
|
||||
def split_main(text: str) -> tuple[str, list[tuple[int, str]]]:
|
||||
body, _, refs = text.partition(REF_HEADER)
|
||||
entries = [(int(m.group(1)), m.group(2)) for line in refs.splitlines() if (m := REF_LINE.match(line))]
|
||||
return body, entries
|
||||
|
||||
|
||||
def first_appearance(body: str, n_refs: int) -> list[int]:
|
||||
order: list[int] = []
|
||||
for m in CIT.finditer(body):
|
||||
for n in expand(m.group("nums")):
|
||||
if n <= n_refs and n not in order:
|
||||
order.append(n)
|
||||
return order
|
||||
|
||||
|
||||
def rewrite(text: str, mapping: dict[int, int], n_refs: int, label: str) -> tuple[str, int, list[str]]:
|
||||
count, suspicious = 0, []
|
||||
|
||||
def sub(m: re.Match) -> str:
|
||||
nonlocal count
|
||||
nums = expand(m.group("nums"))
|
||||
if any(n > n_refs or n < 1 for n in nums):
|
||||
suspicious.append(m.group(0))
|
||||
return m.group(0)
|
||||
count += 1
|
||||
return f"({m.group('pre') or ''}{m.group('cf') or ''}{compress([mapping[n] for n in nums])})"
|
||||
|
||||
return CIT.sub(sub, text), count, suspicious
|
||||
|
||||
|
||||
def main(apply: bool) -> int:
|
||||
main_text = MAIN.read_text()
|
||||
body, entries = split_main(main_text)
|
||||
n_refs = len(entries)
|
||||
assert [n for n, _ in entries] == list(range(1, n_refs + 1)), "reference list is not 1..N"
|
||||
order = first_appearance(body, n_refs)
|
||||
orphans = sorted(set(range(1, n_refs + 1)) - set(order))
|
||||
if orphans:
|
||||
print(f"ERROR: never cited in main text: {orphans}")
|
||||
return 1
|
||||
mapping = {old: new for new, old in enumerate(order, start=1)}
|
||||
changed = {o: n for o, n in mapping.items() if o != n}
|
||||
print(f"{n_refs} references; {len(changed)} renumbered" + (":" if changed else "."))
|
||||
for o in sorted(changed):
|
||||
print(f" {o:3d} -> {mapping[o]:3d} {entries[o - 1][1][:70]}")
|
||||
|
||||
outputs: dict[Path, str] = {}
|
||||
new_body, c, sus = rewrite(body, mapping, n_refs, "main")
|
||||
print(f"main.md: {c} citation groups" + (f"; left alone: {sus}" if sus else ""))
|
||||
by_new = sorted(entries, key=lambda e: mapping[e[0]])
|
||||
new_refs = "\n".join(f"{mapping[o]}. {t}" for o, t in by_new)
|
||||
outputs[MAIN] = f"{new_body}{REF_HEADER}\n\n{new_refs}\n"
|
||||
text, c, sus = rewrite(SI.read_text(), mapping, n_refs, SI.name)
|
||||
print(f"{SI.name}: {c} citation groups" + (f"; left alone: {sus}" if sus else ""))
|
||||
outputs[SI] = text
|
||||
# build.py is Python: only its FIGURES caption block may carry citations, so rewrite that slice
|
||||
# alone — tuples like (0, 1) elsewhere in the code would otherwise look like citations.
|
||||
btext = BUILD.read_text()
|
||||
head = re.search(r"^FIGURES\b[^\n]*\{\s*$", btext, re.M)
|
||||
if head is None:
|
||||
print(f"{BUILD.name}: no FIGURES block found; skipped")
|
||||
else:
|
||||
start = head.start()
|
||||
end = btext.index("\n}\n", start) + 3
|
||||
block, c, sus = rewrite(btext[start:end], mapping, n_refs, BUILD.name)
|
||||
print(f"{BUILD.name} captions: {c} citation groups" + (f"; left alone: {sus}" if sus else ""))
|
||||
outputs[BUILD] = btext[:start] + block + btext[end:]
|
||||
|
||||
if apply:
|
||||
for path, text in outputs.items():
|
||||
path.write_text(text)
|
||||
print("applied.")
|
||||
else:
|
||||
print("dry run — pass --apply to write.")
|
||||
return 0
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
sys.exit(main("--apply" in sys.argv))
|
||||
Binary file not shown.
|
|
@ -1,146 +0,0 @@
|
|||
# Response to the second review
|
||||
|
||||
*This response accompanies a further revision. Every number below is reproduced by a committed script
|
||||
(`figures/stats_llm_epistasis.py`) from committed artifacts; the revised documents are
|
||||
`results/llm_epistasis/README.md` (rewritten around your four analyses), the manuscript, and
|
||||
`paper/si-notes.md`.*
|
||||
|
||||
---
|
||||
|
||||
## 0. A correction first (your §7)
|
||||
|
||||
You are right, and we apologise for the bookkeeping error: the draft you reviewed **already
|
||||
contained** the full-symmetry alignment experiment, the conflict residual, and the
|
||||
compatible-specialisation null. Our previous letter's "new since the review" conflated three things
|
||||
that we now state separately: **new results** (the LLM-tier speciation runs, the multi-seed
|
||||
replication, and the controlled predictive test with its control axis), **new controls and analyses**
|
||||
(the compatible-overlap axis; the robust statistics in this letter), and **revised interpretation**
|
||||
(everything about E13b/c, which was experimental content you had already seen and whose *presentation*
|
||||
we changed). The experimental delta attributable to the review process is the first and second
|
||||
categories only.
|
||||
|
||||
## 1. Your two-conclusion distinction — adopted as the evidential boundary
|
||||
|
||||
We accept the boundary exactly as you drew it:
|
||||
|
||||
- **Demonstrated:** a small-model, controlled predictive test in which pre-merge functional
|
||||
disagreement predicted merge penalties where the selected weight-space measures did not.
|
||||
- **Not demonstrated:** that an epistasis-specific predictor adds value beyond ordinary functional
|
||||
disagreement, or that the prediction improves operator choice.
|
||||
|
||||
The experiment is now titled a **"controlled predictive test"** everywhere ("decisive experiment
|
||||
delivered" is gone), and the manuscript's §1 ladder describes the prediction rung in your conditional
|
||||
formulation, with its four boundary clauses stated in place: constructed grid, small scale, refinement
|
||||
not superior, operator choice open. The measure itself is renamed **"confidence-weighted functional
|
||||
conflict — a proposed proxy for merge-relevant interactions"**; we accept that bilateral confident
|
||||
contradiction measures incompatible endpoint behaviour, not non-additive interaction in the strict
|
||||
biological sense, and the paper no longer calls any measured quantity "epistasis." Your distinction —
|
||||
*the framework motivated the measurement and controls* vs *their success validates the specifically
|
||||
population-genetic mechanism* — is adopted verbatim; we claim the former.
|
||||
|
||||
## 2. The four analyses — run
|
||||
|
||||
**(1) Direct predictor comparison.** Condition-clustered bootstrap (13 clusters, B = 4000), 95% CIs
|
||||
for each predictor's ρ against the pre-registered primary outcome:
|
||||
|
||||
| predictor | ρ | clustered 95% CI |
|
||||
|---|---|---|
|
||||
| raw functional disagreement | +0.460 | [+0.04, +0.69] |
|
||||
| confidence-weighted functional conflict | +0.446 | [+0.02, +0.68] |
|
||||
| gradient alignment | −0.347 | [−0.59, −0.06] |
|
||||
| delta L2 | +0.165 | [−0.27, +0.58] |
|
||||
| delta cosine | +0.030 | [−0.46, +0.51] |
|
||||
| cross-family accuracy | −0.005 | [−0.29, +0.31] |
|
||||
|
||||
**Paired contrasts are not individually significant** (e.g. |ρ(dis_raw)| − |ρ(delta_cos)| = +0.23,
|
||||
CI [−0.23, +0.59]). Held-out prediction (leave-one-condition-out linear fits): functional measures
|
||||
replicate (dis_raw ρ = +0.396, p = 0.013; conf-weighted +0.352, p = 0.028); geometry ≈ 0; the
|
||||
performance baseline is unstable out-of-sample (−0.435). So the supported statement — now the
|
||||
conclusion in the README, the figure title, and the manuscript — is yours: *across this controlled
|
||||
grid, functional disagreement showed a detectable, held-out-robust association with merge penalty;
|
||||
LoRA-delta cosine and L2 showed no statistically detectable association; gradient alignment carried
|
||||
intermediate signal (its CI excludes zero), so this is not a clean functional-versus-all-geometric
|
||||
divide; head-to-head predictor differences are not individually significant; only these baselines were
|
||||
tested.* "Weight divergence does not predict merge failure" has been removed as over-broad.
|
||||
|
||||
**(2) Sample structure.** 39 rows = **13 conditions × 3 seeds**. Parents are retrained per
|
||||
condition × seed, but children share task-data seeds across conditions within a seed (e.g. the
|
||||
duration-3 parent and the conflict-0 parent are trained on essentially the same data), so rows are not
|
||||
independent — hence clustering by condition in all uncertainty estimates, disclosed in the README.
|
||||
|
||||
**(3) Between- vs within-axis.** You were right that the pooled correlation is substantially axis
|
||||
discrimination (mean penalty: conflict 0.061 vs compat 0.005 / duration 0.011). Within the conflict
|
||||
axis (n = 15): functional measures +0.59/+0.62 — but delta-L2 is +0.71 there, because *within that
|
||||
axis* conflict fraction, added-data volume, and delta growth are collinear: **within-axis
|
||||
identification is impossible by design**, and we now say so; the identification comes from the control
|
||||
axes, where the same volumes and L2 ranges occur at ~zero penalty. Scatterplots are coloured by axis
|
||||
in the figure. Predicting penalties for a held-out *conflict mechanism* (not just held-out conditions
|
||||
of the same mechanism) is listed as the next test — we agree it is the more valuable one.
|
||||
|
||||
**(4) Outcome references.** Reported under all three: oracle parent potential (pre-registered
|
||||
primary), best parent, and mean parent. The ordering is **sensitive to the reference** — under the
|
||||
best-parent reference, delta-L2 correlates comparably to the functional measures (+0.48 vs +0.34).
|
||||
Our reading, stated in the README rather than hidden: that reference inherits parent-strength trends
|
||||
that track training volume, which geometry also tracks, coupling predictor and outcome through the
|
||||
reference rather than through merge damage. On structural coupling between the disagreement predictor
|
||||
and the oracle-potential outcome: probe and test sets are disjoint by construction, but we agree
|
||||
definitional coupling through parental complementarity cannot be fully excluded, which is one more
|
||||
reason all three references are now on the table.
|
||||
|
||||
## 3. Hypothesis labels
|
||||
|
||||
Your table is adopted essentially as written — the manuscript's claims-at-a-glance table now carries:
|
||||
pre-merge disagreement predicts penalty (*empirical within the controlled grid*, with the boundary
|
||||
clauses in the limits column); confidence weighting improves rank prediction (***not supported***);
|
||||
functional beats all geometry (*not established — selected baselines only*); operator choice (*open*);
|
||||
cliff, snowball, emergent DMIs (*hypotheses*, unchanged). We also added your snowball distinction
|
||||
where the snowball is discussed: super-linear growth in incompatibility *count* does not by itself
|
||||
entail a sharp *performance* cliff — that needs the count→effect-size→performance link, which the
|
||||
analytic model supplies under its assumptions and any neural test must establish separately.
|
||||
|
||||
## 4. The two technical statements — corrected
|
||||
|
||||
**"Endpoints and chord are invariant."** Accepted; the ambiguity was ours. The SI proposition now
|
||||
defines "chord" precisely as the α-linear interpolation **of the endpoint loss values** — the barrier
|
||||
baseline, a function of endpoints only, which *is* invariant — and states explicitly that the
|
||||
**weight-space interpolation path is generally not invariant** (that being precisely why alignment can
|
||||
lower a barrier). It also now carries your second point: exact recovery of a permuted-and-rescaled
|
||||
copy validates a special case and does not establish global optimality of the alignment for
|
||||
independently trained networks — so the "removable" share is a lower bound and the "residual" an upper
|
||||
bound, stated wherever the decomposition is used.
|
||||
|
||||
**"Frozen base pins the coordinate system, so failure is functional by construction."** Accepted, and
|
||||
your replacement wording adopted verbatim across the module, configs, READMEs, and figure: *the shared
|
||||
frozen base controls a major source of coordinate mismatch, allowing a cleaner test of
|
||||
conflict-associated merging failure* — with the boundary stated (failures of delta-averaging can still
|
||||
reflect nonlinear interaction, scaling, or capacity). "Conflict-associated," not "functional by
|
||||
construction," throughout.
|
||||
|
||||
## 5. Chronology and reliability
|
||||
|
||||
**Chronology (now a section of the README).** Prospective: hypotheses, predictors, primary outcome and
|
||||
falsifiers were in the config before the first grid ran. Adaptive: the compatible-overlap control was
|
||||
added *after* geometry appeared to win, with its own pre-stated readings, run on the same seeds; no
|
||||
existing rows were re-run or altered. Post hoc: the clustered-bootstrap/LOCO/multi-reference analyses
|
||||
were added at your request after all data was collected. We agree this is transparent adaptive
|
||||
experimentation, not wholly prospective confirmation, and it is labelled as such.
|
||||
|
||||
**Reliability.** The CI-width claim is withdrawn. The seed-level statement now reads: routing beat the
|
||||
soup **in every seed** (3/3 paired, both metrics), directed selection beat the soup 3/3, and one seed
|
||||
exhibited a catastrophic soup failure (0.071 overall, 0.000 worst-family) to which routing was immune
|
||||
(0.262/0.225); seed-level sds (0.090 vs 0.023) are reported as an observation, with the explicit note
|
||||
that three seeds do not support a variance estimate.
|
||||
|
||||
## 6. On your bottom line
|
||||
|
||||
We accept your formulation as the paper's claim for this line of work — it now closes the relevant
|
||||
results section nearly verbatim: *we separated overlap, divergence, and conflict experimentally; in
|
||||
this controlled setting, functional disagreement predicted merging damage when simple weight-distance
|
||||
measures did not; the proposed epistasis refinement and the emergent-speciation mechanism remain
|
||||
unconfirmed.* And we take the redirection about what would count next: not 0.5B → 7B alone, but
|
||||
**generalisation to unfamiliar conflict structures** (a held-out conflict mechanism, and real rather
|
||||
than constructed task pairs) and **a demonstrably better budget-matched merging decision**. Those two
|
||||
now head the open-problems list, above the scale replication.
|
||||
|
||||
We would welcome a third pass if you have the appetite — particularly on whether the README's
|
||||
conditional conclusion and the chronology section read at the right strength.
|
||||
|
|
@ -1,96 +0,0 @@
|
|||
# Response to the third review (of the PNAS-format draft)
|
||||
|
||||
*All five priority fixes are made, plus the presentation items. The revised draft is
|
||||
`paper/manuscript/main.md` (rebuilt PDF alongside); the long-form document and the results documentation
|
||||
were corrected wherever they carried the same overstatements. Point-by-point:*
|
||||
|
||||
## 1. The averaging proposition (your §2) — you are right, and the text now proves what it claims
|
||||
|
||||
Your convexity argument is correct: conservation of expected mass does not establish that averaging
|
||||
cannot help, because extinction is convex in mixed mass and averaging reduces its variance. Our result
|
||||
is, exactly as you diagnosed, a **first-order cancellation in the rare-item regime**, and the main
|
||||
text now states the actual proposition with its quantities and assumptions: K parents with independent
|
||||
retention; child draws `n` samples from one random parent vs the parents' output-mean; expected mass
|
||||
identical; and in the regime `n·p/K ≪ 1`, where per-item survival is first-order in sampled mass,
|
||||
expected survival is identical too. Two boundaries follow in the same paragraph: outside that regime
|
||||
averaging's variance reduction can *reduce* extinction relative to a random single parent (your
|
||||
argument, credited to the review process); and the union operator's renormalisation (which itself
|
||||
redistributes mass) and oracle requirement are stated. "Adding parents cannot help" is deleted here
|
||||
and in every other document that carried it. We agree the interesting content is the consequence for
|
||||
retention, not the elementary conservation of a mean — which is how the proposition is now framed.
|
||||
|
||||
## 2. Grounding (your §3) — threshold made operational, floor made probabilistic, rule de-categoricalised
|
||||
|
||||
- `g* ≈ 0.05` is now explicitly an **operational threshold**, with the text stating what our own
|
||||
analysis always showed: the immigration–drift equilibrium is *smooth* in the grounding fraction (no
|
||||
phase transition in aggregate diversity). New wording: under the tested population size and Zipf
|
||||
source, `g ≈ 0.05` retained ≥95% of equilibrium diversity, with dependence on sample size, source,
|
||||
and retention target (SI).
|
||||
- `m·p ≳ 1` is restated as what it is: `1 − e^{−m·p}` observation probability per batch (~63% at
|
||||
`m·p = 1`), confidence-dependent, with retention vs stationary occupancy vs reintroduction
|
||||
distinguished (immigration can restore an absent item).
|
||||
- The design rule now reads in your form: under unstratified grounding rare capabilities are expensive
|
||||
(targeted sampling changes the cost); recombination recovers rare capabilities *still retained
|
||||
across complementary parents*.
|
||||
|
||||
## 3. Grounded inheritance vs grounded evaluation (your §4) — separated and named
|
||||
|
||||
The society section now opens with the definitional distinction: **grounded inheritance** (external
|
||||
samples in the reproduction process — the data channel) vs **grounded evaluation** (true fitness vs
|
||||
conformity in selection — the fitness channel), related but different operators, connected only in
|
||||
that both couple the lineage to a non-drifting external signal. The section is retitled to your
|
||||
formulation ("…make complementary contributions"), the ablation is described as separating failure
|
||||
modes *under the tested conditions*, and general joint necessity is explicitly disclaimed (alternative
|
||||
mutation/restart/archive/selection schemes noted). Table 1's corresponding row now says
|
||||
"complementary… in the tested society"; the same fix is propagated to the long-form document.
|
||||
|
||||
## 4. The alignment contradiction (your §5) — deleted, both statements reconciled
|
||||
|
||||
"This cannot be an alignment failure, because the same aligner succeeded on the control" is removed
|
||||
everywhere (manuscript, long-form document, results documentation), replaced by your formulation: the
|
||||
tested alignment removes the same-task barrier but leaves the conflict-associated barrier largely
|
||||
unchanged — supporting a functional-conflict interpretation without proving optimal alignment. The
|
||||
abstract now says "remaining after permutation-and-rescaling alignment" (not "surviving the full
|
||||
symmetry group"), and the Methods note that the group is the alignment's *search space*, with control
|
||||
recovery not establishing global optimality. The discussion's "expect specialisation alone to be
|
||||
merge-safe" is replaced by the supported lesson: **do not treat divergence or specialisation alone as
|
||||
evidence of incompatibility.**
|
||||
|
||||
## 5. Headline vs detail (your §6) — matched, and the seed-dependence analysed
|
||||
|
||||
The significance statement now ends with your suggested sentence (a controlled small-model test…
|
||||
motivating further comparison). On the clustering point: you are right that condition-clustering does
|
||||
not capture cross-condition dependence through shared task-data seeds. We added the sensitivity you
|
||||
asked for (committed to the statistics script): **per-seed correlations** — each seed alone, n = 13
|
||||
conditions — are stable for the functional measures (+0.37 to +0.53 in every individual seed) and ≈0
|
||||
for geometry in every seed; leave-one-seed-out ranges are [+0.38, +0.56] (functional) vs
|
||||
[−0.04, +0.28] (geometry). One informative surprise: gradient alignment is *seed-unstable*
|
||||
(−0.11 to −0.55), which the manuscript now reports as its own caveat. The text also states plainly
|
||||
that with three seeds, uncertainty about seed generalisation remains substantial.
|
||||
|
||||
## 6. Presentation (your §7) — done
|
||||
|
||||
Meta-language removed ("the honest statement", "sharpest honesty", "earn their place by tempering",
|
||||
"honest deviations" — all gone; results are stated, not described as disclosures). "Exact" is now
|
||||
reserved for closed-form mathematics — NK/simulation results are labelled "analytic model" in Table 1
|
||||
and the text. The headroom relationship is stated qualitatively with "a quantitative form is
|
||||
untested". "Directed sex with no biological analogue" is replaced by your phrasing (the shorthand kept,
|
||||
defined as engineered recombination with flexible parent choice and pre-deployment screening).
|
||||
Muller's ratchet is now a *consequence-level* correspondence, with the text stating that irreversible
|
||||
loss alone does not identify the ratchet's mechanism. A compact results table (Table 2: setting/n,
|
||||
outcome definition, headline with uncertainty, for the eight headline results) is added before the
|
||||
Discussion. Reference numbering and the figure files accompany the rebuilt PDF; the bespoke unified
|
||||
figures and journal-format reflow remain flagged as submission-time work.
|
||||
|
||||
## One point of information, not disagreement
|
||||
|
||||
On §2's closing remark — that conservation of an arithmetic mean's expectation is elementary and the
|
||||
contribution must lie in its consequences — we agree, and would only note that the consequence now
|
||||
stated (first-order cancellation of the multi-parent retention gain under output-mean inheritance,
|
||||
against union-operator retention growth, in the regime where the deep tail actually lives) is the
|
||||
claim we intended all along; the earlier wording claimed more than this and is gone.
|
||||
|
||||
Your bottom-line formulation — minimal models establish conditional results; neural experiments reveal
|
||||
where the correspondences hold and break; a controlled predictive test motivates measuring functional
|
||||
conflict before merging — is now, near-verbatim, how the paper describes itself. Thank you for three
|
||||
rounds of genuinely improving review.
|
||||
|
|
@ -1,224 +0,0 @@
|
|||
# Response to the external review
|
||||
|
||||
*Re: "The Evolution of Sex for Artificial Intelligence" (draft reviewed August 2026). This response
|
||||
accompanies a revised manuscript and a set of new experiments run directly in answer to the review.
|
||||
All results referenced here are committed, reproducible artifacts (configs, seeds, figures, and
|
||||
per-experiment READMEs in the repository); commit-level pointers are listed at the end.*
|
||||
|
||||
---
|
||||
|
||||
Thank you for this review. It is the most useful reading the manuscript has had: it does not dispute
|
||||
the programme, it disputes the *calibration* — and its central instrument, the distinction between
|
||||
**interpretation, explanation, and prediction**, is exactly the right one. We have acted on it in two
|
||||
ways: we revised the manuscript to claim only what the evidence supports, and we **ran the decisive
|
||||
experiment the review proposed** (§5 of the review), together with four supporting experiments. The
|
||||
short version of this letter: we accepted nearly everything, the manuscript is narrower and better for
|
||||
it, and the prediction rung of your ladder — the one the draft "was not yet convincing on" — has now
|
||||
been climbed at the small-model tier, with the falsifiers pre-registered and one internal prediction
|
||||
honestly reported as unconfirmed.
|
||||
|
||||
## 1. The overall take, and the framing
|
||||
|
||||
> *"The strongest idea is … treat multigenerational model populations as systems whose inheritance,
|
||||
> diversity, and compatibility must be managed—not merely as collections of models to optimise."*
|
||||
|
||||
Adopted, verbatim, as the stated core contribution — it now closes the abstract's first paragraph and
|
||||
anchors §1. You articulated our thesis better than we had; we have taken the sentence with attribution
|
||||
to the review process rather than pretend we wrote it first.
|
||||
|
||||
> *"The draft sometimes treats a useful biological correspondence as a mathematical identity, and an
|
||||
> illustrative experiment as confirmation of a general mechanism."*
|
||||
|
||||
Accepted. This was the review's most consequential criticism and drove most of the textual changes
|
||||
below.
|
||||
|
||||
## 2. Novelty: interpretation / explanation / prediction
|
||||
|
||||
The ladder is now explicit in §1: we state which of our claims are interpretation (merged offspring
|
||||
as Fisher–Muller), which are explanation (the coordinate-vs-functional decomposition of merge
|
||||
failure), and which are prediction. The priority-dispute language — "nobody has," "none imports,"
|
||||
"the theory the tinkering has outrun" — has been removed entirely, replaced with "to our knowledge"
|
||||
and positive statements of what population genetics contributes. Merge-success *prediction* is now
|
||||
explicitly conceded as an occupied area (interpretable pairwise metrics; capacity/rate-distortion
|
||||
accounts), with our delta stated as mechanism, not existence.
|
||||
|
||||
And the prediction rung is no longer only proposed — see §7 below.
|
||||
|
||||
## 3A. Drift, Muller's ratchet, and model collapse
|
||||
|
||||
Accepted in full. The manuscript now says: the *minimal inheritance model* is exactly Wright–Fisher;
|
||||
a real learner is Wright–Fisher **plus a signed, architecture-specific estimator-bias operator** — and
|
||||
we cite our own learning-kernel measurement against ourselves (the smoothing RNN resists collapse,
|
||||
the sharpening VAE accelerates it; the drift *signs* survive in every architecture tested). Muller's
|
||||
ratchet is scoped to the **irreversible arm** of collapse — the capabilities that, once lost from
|
||||
every parent and source, no recombination can rebuild — with your implication stated as the reason
|
||||
the correspondence earns its keep: recombination only reassembles what still survives, so the cure
|
||||
must act before fixation-by-loss. The glossary entries were carrying the same identity overclaims and
|
||||
have been fixed to match.
|
||||
|
||||
## 3B. "Merge, don't average" — the operator boundaries
|
||||
|
||||
Accepted. A dedicated boundary paragraph now answers your five questions in order:
|
||||
|
||||
- **What is conserved?** Expected rare-item mass, at the single-parent level, exact in the minimal
|
||||
model's rare-item regime.
|
||||
- **Under which operator?** Refitting a child to the **mean of the parents' output distributions** —
|
||||
that operator only. The 1/K dilution exactly cancels the K-parent union gain there.
|
||||
- **Weight averaging and routing?** Explicitly labelled *empirical cousins*, not instances: a
|
||||
nonlinear network's weight-mean does not compute its parents' output-mean, and a router keeps K
|
||||
models' storage plus a classifier — a different parameter and inference budget from one fixed-size
|
||||
child. The measured **headroom rule** is presented as the empirical bridge between the exact law
|
||||
and the weight-space operators, which is all it is.
|
||||
- **Does the strongest-source operator need an oracle?** Yes, and the text now says so.
|
||||
- **Capacity?** When parental capabilities cannot coexist in the child's capacity, no operator
|
||||
preserves the union — stated, with an explicit hand-off to the speciation section as the regime
|
||||
where that boundary lives.
|
||||
|
||||
New supporting evidence since the review: the multi-seed replication (below) adds that fusion is not
|
||||
only worse than union-preserving operators where headroom exists — it is far **less reliable**
|
||||
(95% CI ±0.10 across training seeds vs ±0.026 for routing/selection), which we think sharpens the
|
||||
practical half of this claim.
|
||||
|
||||
## 3C. Model speciation
|
||||
|
||||
Accepted, and this section received the most work — textual and experimental.
|
||||
|
||||
**Textual.** A closing block, "What these experiments do and do not establish," now states the
|
||||
supported conclusion at exactly your formulation — *some merge failures reflect incompatible
|
||||
functional requirements rather than a mismatch in coordinates* — and then lists the qualifiers: (i)
|
||||
the conflict-condition impossibility is **information-theoretic and needs no population genetics**
|
||||
(now also a formal SI proposition: endpoints and chord are invariant under any function-preserving
|
||||
transformation, and any single merged model errs at rate ≥ μ(S)/2 against at least one parent); what
|
||||
the genetic frame adds is locating *which divergences generate such conflicts*; (ii) the
|
||||
epistasis-positions-the-cliff claim and the snowball are labelled **hypotheses at the neural tier**,
|
||||
verified only in the analytic model; (iii) alignment claims are scoped to the enumerated symmetries
|
||||
of the architecture tested, and "unmergeable" means by aligned linear interpolation — a barrier to
|
||||
that operator does not preclude every recombination method (routing sidesteps it by not blending).
|
||||
Emergent Dobzhansky–Muller incompatibilities are carried as the flagship *hypothesis*, with the
|
||||
regimes where our tests found none stated as bounds.
|
||||
|
||||
**Experimental (new since the review).**
|
||||
|
||||
1. *Alignment under the full symmetry group.* Anticipating the "one control does not prove the
|
||||
optimum over all allowed symmetries" objection — and the 2026 richer-symmetry results — we
|
||||
re-ran the decomposition aligning modulo the **complete** function-preserving unit symmetry group
|
||||
of the ReLU MLP (per-unit positive rescaling ∘ permutation; the aligner provably recovers a
|
||||
permuted-and-rescaled copy exactly). The conflict residual is unchanged (0.502 → 0.497); the
|
||||
independent-init barrier still vanishes (0.001). The cliff now also carries a hybrid-fitness
|
||||
readout: merged accuracy 0.97 → 0.03 with conflict.
|
||||
2. *The emergent test, pre-registered.* Divergent-but-compatible specialists (disjoint classes;
|
||||
shifted-view conventions), out to 6.4× the base training: residual 0.000 everywhere, and the merge
|
||||
*rescues* the two forgetting parents (~0.50 → 0.955). We report this null prominently — you
|
||||
identified the sharper question ("which kinds of specialisation create merge-breaking
|
||||
interactions, and which remain complementary?") and this is its first half of an answer:
|
||||
*specialisation on shared ancestry did not break merging in any regime we tested; imposed
|
||||
functional conflict always did.*
|
||||
3. *The LLM tier.* The same two knobs in 0.5B LoRA children of a frozen base (which pins the
|
||||
coordinate system, so merge failure is functional by construction): conflicting conventions
|
||||
produce **function-specific** hybrid breakdown (merged coherence below both parents; private,
|
||||
disjoint skills unharmed in a budget-controlled design, 3 seeds), and over-training disjoint
|
||||
specialists 1→12 epochs produces **no** emergent isolation (the merge improves, staying above the
|
||||
best parent).
|
||||
|
||||
## 4. Importance, scope, and the supporting overstatements
|
||||
|
||||
- **"Three task families and one seed."** The LLM claims are now multi-seed with fixed test sets:
|
||||
merges beat every specialist with non-overlapping CIs on the sharper metric (5 seeds); union vs
|
||||
fusion and directed-selection vs soup replicated at 3 seeds on the hard benchmark. Three
|
||||
lexically-distinct families remain a stated limitation; the full grounded LLM society remains
|
||||
explicitly unbuilt and is flagged as such.
|
||||
- **Open-ended growth.** Accepted — the §11 closing has been rewritten: the architecture removes the
|
||||
*storage* obstacle to indefinite accumulation; that is bookkeeping, not a demonstration of
|
||||
unbounded capability growth, which our deliberately finite models do not test.
|
||||
- **Frozen base ≠ unchanged behaviour** — fixed (§3 now guarantees a recoverable core, not
|
||||
unchanging conduct).
|
||||
- **Baldwin effect** — now an *echo*, with the mechanism difference stated (selection for genetic
|
||||
assimilation vs direct distillation).
|
||||
- **Consolidation and the archive** — fixed: a digital system can and should keep every ancestor;
|
||||
the irreversibility is *operational* (nothing in the production loop consults the archive by
|
||||
default), and the safeguard now includes an audit that diffs against the archived ancestor.
|
||||
- **"Control theory" → "framework"** throughout, subtitle included.
|
||||
- **The claim–assumptions–evidence–limitation table** is in §13 ("The claims at a glance"), ten rows,
|
||||
each labelled exact / empirical / hypothesis with known limits.
|
||||
|
||||
## 5. The decisive experiment — run
|
||||
|
||||
We implemented your six-step design as specified, at the 0.5B tier (39 parent pairs, 3 seeds, fixed
|
||||
held-out test sets, falsifiers pre-registered in the config before running):
|
||||
|
||||
1. **Controlled interaction structure:** three axes decorrelated by construction — *conflict*
|
||||
(contradictory conventions on shared ambiguous prompts, private budgets fixed), *compat* (the
|
||||
same shared prompts learned under the **same** convention: overlap without conflict), and
|
||||
*duration* (weight divergence with zero conflict, 1→12 epochs).
|
||||
2. **Functional divergence separated from duration and weight distance:** the duration and compat
|
||||
axes span the same weight-divergence and data-volume ranges as the conflict axis, at ~zero merge
|
||||
penalty.
|
||||
3. **Operational epistasis, pre-merge:** confidence-weighted bilateral disagreement on a probe mix
|
||||
drawn blind to where the conflict lives — the theory's point being that raw disagreement counts
|
||||
harmless *complementation* (one parent ignorant) as conflict, while the Dobzhansky–Muller
|
||||
structure is *bilateral confident contradiction*.
|
||||
4. **Against existing predictors:** gradient alignment at the shared base, LoRA-delta cosine and L2
|
||||
(computed exactly), and a performance-based (cross-family accuracy) baseline.
|
||||
5. **Operator choice under matched budgets:** partially — see honest riders.
|
||||
6. **Held-out tasks, multiple seeds:** yes (fixed tests, 3 training seeds).
|
||||
|
||||
**Result.** Against the pre-registered primary outcome (merge penalty = parent potential − merged
|
||||
achieved, the hybrid-load analogue): functional measures predict (raw disagreement ρ = +0.46,
|
||||
operational epistasis ρ = +0.45, both p < 0.005); gradient alignment is weakly informative (−0.35);
|
||||
**both geometry predictors are uninformative** (delta-cosine +0.03, delta-L2 +0.17, n.s.);
|
||||
performance-based ~0. *Functional conflict, measured before merging, predicts merge failure; weight
|
||||
divergence does not.*
|
||||
|
||||
Two things about how this result was reached that we want on the record:
|
||||
|
||||
- **The control that broke our own experiment first.** In the initial two-axis grid, the *best*
|
||||
predictor was delta-cosine (ρ = +0.60) — geometry appeared to win. We identified the confound
|
||||
(every shared-data pair in that pool was a conflicted pair, so geometry could succeed as a mere
|
||||
overlap/volume detector), added the compat control axis, and geometry's correlation collapsed to
|
||||
+0.03 while the functional measures held. We report this sequence in the results README rather
|
||||
than presenting only the final table.
|
||||
- **An internal prediction failed, and we say so.** We pre-registered that confidence-weighting
|
||||
should beat raw disagreement as a rank predictor. It does not (they are statistically
|
||||
indistinguishable at n = 39); the weighting does double the conflict-vs-compat contrast in levels
|
||||
(2.0× vs 1.5×). The paper reports the functional-vs-geometric verdict, not a win for the
|
||||
refinement.
|
||||
|
||||
**Honest riders:** correlations are moderate (|ρ| ≈ 0.45), bounded by the large intrinsic seed
|
||||
variance of 0.5B weight-averaging (itself now a documented finding); your step 5 (operator choice
|
||||
under matched budgets) is only partially delivered — the soup-vs-route gap readout is
|
||||
noise-dominated at this scale; and the whole result is one model family at one scale. The 7B
|
||||
replication on the HPC cluster is the planned firm-up before we treat this as more than a
|
||||
small-model demonstration.
|
||||
|
||||
## 6. Where we (mildly) push back
|
||||
|
||||
Only two places, both narrow. First, on *"the impossibility does not require population genetics"* —
|
||||
agreed, and now stated; but we would defend the framework's role in the surrounding structure: it
|
||||
told us *which* pre-merge measurement to make (bilateral confident contradiction rather than raw
|
||||
disagreement or distance), *which* control to build (complementation ≠ conflict), and *which* null to
|
||||
pre-register (emergent isolation) — and those choices are what the decisive experiment's outcome
|
||||
vindicated against the geometry baselines. Second, on *"union preservation risks being built into the
|
||||
operator's definition"* — the conservation law's content is the exact *failure* of the mean operator
|
||||
(the 1/K cancellation), not the definitional success of the max operator; we have tried to make the
|
||||
text carry it that way, with the oracle requirement explicit.
|
||||
|
||||
## 7. What we have not done
|
||||
|
||||
The full grounded, diversity-preserving multigenerational LLM society (still the stated largest gap);
|
||||
7B replication of the decisive experiment; an entanglement measure for *real* task pairs (our
|
||||
epistasis knob is constructed); the operator-choice decision test at usable signal-to-noise; and
|
||||
ambiguous/overlapping task families where routing stops being trivially easy. These are listed in the
|
||||
manuscript's open-problems section in this form.
|
||||
|
||||
## Changelog
|
||||
|
||||
Manuscript revision: commit `58e6c74` (claim-narrowing; all §1–§4 and draft-level items above).
|
||||
New experiments: `ea051a5` (full-symmetry alignment + emergent null, MLP tier), `5a23dda` (LLM-tier
|
||||
speciation + multi-seed replication), `287d232` (the decisive experiment + its control axis). The
|
||||
revised manuscript is `paper/the-evolution-of-sex-for-ai.md`; per-experiment analyses are in
|
||||
`results/*/README.md`; every figure regenerates from committed artifacts.
|
||||
|
||||
We would welcome another pass — in particular on whether the decisive experiment's design and its
|
||||
riders are stated at the right strength, and on whether the remaining hypothesis labels
|
||||
(epistasis-cliff and snowball at the neural tier; emergent DMIs) are placed where you would place
|
||||
them.
|
||||
|
|
@ -1,304 +0,0 @@
|
|||
# The Lamarckian Society — Summary of results
|
||||
|
||||
*The complete laptop-reproducible body of work: the analytical core (Layer 1), the
|
||||
architecture-general neural existence proof (Layer 1.5, including real MNIST), the learning
|
||||
kernel, and the sexual-reproduction society (E7–E11). Two summaries of the same work — one
|
||||
technical, one accessible.*
|
||||
|
||||
**The arc in one breath.** Model collapse is **asexual, self-consuming degradation**: a lineage
|
||||
trained on its own outputs drifts to its own mode and loses the rare tail. We show this is
|
||||
*literally* a Wright–Fisher drift process (validated against closed forms), reproduce it in real
|
||||
trained neural weights and on real MNIST images, and then establish the **cure** — a **grounded
|
||||
sexual society**: reality-checking (grounding) plus **recombination across many decorrelated
|
||||
parents** (sexual reproduction, not teacher→pupil copying) plus **quality-diversity** selection.
|
||||
The payoff is not merely arrested collapse but a population whose **offspring exceed their
|
||||
parents** and whose general capability **climbs** while specialties are re-earned — and removing
|
||||
any one operator breaks it, and a first **real-LLM prototype** (up to 7B on HPC) confirms the
|
||||
recombination claims in trained weights. **131 tests pass**; three of the core predictions are exact
|
||||
closed forms, so the headline curves sit on analytic targets rather than eyeballing.
|
||||
|
||||
---
|
||||
|
||||
## A. Technical summary
|
||||
|
||||
### 1. The analytical core — collapse as Wright–Fisher drift (Layer 1)
|
||||
|
||||
Knowledge is a distribution `p_t` over `K` items on the simplex; a fixed Zipf-tailed truth `p*`;
|
||||
the generational step — *sample `n` from the parent, mix in `m` fresh real samples, refit* — is
|
||||
**literally a Wright–Fisher process with immigration**, not an analogy. Each safeguard from the
|
||||
perspective paper is one operator on that step (grounding `g=m/(n+m)`; region-matched grounding;
|
||||
multi-teacher recombination; directional vs quality-diversity selection; re-minting). Because the
|
||||
process is Wright–Fisher it inherits **closed-form validation targets**, enforced as
|
||||
`<0.5%`-tolerance assertions (the "spine of trust"): neutral heterozygosity decay
|
||||
`E[H_t]=H₀(1−1/n)^t`; fixation probability = initial frequency; the *exact* mutation–drift
|
||||
equilibrium `H_eq = H*·m(2n+m−1)/(n+2nm+m²)`; the tail-persistence threshold `m·p*ᵢ ≳ 1`; and the
|
||||
recombination union coverage `U(K_T,ρ,q)=T[ρq+(1−ρ)(1−(1−q)^{K_T})]`.
|
||||
|
||||
Findings **E1–E6**:
|
||||
- **E1 — collapse (null).** Neutral drift reproduces the geometric `H` decay to Monte-Carlo error;
|
||||
support collapses `K→1`; forward-KL diverges; tail *items* die ≈10× faster than head items.
|
||||
(Aggregate tail *mass* is a drift martingale — a misleading metric; tail-*item* survival is the
|
||||
honest one.)
|
||||
- **E2 — grounding phase boundary (headline).** Stationary `H` tracks the exact `H_eq`; a critical
|
||||
**`g* = 0.048` (CI [0.047, 0.050]) ≪ 1** — as little as one real sample against 200 inherited
|
||||
restores ~68% of the truth's diversity; `g=0.05` reaches 96%. The sharp threshold lives in
|
||||
discrete tail-item survival, not the smooth `H`. The **deep tail is unrescuable** by grounding at
|
||||
feasible budgets (`m* ∼ 1/p_min`) — which is what recombination is for.
|
||||
- **E3 — region-matched grounding.** At fixed budget, matched grounding holds the exercised region's
|
||||
tail (0.49) where uniform lets it collapse (0.07). Grounding protects only what it overlaps.
|
||||
- **E4 — multi-teacher recombination ("merge, don't average").** Union coverage matches the closed
|
||||
form exactly (recombination *supplies* the tail). **Principal finding:** under mean-mixture
|
||||
distillation surviving tail coverage is **flat in `K_T`** — a conservation law (averaging's `1/K_T`
|
||||
dilution exactly cancels the union gain). The benefit is realised only under a **union-preserving
|
||||
merge** (`max` over teachers, à la M2N2 model-merging). *Merge weights; don't average outputs.*
|
||||
- **E5 — QD vs greedy.** Greedy selection fixes (`H≈0.01`); quality-diversity (`w_i ∝ f_i·p_i^{−α}`)
|
||||
holds `H` at a positive plateau (0.48–0.88, rising with novelty `α`).
|
||||
- **E6 — re-minting gate.** Re-minting a *collapsed* lineage makes forward-KL to the original
|
||||
diverge (irreversible lock-in); a diversity gate (`H≥H_gate`) prevents it; healthy re-mint is
|
||||
harmless.
|
||||
|
||||
### 2. Collapse in real trained weights, and on real images (Layer 1.5)
|
||||
|
||||
A re-scoped, cheaper Layer 2: realise the *same* Wright–Fisher abstractions in **real trained
|
||||
generative models** on a fully-synthetic sandbox with an exact oracle, then confirm on real MNIST.
|
||||
A model's "knowledge" is its oracle-measured distribution over `K` modes; the generational step is
|
||||
*train-a-model-on-the-previous-model's-samples + grounding*.
|
||||
|
||||
- **The histogram bridge (HARD GATE).** A memoryless histogram model reduces Layer 1.5 *exactly* to
|
||||
Layer 1: run through the neural runner it recovers `g* = 0.047` and sits on the exact `H_eq` curve.
|
||||
This licenses every trained-model result to be read against the analytic core.
|
||||
- **Collapse in an RNN, and the metric reframing.** A GRU retrained each generation on its own
|
||||
output drifts from truth (forward-KL climbs) and grounding arrests it — the sign confirmed. But
|
||||
the **operative neural collapse metric is forward-KL, not `H` or tail-survival**: the RNN's
|
||||
*smoothing* inductive bias keeps spurious tail modes alive, so `H` stays ~80% of `H*` and
|
||||
tail-survival is non-monotone in `g`. On forward-KL, half the divergence gap closes by a
|
||||
median-recovery grounding `g≈0.04` (echoing Layer-1's 0.048), but *full* recovery needs `g≈0.19` —
|
||||
the sharp `g*≪1` is an exact-operator feature the trained net *softens*.
|
||||
- **Architecture-generality.** Collapse + grounding-rescue appear in the **histogram, GRU, and MLP**
|
||||
alike — the operator is not an artefact of one model class.
|
||||
- **Recombination in real weights.** The E4 "merge, don't average" law reproduces: construction-level
|
||||
union rises 0.49→0.96, oracle-guided max-merge surviving coverage rises while mean-distill stays
|
||||
flat — the conservation law holds in trained weights (compressed/noisier, the expected smoothing
|
||||
caveat).
|
||||
- **Real-MNIST external validity.** A convolutional VAE (the canonical collapse vehicle) retrained on
|
||||
its own generated digits, modes = digit-class × stroke-thickness (K=30, Zipf), read by a frozen
|
||||
CNN oracle (98.5% mode accuracy, confusion matrix recorded as the noise floor): the **dry lineage
|
||||
collapses to a single mode** (forward-KL 0.5→18, support 30→1, tail wiped out, H→0), while **10%
|
||||
grounding holds all 30 modes**. The eyeball montage shows varied gen-0 digits degenerating into one
|
||||
blurry blob. Collapse and its cure are real on real images — not a synthetic artefact.
|
||||
|
||||
### 3. The learning kernel — neutral drift is a null both neural models fail, oppositely
|
||||
|
||||
Prompted by revisiting the neural deviations, the refit step is generalised from a pure resample to
|
||||
`p_{t+1} = T_θ(counts/n)`: a **learning kernel** with a *smoothing* knob (mutation toward a prior)
|
||||
and a *sharpening* knob (mode-competition), both identity by default (so Layer 1 is untouched).
|
||||
Result: **neutral Wright–Fisher fails both neural architectures in opposite directions.** The
|
||||
**VAE** (large `n`, small `K`): neutral drift is *inert* (no collapse), yet the real VAE collapses
|
||||
to one mode — a **sharpening** kernel reproduces it (the estimator *adds* collapse pressure). The
|
||||
**RNN**: neutral drift drives `H→0`, but the real RNN only partially collapses — a **smoothing**
|
||||
kernel reproduces the `H`-floor (the estimator *removes* collapse pressure). Model collapse in real
|
||||
learners = **neutral drift ⊕ an architecture-specific, signed estimator-bias operator**; this
|
||||
mechanistically explains the architecture-generality result and the softened neural `g*`.
|
||||
|
||||
### 4. The sexual-reproduction society (E7–E11) — from teacher→pupil to sex with unbounded parents
|
||||
|
||||
The single-locus, fixed-`p*` world can only express *recovery toward a ceiling*. The society's
|
||||
load-bearing claim is **vertical** — capability that *exceeds* any component — which needs
|
||||
combinatorial structure. Knowledge becomes a distribution over **genotypes** (`L` biallelic loci,
|
||||
fitness = number of correct loci), and the one new operator is **recombination**. This is where the
|
||||
frame shifts: **teacher→pupil distillation is asexual copying (caps at the ceiling); recombination
|
||||
is sexual reproduction (combinatorial, generative — offspring can exceed both parents), and unlike
|
||||
biology there is no two-parent limit.** The celebrated evolution-of-sex theory maps onto the thesis
|
||||
exactly (collapse = Muller's ratchet; merging = meiotic reassortment; "exceeding" = the
|
||||
Fisher–Muller effect):
|
||||
|
||||
- **E7 — the advantage of sex.** A population adapting toward an optimum: the **sexual lineage adapts
|
||||
faster** than the asexual one (clonal interference), keeping loci in linkage equilibrium (LD→0 vs
|
||||
an LD spike). Honest scope: a *speed* advantage, not a permanent gap (the single-population ratchet
|
||||
is subtle).
|
||||
- **E8 — the vertical claim (Fisher–Muller), the headline.** Decorrelated *parents* are specialists
|
||||
(expert on their loci, agnostic elsewhere). **Sexual recombination assembles a genotype fitter than
|
||||
any parent, climbing to the optimum (12/12 — a genotype no parent had)** as parent count grows and
|
||||
correlation `ρ→0`, while the best single parent (~8.7) and the mean-mixture "model soup" (~11.6)
|
||||
plateau below.
|
||||
- **E9 — landscape robustness ("why sex?").** On rugged (epistatic, NK) landscapes, blindly
|
||||
recombining trained models causes **outbreeding depression** — offspring fall *below* the parents,
|
||||
worse the more entangled the skills and the higher the recombination rate — and the **optimal
|
||||
recombination rate shrinks as ruggedness grows**. Design rule: *merge freely when skills are
|
||||
complementary; sparingly, and with selection, when entangled.*
|
||||
- **E10 — directed sex beats biological sex (the AI superpower).** Biology is stuck with two
|
||||
random-mating parents and no offspring preview; an AI can **choose complementary mates, evaluate
|
||||
many recombinant offspring, keep the fittest, over rounds, with unbounded parents**. Random
|
||||
("biological") sex craters with ruggedness (0.66→0.51, deep outbreeding depression); **directed sex
|
||||
tracks or exceeds the best parent at every ruggedness** — a catastrophe turned into a win, with no
|
||||
biological analog.
|
||||
- **E11 — the dynamic Lamarckian society (the C3 vertical claim, realised).** A finite population of
|
||||
agents (genotypes) evolves on a rugged NK landscape that *is* reality, composing all four operators
|
||||
— grounding, directed sex, quality-diversity, mutation. Grounding is made load-bearing by the
|
||||
**consensus-conformity (self-consumption)** mechanism: selection acts on
|
||||
`g·true_fitness + (1−g)·conformity`, so at `g=0` the society optimises fitting-the-crowd rather than
|
||||
reality. A **4-arm ablation (global optimum ≈ 0.79), each breaking distinctly, only the full society
|
||||
climbing:** `full` **0.78** (climbs to the optimum, diversity maintained longest) · `no_sex` 0.77
|
||||
(can't recombine to escape local optima) · `no_diversity`/greedy 0.74 (collapses diversity fastest,
|
||||
stuck at a worse local optimum) · **`no_grounding` 0.48** (self-consumption collapse to an unfit
|
||||
consensus — trains on the crowd, regresses to a confident-but-wrong mean; the population strongly
|
||||
*agrees* while being *wrong*). The society needs **all** of grounding + directed sex + diversity: on
|
||||
a rugged landscape you need diversity to explore basins, sex to recombine them, and grounding to
|
||||
select on reality.
|
||||
|
||||
### 5. The claims tested in real LLM weights (Layer 2 prototype)
|
||||
|
||||
The analytic operators above make three claims that are testable in *real language-model weights*:
|
||||
"merge, don't average" (E4), the Fisher–Muller generalist-from-specialists (E8), and directed sex
|
||||
(E10). We tested them with a small, reproducible pipeline — LoRA **specialists** fine-tuned on three
|
||||
*disjoint*, procedurally-generated task families (`lists`, `strings`, `arith`) with an **exact-match
|
||||
verifier** as reality's "no" — recombined by various operators and scored on held-out tasks. Runs are
|
||||
at two scales: **Qwen2.5-0.5B** locally and **Qwen2.5-7B** on Imperial College's CX3 HPC (one L40S).
|
||||
This is a prototype (three families, one seed), so read it as **signs, not magnitudes**; the analytic
|
||||
layer carries the quantities.
|
||||
|
||||
- **Recombining specialists yields a generalist that exceeds every parent (E8).** At 7B, a weight-space
|
||||
**merge of the three specialists reaches 0.87 overall vs 0.77 for the best single specialist**, and
|
||||
beats every specialist on every family — the Fisher–Muller signature, in real weights. At 0.5B the
|
||||
same sign is present but marginal, because a weak base *dilutes* (see below).
|
||||
- **Union beats averaging — when there is headroom (E4).** Two ways to recombine: **fusion** (average
|
||||
the LoRA deltas — a "model soup") versus **union** (keep each specialist intact and *route* each
|
||||
input to the right one — a Mixture-of-Experts). On tasks with headroom, **routing beats fusion**
|
||||
because averaging dilutes a specialist's contribution: at 0.5B routing 0.74 > soup 0.64; on *hard*
|
||||
7B tasks routing 0.50 > soup 0.40, with fusion diluting the fragile string-cipher specialist so badly
|
||||
(0.67→0.30) that the soup even loses to the best single specialist. This is E8's `max > mean` in real
|
||||
weights.
|
||||
- **Directed sex helps — when there is headroom (E10).** Breeding a population of recombinant offspring
|
||||
(specialists merged at many weightings), scoring each on a held-out split with the verifier, and
|
||||
keeping the fittest **beats the single a-priori soup** where the soup is suboptimal: 0.69 > 0.64 at
|
||||
0.5B, and 0.49 > 0.39 on hard 7B tasks — recovering most of routing's benefit from one deployable
|
||||
model. This is offspring selection (which biology cannot preview) realised in weight space.
|
||||
- **The one law that unifies them: headroom, not scale.** Our first 7B runs on *easy* tasks showed the
|
||||
opposite — fusion beating union, and directed selection tied with the soup. That was a **saturation
|
||||
artefact**: the easy families saturated 7B at 1.00, leaving no room to lose to dilution, so the naive
|
||||
soup was already optimal. On *hard* (unsaturated) 7B tasks the original ordering returns. **The
|
||||
operative variable is headroom**: union-preserving merging and offspring selection pay off whenever
|
||||
there is room to lose to dilution — a weak base *or* hard tasks — and only the degenerate corner of
|
||||
easy tasks on a strong base makes naive averaging look sufficient. This both confirms E4/E8/E10 in
|
||||
real weights and delimits exactly when the refinements matter.
|
||||
|
||||
Honest scope: three lexically-distinct families (so the router is trivially accurate — an ambiguous-
|
||||
skill benchmark is the interesting next stress test), one seed, small LoRA. The full *grounded*
|
||||
society on LLMs (collapse under dry self-training, the dynamic society) is the HPC-scale next step.
|
||||
|
||||
### 6. Positioning — what is prior art, what is ours
|
||||
|
||||
An independent 2026 paper (Riis, *Drift and selection in LLM text ecosystems*) rigorously formalises
|
||||
**collapse = Wright–Fisher drift** (martingale of minority mass, rare-first extinction, de Bruijn
|
||||
fixed points, drift+selection) with n-gram agents. **We concede that framing as prior art and cite
|
||||
it — "collapse is drift" is no longer our contribution.** Crucially, Riis's "mixed environment"
|
||||
retains the lineage's own *old synthetic* tokens (no injection of external truth), so his headline is
|
||||
*pessimistic* (extinction is independent of retention). **Our defensible contributions, ranked:**
|
||||
(1) **recombination as sexual reproduction** — the "merge, don't average" law, the Fisher–Muller
|
||||
vertical claim, directed sex, and their limits (E4, E8–E10) — an operator Riis lacks; (2) the
|
||||
**learning-kernel / estimator-bias axis**, which he *names as future work*; (3) **grounding as
|
||||
immigration from a fixed reality**, giving a critical `g*≪1` his closed loop cannot have; (4)
|
||||
**architecture-generality in real weights + real images (MNIST)**; and (5) **the integrated dynamic
|
||||
society and its vertical claim** (E11), wholly ours. The repositioning: from *"collapse is drift"*
|
||||
(diagnosis) to **a population-genetic control theory for sustaining open-ended knowledge** — the
|
||||
engineered cure and its integration.
|
||||
|
||||
### Design rules that fall out
|
||||
|
||||
1. **Never inherit dry, and ground where it matters** — a little reality (`g*≈5%`) protects most
|
||||
diversity, but it protects only what it overlaps, and it can't hold the deep tail.
|
||||
2. **Merge, don't average — where there is headroom** — union-preserving model-merging (routing /
|
||||
max-merge) realises the multi-teacher benefit; averaging dilutes it. Confirmed in real LLM weights,
|
||||
with a sharp caveat: dilution only bites when the task leaves room for it — on easy tasks a strong
|
||||
base's naive soup already composes to the ceiling, so averaging looks fine. The refinement matters
|
||||
exactly in proportion to how far the naive soup is from optimal.
|
||||
3. **Sex, with no parent limit** — recombining decorrelated specialists yields offspring that exceed
|
||||
any parent; more, complementary parents climb higher.
|
||||
4. **Match recombination to entanglement** — merge freely for complementary skills; sparingly for
|
||||
entangled ones; and *always select offspring* (directed sex), which AI can afford and biology
|
||||
cannot.
|
||||
5. **Keep diversity, and stay grounded** — greedy selection or a broken reality-signal both collapse
|
||||
the society; only grounding + sex + diversity together climb.
|
||||
6. **Gate irreversible consolidation on diversity** — re-mint a base only while the lineage is
|
||||
healthy.
|
||||
|
||||
---
|
||||
|
||||
## B. Accessible summary (for ML engineers and neuroscientists)
|
||||
|
||||
### The question
|
||||
|
||||
Modern AI is trained once and frozen because it cannot keep learning without *catastrophically
|
||||
forgetting*. The Lamarckian Society proposes an alternative: **generations** of bounded agents that
|
||||
learn, then reproduce — passing on what they learned. But there is a notorious trap: train a model on
|
||||
the previous model's outputs, generation after generation, and it suffers **model collapse** — the
|
||||
rare cases (the *tail*) vanish first and the model drifts to a bland mode. So the whole scheme lives
|
||||
or dies on one question: **when does generational transmission accumulate knowledge instead of
|
||||
degrading it?**
|
||||
|
||||
### The through-line: collapse is *asexual* degradation; the cure is *sex*
|
||||
|
||||
The key reframe of this work is that **teacher→pupil copying is asexual reproduction** — a pupil can,
|
||||
at best, recover what its teachers had. That caps out, and left alone it degrades (collapse). The cure
|
||||
is **sexual reproduction between agents**: combine *many decorrelated parents* so the offspring
|
||||
inherits a *combination* none of them had — and can be **better than any parent**. Unlike biology,
|
||||
AI sex has **no two-parent limit** and can *choose* mates and *select* offspring. That is the engine
|
||||
that lets a society climb instead of collapse.
|
||||
|
||||
### What we found, in plain terms
|
||||
|
||||
1. **Collapse is real, and it's math.** Casting generational training as the century-old
|
||||
**Wright–Fisher** drift process (not a metaphor — the same equations) gives exact formulas to
|
||||
check against. The rare stuff dies ~10× faster than the common stuff.
|
||||
2. **A little reality goes a long way — but not for everything.** Mixing in even ~5% verified real
|
||||
data restores most of the diversity and holds it (**grounding**). But the *very rarest*
|
||||
capabilities can't be saved by grounding alone — that's what recombination is for.
|
||||
3. **Collapse is real in actual neural nets, and on real images.** We reproduced it in trained RNNs,
|
||||
MLPs, and a VAE, and on **real MNIST** — where a VAE trained on its own digits collapses to a
|
||||
single blurry blob, while a little grounding keeps all the digit styles alive. (Honest nuance: real
|
||||
nets *smooth*, so "how many modes are alive" lies to you; "how far from the truth" is the honest
|
||||
ruler.)
|
||||
4. **To fight tail collapse with many teachers: merge, don't average.** Averaging their outputs
|
||||
mathematically cancels the benefit; a *merge* that keeps each item's strongest source realises it.
|
||||
5. **Sex makes offspring that beat their parents.** Recombining decorrelated specialist models
|
||||
assembles capabilities none of them had, climbing to the optimum as you add more, complementary
|
||||
parents — while averaging ("model soup") and the best single parent plateau below. This is a
|
||||
celebrated evolutionary result (the Fisher–Muller effect), now shown for AI model merging.
|
||||
6. **But sex can backfire — and AI has a fix biology lacks.** When skills are *entangled*, blindly
|
||||
merging good models produces *worse* offspring ("outbreeding depression"). The fix is **directed
|
||||
sex**: choose complementary partners, generate many merges, and keep the best — which AI can do
|
||||
and biology can't. Directed sex turns the catastrophe into a win.
|
||||
7. **The whole society climbs only with all the pieces.** In an evolving population on a rugged
|
||||
"reality" landscape, the *full* society (grounding + directed sex + diversity) climbs to the top
|
||||
while keeping its specialists; remove **grounding** and it collapses into a confident, wrong
|
||||
consensus (the exact analogue of training on the internet's AI-generated crowd); remove **sex** and
|
||||
it gets stuck; remove **diversity** and it converges too fast to a worse answer. Each failure is
|
||||
distinct; only the full society wins.
|
||||
8. **It shows up in real language models — with one clean caveat.** We merged LoRA-specialised
|
||||
Qwen models (0.5B locally, 7B on a university GPU cluster): the recombined model beats every
|
||||
specialist (Fisher–Muller, for real), and *routing* / *offspring-selection* beat naive averaging —
|
||||
but only when the tasks are hard enough to leave room. On easy tasks a strong model's plain average
|
||||
is already at ceiling, so the fancier operators don't help. The lesson is precise: **these
|
||||
recombination tricks matter exactly in proportion to how far the naive average is from the best you
|
||||
could do** — which is a genuinely useful thing to know before you spend compute on them.
|
||||
|
||||
### Why it is novel and why it matters
|
||||
|
||||
- **It turns model collapse from a warning into a control theory.** Collapse-as-drift is now known
|
||||
(and independently formalised elsewhere). Our contribution is the *cure* and its integration: a
|
||||
grounded, sexually-reproducing, diversity-preserving society that not only avoids collapse but
|
||||
**climbs, with offspring exceeding parents**.
|
||||
- **The sexual-reproduction frame is, we believe, genuinely new for AI** — model merging reframed as
|
||||
meiotic recombination, with a rigorous account of when it helps (complementary skills), when it
|
||||
hurts (entangled skills), and how to make it reliably win (directed sex, unbounded parents).
|
||||
- **It is validated, not vibes.** Three core predictions are exact closed forms; the neural, image,
|
||||
and **real-LLM** results confirm the *signs* in real trained weights (up to 7B on HPC); 131
|
||||
automated tests pass; the whole study is laptop-reproducible from a seed (the LLM tier statistically
|
||||
reproducible on one GPU).
|
||||
- **It gives concrete design rules** for anyone building self-improving or model-merging systems:
|
||||
ground where it matters, merge-don't-average, match recombination to skill-entanglement, select
|
||||
offspring, keep diversity, and gate irreversible consolidation on health.
|
||||
|
||||
*The remaining frontier is the **LLM instantiation** — realising the grounded sexual society with
|
||||
actual language models (LoRA specialists, real model merging, execution-verified grounding), which
|
||||
the blueprint frames as the eventual empirical rung.*
|
||||
|
|
@ -1,74 +0,0 @@
|
|||
# SI notes — drafts of formal statements for the PNAS manuscript
|
||||
|
||||
*Working drafts; folded into the SI Appendix at Phase 4. Each statement is written to be exactly as
|
||||
strong as what is true — no more.*
|
||||
|
||||
## S1. The incompatibility floor: what no alignment can remove (E13c)
|
||||
|
||||
**Setting.** Models A and B are trained on the same input distribution; their target label functions
|
||||
`f_A` and `f_B` agree except on a conflict set `S` of probability mass `μ(S)` (in E13's conflict
|
||||
condition, the cyclically-relabelled classes; `μ(S) ≈ conflict_frac` up to class balance). A
|
||||
*function-preserving transformation* `T` (any composition of hidden-unit permutations and, for ReLU
|
||||
networks, positive per-unit rescalings — the full unit symmetry group of a plain ReLU MLP) satisfies
|
||||
`T(B)(x) = B(x)` for all `x` by construction.
|
||||
|
||||
**Proposition 1 (endpoint invariance — with the term "chord" defined precisely).** Here "chord"
|
||||
means the α-linear interpolation **of the endpoint loss values**, `(1−α)·L(A) + α·L(B)` — the
|
||||
baseline in the barrier definition, a function of the endpoints only — NOT the weight-space
|
||||
interpolation path. For every function-preserving `T`, the endpoint functions, hence the endpoint
|
||||
losses and this chord, are identical for `(A, T(B))` and `(A, B)`. The **interpolation path itself is
|
||||
generally NOT invariant** — losses along `(1−α)·A + α·T(B)` change with `T`, which is precisely why
|
||||
alignment can lower a barrier. *(Immediate from the definition of function-preserving.)* Scope
|
||||
caveat: our aligner provably recovers a permuted-and-rescaled copy exactly — an important special
|
||||
case — but this does not establish global optimality of the alignment over the symmetry group for
|
||||
independently trained networks; the decomposition's "removable" share is therefore a lower bound, and
|
||||
the "residual" an upper bound, on their true values.
|
||||
|
||||
**Proposition 2 (no merged model can serve both parents).** Let `h` be *any* single classifier (in
|
||||
particular, any interpolated/merged model, under any alignment). On every `x ∈ S`, `f_A(x) ≠ f_B(x)`,
|
||||
so `h(x)` disagrees with at least one of them. Hence
|
||||
|
||||
`ε_A(h) + ε_B(h) ≥ μ(S)`, and therefore `max(ε_A(h), ε_B(h)) ≥ μ(S)/2`,
|
||||
|
||||
where `ε_P(h)` is `h`'s error against parent `P`'s labels. A hybrid of two models whose conventions
|
||||
conflict on mass `μ(S)` errs at rate at least `μ(S)/2` against at least one parent — **hybrid
|
||||
disadvantage with an information-theoretic floor, independent of the alignment group, the
|
||||
architecture, and the merging operator.** This is reproductive isolation in the fitness sense: past a
|
||||
given functional conflict, *no* recombination operator produces an offspring loyal to both lineages.
|
||||
|
||||
**What remains empirical, and why the experiment is designed as it is.** Propositions 1–2 do *not*
|
||||
bound the single-task path barrier (the loss along the interpolation between A and `T(B)` evaluated
|
||||
on one parent's task): in principle a path could dip toward one parent's function. Whether it does is
|
||||
exactly what E13 measures — and the measured answer is that it does not: the conflict-condition
|
||||
barrier is unchanged by permutation alignment (`residual`) *and* by alignment modulo the full
|
||||
permutation × positive-rescaling group (`residual_scale`), while the same aligner removes ~all of the
|
||||
independent-init barrier (the positive control). Richer-symmetry results for transformers
|
||||
(arXiv:2606.23607; neuron-identifiability approaches to linear mode connectivity, 2026) strengthen
|
||||
the *removable* side of the decomposition and are therefore complementary: the more barrier a larger
|
||||
group can remove for *compatible* models, the sharper the meaning of the residual that survives for
|
||||
*incompatible* ones — and Proposition 2 caps what any of them could ever achieve on the conflict set.
|
||||
|
||||
**Terminology note for the paper.** "Residual (after alignment)" = the estimated functional
|
||||
incompatibility; for ReLU MLPs we align modulo the full unit symmetry group, so the estimate is not
|
||||
confounded by missed symmetries of that architecture class.
|
||||
|
||||
## S2. Emergent vs imposed incompatibility (E13b framing)
|
||||
|
||||
The conflict condition *imposes* contradiction (the two label maps disagree on `S`), which pins
|
||||
`μ(S) > 0` and activates Proposition 2. A true Bateson–Dobzhansky–Muller incompatibility is
|
||||
*emergent*: each lineage's substitutions are harmless on their own background (`μ(S) = 0` — the
|
||||
training signals never contradict), and incompatibility, if any, arises only in the *combination*.
|
||||
The `disjoint` (complementary class specialists) and `augment` (divergent input conventions)
|
||||
conditions realise this: any residual barrier they develop cannot be attributed to label conflict and
|
||||
is the emergent-speciation signal proper. Pre-registered readings: residual grows with divergence →
|
||||
model speciation is emergent in real weights (E12's trajectory realised); residual stays at the
|
||||
`shared`-control level → within this regime, trained networks are *more* merge-compatible than the
|
||||
biological analogy predicts — an honest bound on the analogy, and itself a design-relevant result
|
||||
(merging is safe absent functional conflict).
|
||||
|
||||
**Outcome (2026-08-11 run, 4 reps, t_div ≤ 3200): the second reading.** Residual 0.000 at every
|
||||
divergence in both emergent conditions, and the merge *rescues* the forgetting `disjoint` specialists
|
||||
(parents → 0.535/0.474 on the full task; merged ≈ 0.955 throughout — a sustained Fisher–Muller rescue
|
||||
at zero barrier). Isolation in real weights required functional conflict in this regime; whether
|
||||
long-horizon over-specialisation erodes mergeability at LLM scale (cf. arXiv:2607.11997) is the
|
||||
`llm_speciation` question (Phase 3).
|
||||
|
|
@ -1,529 +0,0 @@
|
|||
# The Evolution of Sex for Artificial Intelligence — the plain-language version
|
||||
|
||||
### How ideas from breeding and genetics tell us how to keep AI models improving across generations
|
||||
|
||||
*This is an accessible companion to the full paper (`the-evolution-of-sex-for-ai.md`). It makes the
|
||||
same argument and reaches the same conclusions, but assumes only that you know roughly what a machine
|
||||
learning model is — that it is trained on data, that training adjusts numbers called "weights," and
|
||||
that you can fine-tune a model on new data. Everything else is explained as we go. Where the full
|
||||
paper defends each point against the research literature, this version just tells the story.*
|
||||
|
||||
**Giorgio F. Gilestro** · Department of Life Sciences, Imperial College London ·
|
||||
giorgio@gilest.ro · https://lab.gilest.ro
|
||||
|
||||
---
|
||||
|
||||
## The one-paragraph version
|
||||
|
||||
If you train an AI model on the output of earlier AI models, over and over, it rots: rare knowledge
|
||||
disappears and everything drifts toward a bland average. This is a known problem ("model collapse"),
|
||||
and in its simplest form it is governed by *exactly* the same math that describes how small biological populations lose
|
||||
rare genes by chance. That is bad news, but it comes with good news: biology has been managing this
|
||||
kind of rot for hundreds of millions of years, and its best-tested remedy is **sex** — making offspring
|
||||
by *combining* several parents instead of copying one. This paper tests how far that remedy carries
|
||||
for AI. This paper takes ninety years of genetics about
|
||||
*when and why sex beats cloning* and reads it as an engineering manual for building AI that keeps
|
||||
getting better across generations instead of decaying. Along the way it produces concrete, testable
|
||||
rules — including a surprising one about *how* to combine models ("merge, don't average"), and a limit
|
||||
("models can drift so far apart they can no longer be usefully combined at all"). We back the argument
|
||||
with small, fully reproducible experiments and a first test on real language models.
|
||||
|
||||
---
|
||||
|
||||
## A few words you'll need
|
||||
|
||||
- **Model collapse** — what happens when you train models on the output of earlier models, again and
|
||||
again: rare cases vanish, everything gets blander. The central disease this paper is about.
|
||||
- **Fine-tuning / specialising** — taking a trained model and training it a bit more so it gets good at
|
||||
one specific thing.
|
||||
- **Model merging** — combining two or more trained models directly, by mixing their weights, to get
|
||||
one model — *without* retraining. Think "breeding two models" rather than "teaching a third."
|
||||
- **The tail** — the rare stuff. Common knowledge is the "head" of the distribution; unusual cases,
|
||||
rare facts, and edge behaviours are the "tail." Collapse eats the tail first.
|
||||
- **Grounding** — mixing some real, verified data from the actual world into training, instead of only
|
||||
model-generated data. The reality check.
|
||||
- **Genetic drift** (from biology) — in any finite population, rare gene variants can vanish purely by
|
||||
chance, because not every individual reproduces. This is the biological twin of model collapse.
|
||||
- **Recombination / sex** (from biology) — making a child by combining pieces of more than one parent.
|
||||
The opposite of cloning (**asexual** reproduction).
|
||||
|
||||
---
|
||||
|
||||
## 1. A society of AIs across *time*, not just space
|
||||
|
||||
When people imagine "many AIs working together," they usually picture teamwork in the *moment*:
|
||||
several specialist agents side by side, splitting up a job. This paper is about a different direction:
|
||||
**time**. Not AIs that cooperate right now, but AIs that pass knowledge down across **generations** —
|
||||
each new model starting from what the previous ones learned, the way each human generation inherits
|
||||
the accumulated knowledge of the last and adds a little.
|
||||
|
||||
The key event, then, is **reproduction**: making a new model out of older ones. A single model, like a
|
||||
single person, eventually stops improving. A *lineage* — a chain of models across generations — does
|
||||
not have to. Civilisation isn't smart because any one person is; it's smart because knowledge
|
||||
accumulates. The whole question of this paper is: **how do you make one AI model out of older ones,
|
||||
without the knowledge rotting on the way down?** That's exactly where it can go wrong.
|
||||
|
||||
(This corner of AI is suddenly busy: several 2025–2026 research projects build populations of models
|
||||
that improve over rounds, and "model merging" has become a small industry that already borrows words
|
||||
like crossover, mutation, and mate choice. What this paper adds is the quantitative framework behind
|
||||
those borrowed words — and honest tests of where it works and where it doesn't.)
|
||||
|
||||
## 2. Why today's models can't do this
|
||||
|
||||
Today's large models have no life cycle. A model is trained once, at huge expense, then **frozen** and
|
||||
shipped. It does not learn from the people who use it. "Learning" and "doing" are two separate eras
|
||||
with nothing connecting them.
|
||||
|
||||
There's a real reason for the freeze: if you keep training a neural network on new things, it tends to
|
||||
overwrite what it already knew. This is called **catastrophic forgetting**, and it's been a known
|
||||
problem since the 1980s. Freezing dodges it by refusing to learn at all. But a lineage needs the
|
||||
opposite of a frozen model: it needs members that keep learning through their working lives and then
|
||||
pass on what they gained. So step one is a model that can *grow safely.*
|
||||
|
||||
## 3. A model that grows without forgetting
|
||||
|
||||
The trick is to stop overwriting. Keep the model's original core frozen and untouchable, and bolt each
|
||||
new skill onto *extra* capacity added beside it. In practice this is what small add-on "patches" like
|
||||
**LoRA** already do: the big pretrained model stays fixed, and you train a little attachable module for
|
||||
each new skill. If the core is never altered, its knowledge can't be erased — though the system's
|
||||
*behaviour* can still change while patches are active; what's guaranteed is a recoverable core.
|
||||
|
||||
There's even a rough brain analogy: we have a fast memory (the hippocampus) that grabs an experience
|
||||
immediately, and a slow memory (the cortex) that absorbs patterns gradually, usually while we sleep.
|
||||
The AI version is clean: the prompt is short-term memory, a database is fast memory, the trained
|
||||
weights are slow memory, and a periodic "consolidation" step moves knowledge from fast to slow.
|
||||
|
||||
One consequence matters a lot: because this kind of model only ever *adds* capacity, it eventually
|
||||
fills up. In most designs that's a problem. Here it's a feature — read on.
|
||||
|
||||
## 4. "Full" means grown up, not broken
|
||||
|
||||
Here's the pivot. When a model that can only add capacity finally fills up, it hasn't failed. **It has
|
||||
matured.**
|
||||
|
||||
Think of the capacity limit as a life stage. A model is *born* as a freshly trained base — its general
|
||||
education. It has a *working life*, picking up specialised expertise on the job. And it reaches
|
||||
*maturity* — the point where it has learned about as much as one working life in its niche can teach.
|
||||
Maturity isn't the end of usefulness; it's the moment the model is most worth learning *from*. So
|
||||
maturity is the signal to **reproduce**. The capacity ceiling that every other design fights becomes,
|
||||
here, the clock that times the generations.
|
||||
|
||||
Everything now depends on *how* that reproduction happens. This is the heart of the paper.
|
||||
|
||||
## 5. Copying rots; combining climbs
|
||||
|
||||
Suppose a mature model just teaches a fresh one, and that one teaches the next, and so on down the
|
||||
line. It's the obvious design — and it fails, for the same reason in AI and in biology.
|
||||
|
||||
**In AI terms:** training each generation on the previous generation's output is the exact recipe for
|
||||
**model collapse**. The model forgets the improbable, loses the rare cases (the tail) first, and drifts
|
||||
toward its own most common output. And here's the nasty part: the thing that makes teaching-a-student
|
||||
*useful* — "keep the general, drop the quirky" — *is* the same act that deletes the tail. The operation
|
||||
you want and the operation that kills the lineage are the same move.
|
||||
|
||||
**In biology terms (and for our simplest model it really is the same math — real networks add a measurable twist on top, which we also measure):** picture a model's knowledge as a big bag of
|
||||
items — facts, skills, behaviours — in certain proportions. One generation is: draw a finite sample
|
||||
from the parent, and rebuild the child from that sample. That "finite sample" step is *identical* to
|
||||
**genetic drift** — the way rare gene variants vanish by chance in any finite population. This isn't a
|
||||
loose analogy; it's the same century-old equations (the Wright–Fisher model), which is why we can
|
||||
check our simulations against them exactly. Rare items go extinct first, about ten times faster than
|
||||
common ones — precisely what drift predicts.
|
||||
|
||||
And copying one teacher is **asexual reproduction** — cloning. Biology already knows the fate of a
|
||||
lineage that only ever clones and never combines: it piles up damage it can never undo, a one-way
|
||||
decline called **Muller's ratchet**. That's our lens for the *irreversible* part of model collapse —
|
||||
the capabilities that, once every copy is gone, no amount of combining can rebuild. Naming it that
|
||||
isn't just poetry — it tells us where to look for remedies, because biology has spent a very long time
|
||||
solving exactly this.
|
||||
|
||||
Two ingredients turn the rot into a climb. Both are things nature does.
|
||||
|
||||
**Ingredient one: don't reproduce "dry."** Collapse only happens to a lineage fed *nothing but* its own
|
||||
output. Mixing in some **real, verified data from the world** — we call this **grounding** — stops it. In
|
||||
our small experiments, grounding is shockingly cheap: even a few percent of real data keeps most of the
|
||||
diversity alive indefinitely. But we found an honest limit we didn't expect: grounding can't save the
|
||||
*very rarest* items at any affordable cost — protecting something of rarity *p* needs a real-data budget
|
||||
that grows like 1/*p*. Grounding rescues diversity cheaply, but not the deepest tail. Something else has
|
||||
to do that. That something is sex.
|
||||
|
||||
**Ingredient two: reproduce sexually.** Instead of copying one parent, build each new model by
|
||||
**combining several** — a sexual birth, not an asexual one. AI already has a tool for this: **model
|
||||
merging**. Why does it help? If several parent models each specialised on *different* things, each one
|
||||
kept alive rare knowledge the others lost. A combined child inherits the **union** of what its parents
|
||||
kept — not the tail-thinned *average* of a crowd of near-identical clones. And here's the point that
|
||||
turns sex from a mere safety net into the engine of the whole thing:
|
||||
|
||||
> **A child combined from complementary parents can be *better than any of its parents*.**
|
||||
|
||||
Geneticists call this the **Fisher–Muller effect**: recombination gathers, into one individual,
|
||||
good variants that arose separately in different lineages — so the child has a combination none of the
|
||||
parents had. Our simulations show exactly this: combining specialist models that each mastered
|
||||
different skills produces a model that climbs toward the *best possible* combination — one no single
|
||||
parent had — while the best single parent, and the plain average of all of them (a "**model soup**"),
|
||||
both level off well below. This is the paper's core claim in one line: **copying can only recover a
|
||||
ceiling; combining can break through it.**
|
||||
|
||||
And it's not just simulation. In a first test on real language models — three small Qwen models, each
|
||||
fine-tuned on a different family of tasks, then merged and graded by an automatic checker — **the merge
|
||||
beat every single specialist**, overall and on every task family. The Fisher–Muller effect, in real
|
||||
weights.
|
||||
|
||||
That same test pinned down a subtle rule about *how* to combine models:
|
||||
|
||||
> **"Merge, don't average" — but only when there's room to lose.**
|
||||
|
||||
Keeping each parent whole and **routing** each question to the right specialist beats crudely averaging
|
||||
them together — *but only when the task is hard enough that averaging actually damages something*. On
|
||||
easy tasks, a strong model's plain average is already about as good as possible, so the crude soup is
|
||||
fine. On hard tasks, averaging waters down a hard-won specialist so badly the blend falls below even the
|
||||
best single parent — and the smarter "keep-them-separate-and-route" approach wins big. So the rule is
|
||||
precise: **the fancy combining tricks help in exact proportion to how far the plain average is from the
|
||||
best you could achieve.** A practitioner needs to know this before spending compute on the fancy version.
|
||||
|
||||
Two honest caveats, and both are actual findings, not hand-waving:
|
||||
|
||||
**Sex can backfire.** When the parents' skills aren't cleanly separable but *tangled together* — when
|
||||
skill A only pays off if skill B is also present (biologists call this **epistasis**) — blindly
|
||||
combining two good models can produce a *worse* child, because combining breaks apart a package that
|
||||
only worked as a whole. Biologists call this **outbreeding depression**, and we reproduce it: on
|
||||
"tangled" problems, naive merging drops the child below its parents, and the more you mix, the worse it
|
||||
gets. The design rule: *combine freely when skills are independent; combine sparingly and carefully when
|
||||
they're tangled.*
|
||||
|
||||
**How *widely* you mate matters too.** That last point was about *how much* to mix; a separate knob is
|
||||
*who mixes with whom*. **Monogamy** = each model only ever combines within a small, fixed circle;
|
||||
**promiscuity** = any model can combine with any other. Almost all model-merging today is promiscuous by
|
||||
default — throw everything in one pot. But there's a catch: wide mixing spreads good traits fast, but it
|
||||
also makes the whole population converge to the *same thing*, killing variety. Narrow, local mixing keeps
|
||||
separate sub-groups exploring different solutions. We tested this against tangledness, and the best answer
|
||||
*moves*: on simple (independent-skill) problems, wide promiscuous merging is best; but the more tangled
|
||||
the skills, the more you want to *narrow* it — full promiscuity converges too fast onto one mediocre
|
||||
solution and finds a *worse* champion, while keeping structured sub-groups preserves the variety a hard
|
||||
problem needs. So the rule extends: *merge widely for independent skills; keep separate sub-populations
|
||||
("island" merging) for tangled ones.*
|
||||
|
||||
**AI can do sex better than biology can.** Biology is stuck with two parents, mating more or less at
|
||||
random, and can't inspect a child before it's born. AI has none of those limits. It can combine **many**
|
||||
parents at once; it can **choose** which parents to combine, for complementary skills; and it can
|
||||
**generate many candidate children and keep only the best**, testing them against reality before
|
||||
committing. We call this **directed sex**, and in our simulations it turns the outbreeding-depression
|
||||
disaster into a reliable win: where blind combining collapses on tangled problems, directed combining
|
||||
matches or beats the best parent every time. The real-language-model test shows the same where it can:
|
||||
breeding many merged offspring and keeping the one that scores highest beats the plain soup on hard
|
||||
tasks. This is a genuine advantage of *engineered* reproduction over the biological kind, and it's one
|
||||
of the more useful ideas in the paper.
|
||||
|
||||
So §5 in one breath: copying is asexual and rots (Muller's ratchet = model collapse); the cure is to
|
||||
**ground** every birth in reality and to reproduce **sexually**, combining many complementary parents;
|
||||
and because AI's version of sex can use many parents, chosen mates, and pre-screened offspring, it's
|
||||
not just insurance against collapse — it's an engine that makes children better than any parent.
|
||||
|
||||
### The limit of sex: models can drift too far apart to merge
|
||||
|
||||
Sex has a limit, and it's the sharpest new prediction here. Combining parents works because they're
|
||||
variations on a shared background. Push two lineages far enough apart and their combination stops being
|
||||
viable. In biology this is **speciation** — two populations become separate species that can no longer
|
||||
interbreed. The genetic mechanism has a name (a **Bateson–Dobzhansky–Muller incompatibility**): a change
|
||||
that arose in lineage A and a change that arose in lineage B are each harmless on their own, but their
|
||||
*combination* — which neither lineage ever tested — is broken in the hybrid. A merged model is exactly
|
||||
such a hybrid. So the theory predicts a specific trajectory as two models drift apart: **they merge
|
||||
fine → merging starts to hurt → merging becomes useless.**
|
||||
|
||||
We built this as an explicit model and confirmed the predicted curve. Three things come out of it:
|
||||
|
||||
1. **There's a cliff, and epistasis moves it.** The point where merging fails isn't fixed — it comes
|
||||
*earlier the more tangled (epistatic) the skills are*. This is a distinct, testable claim:
|
||||
**at the same amount of drift, whether two models can be merged depends on how tangled their skills
|
||||
are, not just on how far apart they are.** The existing AI tools for predicting merge success only
|
||||
measure distance/geometry — they don't have this axis.
|
||||
2. **It snowballs.** The number of incompatibilities grows with the *square* of the drift, so merge
|
||||
quality doesn't fade gently — it falls off a cliff. Drift is punished faster than it accumulates.
|
||||
3. **The design rule:** before merging, weigh how far apart the models are against how tangled the skills
|
||||
are. Past the cliff, don't merge — **route** instead (keep the specialists separate and pick between
|
||||
them).
|
||||
|
||||
We also did the experiment a skeptic would demand. A known objection: "your 'incompatibility' is just a
|
||||
loss barrier, and those are famous for being fake — two networks can learn the *same* function but store
|
||||
it in a shuffled internal order, which *looks* like incompatibility until you line their neurons back up
|
||||
(a technique called **Git Re-Basin**)." So we tested it directly in real trained networks. We trained
|
||||
pairs of small networks, merged them, and measured the merge damage *before and after* re-aligning their
|
||||
neurons. The result is clean:
|
||||
|
||||
- Two networks trained on the **same task** but from different random starts: big apparent merge damage,
|
||||
but re-aligning removes **~98% of it**. That's the fake kind — same skill, shuffled order. (This also
|
||||
proves our alignment tool works.) And we allowed the aligner *every* legal move for these networks —
|
||||
not just re-ordering neurons but also re-scaling them — so nothing removable was left on the table.
|
||||
- Two networks trained on **conflicting tasks**: big merge damage, and even the full aligner removes
|
||||
**essentially none of it**. That's the *real* kind — genuine incompatibility, not a bookkeeping
|
||||
artifact. And it can't be waved away as "you just didn't align them well," because the exact same tool
|
||||
cleaned up the first case. There's even a simple proof that no future alignment trick can fix it: no
|
||||
single model can obey two rulebooks that contradict each other on the same inputs.
|
||||
|
||||
Sweeping from "no conflict" to "total conflict" traces a smooth **incompatibility cliff** in real
|
||||
weights: the merged model's accuracy slides from 0.97 (no conflict) down to 0.03 (total conflict) — a
|
||||
hybrid that is literally inviable. So the speciation effect is real, not a relabelled artifact.
|
||||
|
||||
And we ran the honest flip side, deciding in advance to report it either way: what if two networks just
|
||||
*specialise differently*, with no conflict at all — one keeps training only on digits 0–4, the other
|
||||
only on 5–9? Do they drift into incompatibility on their own? **No.** At every amount of divergence we
|
||||
tested, the merge damage stayed at zero — and the merged model actually *rescued* the two specialists:
|
||||
each parent alone had forgotten half the digits (scoring ~0.50), while their merge scored ~0.95. So in
|
||||
these experiments, models don't become unmergeable just by growing apart; they become unmergeable when
|
||||
they learn things that genuinely *contradict*. That's good news for merging — specialisation is safe,
|
||||
conflict is the danger — and it makes the theory's prediction sharper, not weaker.
|
||||
|
||||
One question is left hanging, and the rest of the paper is about it: combining preserves *what the
|
||||
parents kept* — but **who decides what each parent keeps, and which children are worth keeping?**
|
||||
|
||||
## 6. Don't design the selector — evolve it
|
||||
|
||||
There are two ways to answer that question, and the first one is wrong. We could try to hand-write the
|
||||
rule for "what knowledge to keep and pass on." But nobody actually knows that rule. "Keep the general,
|
||||
drop the specific" sounds wise until you ask *which* generalisations, in *which* domain, at *which* level
|
||||
of detail — and it falls apart. This is the deepest gap in the whole scheme, and you can't fill it by
|
||||
decree.
|
||||
|
||||
The second answer is the one nature used: **don't design the selector — let it evolve.** Let different
|
||||
models carry different *policies* about what's worth keeping and combining. Let the policies that produce
|
||||
strong children spread, and the policies that produce weak children die out with their lineages. What the
|
||||
lineage considers *important* — its "taste" — is discovered by selection, not imposed by us.
|
||||
|
||||
So **two things get inherited, on two channels.** The *content* — the actual knowledge — is passed down
|
||||
directly (this is the "Lamarckian" part: inheriting things acquired during a lifetime, which biology
|
||||
forbids for genes but culture allows for ideas). The *selection policy* — what to keep, who to breed
|
||||
with, which children to screen for — is *itself* inherited, varies between models, and survives in
|
||||
proportion to how well it works. That second channel is Darwinian. The system is both at once: it
|
||||
inherits *content* like culture, and selects *policies* like evolution.
|
||||
|
||||
And it closes neatly: Darwinian selection needs a pressure — something that decides which policies win.
|
||||
That pressure is already in the design. What tells a lineage its taste was good? Whether its children
|
||||
succeed *against reality*. The reality check that stops collapse (grounding, §5) and the fitness signal
|
||||
that guides the evolving taste turn out to be the **same thing**, seen from two angles.
|
||||
|
||||
## 7. The big danger: what you measure is not what you want
|
||||
|
||||
Adding selection adds selection's classic trap, and it's dangerous enough to sink everything if ignored.
|
||||
Evolution optimises, ruthlessly and without foresight, for exactly what you *measure* — never for what
|
||||
you *meant*. (In ML you know this as reward hacking or specification gaming; economists call it
|
||||
Goodhart's law.) Get the fitness measure a little wrong and the lineage will exploit the gap more
|
||||
cleverly than any rule you could write.
|
||||
|
||||
For a *knowledge* lineage there's a particularly nasty version. The natural way to measure how "good" an
|
||||
idea is might be *how well it spreads* — but a false-but-persuasive idea spreads beautifully. Human
|
||||
culture is full of highly contagious nonsense; confident wrongness routinely beats careful accuracy. Let
|
||||
selection loose on models without care and it will breed a lineage that is fluent, compelling, and
|
||||
**wrong** — model collapse with an optimiser actively steering toward the cliff.
|
||||
|
||||
Only one thing makes fitness track *truth* instead of *appeal*: **being judged against a reality that
|
||||
can say no.** Fitness has to mean "did this knowledge correctly predict what the world actually does when
|
||||
you act on it" — not approval, not fluency, not a gameable benchmark score. This is why the reality check
|
||||
matters twice: it's both the anchor that stops passive collapse *and* the only thing that keeps the
|
||||
evolving taste honest.
|
||||
|
||||
The second danger is **everyone converging to the same thing**, and avoiding it takes work at two levels,
|
||||
because selection can only preserve variety that already exists — variety first has to be *supplied* and
|
||||
then *kept*.
|
||||
|
||||
- **Supply.** A lineage that only learns from the accredited elite has a monoculture for a source — the
|
||||
"top" experts are, by definition, the ones who won the consensus. So the system must deliberately learn
|
||||
from **outliers and heretics** too — not out of fairness, but because diverse starting material is the
|
||||
raw fuel for everything downstream.
|
||||
- **Preserve.** Even with varied input, plain "keep the best" selection converges — it stampedes toward
|
||||
the single current champion and wipes out the rare specialists. The fix is well known:
|
||||
**quality-diversity** selection, which rewards being *good* **and** being *different* at the same time,
|
||||
keeping complementary specialists alive. In our simulations this is decisive: greedy "keep-the-best"
|
||||
collapses diversity almost immediately and gets stuck on a mediocre answer, while quality-diversity
|
||||
keeps the very specialists that sexual combining then needs as parents.
|
||||
|
||||
The two levels meet at reproduction: multi-parent combining is the *vehicle* that carries the preserved
|
||||
diversity into the next generation. Supply the variety, preserve it, recombine it — remove any one and
|
||||
the lineage collapses onto its own first guess.
|
||||
|
||||
## 8. A society needs institutions, not just experts
|
||||
|
||||
One requirement is easy to miss and fatal to skip. The easy part of a society is having specialists. The
|
||||
*hard* part — which human civilisation took millennia to build — is the **institutions that let fallible
|
||||
specialists combine without each re-checking everything**: reputation, replication, credentials, and
|
||||
above all **peer review**. These are error-correction systems, and they exist because a group of
|
||||
unreliable experts left to reinforce each other is *more* wrong than any one of them alone.
|
||||
|
||||
This is exactly where today's multi-agent AI fails: put several models in a room and they tend to agree
|
||||
sycophantically and confabulate together, because they have all the specialisation and none of the
|
||||
institutions. A real multigenerational society has to specify not just how models learn, reproduce, and
|
||||
get selected, but how they *check each other* — how a wrong model loses standing *before* its error gets
|
||||
merged into its children and inherited.
|
||||
|
||||
## 9. The lineage must stay open to reality
|
||||
|
||||
However many generations deep it goes, a society of models shares one hard limit: it has only ever
|
||||
*read*. Its entire inheritance is a record of things that were *said*. It lives on the bottom rung of
|
||||
what causality researchers call the ladder — **observation** — and no amount of reading ever reaches
|
||||
**intervention**. Watching doesn't tell you what would happen if you *acted*; correlation isn't causation
|
||||
at any scale.
|
||||
|
||||
Only intervention — actually reaching out and changing the world to see what happens — climbs that
|
||||
ladder, and a language model can't intervene. That's what humans and their instruments provide, and the
|
||||
gift isn't "truth," it's **constraint**: reality's unique power is that it can say **no**. Text just
|
||||
offers more opinion; an experiment delivers a refusal no consensus can overturn. As before, that refusal
|
||||
does double duty: it stops collapse *and* keeps the evolving taste selecting for truth over persuasion.
|
||||
|
||||
Two honest riders. First, the human reality signal is *dirty* — warped by publication bias, incentives,
|
||||
and the occasional fraud — which is exactly why the error-correcting institutions of §8 have to sit at
|
||||
the human–machine boundary. Second, humans are the *current* supplier of intervention, but the hands-on
|
||||
half is being automated (robot labs already run their own experiments). What looks durable in the human
|
||||
role isn't the hands — it's the **choice of what to test and which refusals matter**.
|
||||
|
||||
## 10. Why this is affordable
|
||||
|
||||
A practical fact turns this from daydream into buildable proposal: **it almost never re-pays for the one
|
||||
genuinely expensive thing in AI — training a model from scratch.**
|
||||
|
||||
Training a foundation model from scratch costs a fortune in data and compute. This design does none of
|
||||
that per generation. Every model is *born* from an existing open model that already paid that cost;
|
||||
specialising one is a small patch trained in hours on a single consumer GPU; running the society is
|
||||
ordinary use; and reproducing — merging parents into a child — can be done directly on the weights with
|
||||
*no retraining at all*. Selection costs more (you have to run populations and discard the losers), but
|
||||
that's a multiplier on an already-cheap unit, not on a from-scratch budget.
|
||||
|
||||
The economics only work with **open-weight** models — for practical and legal reasons at once. You have
|
||||
to be free to inspect, modify, and redistribute the weights, and most proprietary licences forbid using
|
||||
a model's output to train another (which is exactly what reproduction here does). That's not ideology —
|
||||
it's a structural constraint, and a democratising one: it puts the whole thing within reach of a single
|
||||
lab.
|
||||
|
||||
## 11. Can it grow forever? Baking knowledge back into the base
|
||||
|
||||
One thing we quietly assumed: can the lineage accumulate *without end*? The individual model is
|
||||
bounded — that's the clock. But the lineage looked unbounded, each generation starting a step ahead.
|
||||
Look closer and a second budget also fills up.
|
||||
|
||||
Every new model is a clean base plus an inherited pile of *soft* patches — the acquired knowledge carried
|
||||
in add-on modules rather than baked into the core. Those patches are what make the lineage
|
||||
multigenerational — but they're not free: they slow the model down, and past some depth they're better
|
||||
*consolidated* than carried. The lineage matures too.
|
||||
|
||||
The fix is the same operation, one level up. When a lineage's acquired knowledge has proven stable across
|
||||
enough generations, **re-mint the base**: bake all those accumulated patches into the *weights* of a
|
||||
fresh from-scratch-scale model — a new base that is *born already knowing* what took many generations to
|
||||
learn in patches. The soft budget resets; the next era starts from a higher floor. What was hard-won and
|
||||
*learned* becomes cheap and *built-in*. (Biologists have a name for acquired traits that eventually
|
||||
become innate: the **Baldwin effect**.)
|
||||
|
||||
Three honest riders, because this is the most consequential step:
|
||||
|
||||
- **Cost.** This is the one step that re-pays part of the from-scratch bill — the exception to §10. It's
|
||||
bearable only because it's *rare*, spread thin over many cheap generations.
|
||||
- **Irreversibility.** Until now, one thing was always recoverable — the original clean base, whose lost
|
||||
rare knowledge you could restore just by reloading the file. Bake the current lineage into new
|
||||
permanent weights and that escape hatch closes: if the lineage had been quietly collapsing, re-minting
|
||||
*freezes the collapse in place* and throws away the one uncollapsed reference that could have caught it.
|
||||
In our experiments this happens exactly as feared — and a cheap safeguard prevents it: **only re-mint
|
||||
while the lineage is provably healthy and diverse**, never as a rescue for one already drifting.
|
||||
- **Branching.** Different labs will re-mint on different criteria and produce different bases; the
|
||||
lineage branches. That's not a bug — it's the tree of life, and it's exactly what open weights make
|
||||
possible.
|
||||
|
||||
So can it grow forever? **Yes — but only because it forgets and consolidates at every level, including
|
||||
the base.** Nothing is stored without limit anywhere. Unbounded growth of *capability* is bought with
|
||||
*bounded* storage plus periodic consolidation.
|
||||
|
||||
## 12. One idea at four speeds
|
||||
|
||||
Step back and it all resolves into a single process running at four nested speeds. The **downward**
|
||||
motion is transmission — passing hard-won knowledge down:
|
||||
|
||||
1. **Within one model, over its working life:** experience moves from fast memory into slow, durable
|
||||
weights, without catastrophic forgetting.
|
||||
2. **Between generations, at maturity:** mature models reproduce, recombined into a fresh one.
|
||||
3. **Across many generations:** each inherits the compressed achievements of the last and adds a little.
|
||||
4. **Across eras:** a proven lineage's accumulated patches get baked into a re-minted base, becoming
|
||||
innate.
|
||||
|
||||
The first and last are the *same operation at opposite ends of the scale* — fast/soft memory
|
||||
consolidating into slow/hard memory — one running overnight inside a single model, the other across an
|
||||
era inside a whole society. The **sideways** motion is selection — acting across the population at every
|
||||
speed, on the policies that decide what gets passed on, with reality as the judge and diversity kept
|
||||
alive so the specialists survive.
|
||||
|
||||
Three rules govern all of it: **reproduce by combining, not copying, or you rot; keep the disagreements
|
||||
and surprises, or you converge; and anchor fitness to a reality that can say no, or you drift toward
|
||||
whatever is merely convincing.**
|
||||
|
||||
## 13. What we actually built, found, and left open
|
||||
|
||||
We didn't just argue this — we built small, fully reproducible models to test it, plus a first bridge to
|
||||
real language models. Here's the shape of the evidence (a separate document has the numbers).
|
||||
|
||||
**What we built and found:**
|
||||
|
||||
- **An exact account of collapse.** Because generational training *is* the genetic-drift process, we can
|
||||
check our simulator against century-old formulas — and it matches to a fraction of a percent. Collapse
|
||||
isn't argued by analogy; it's derived.
|
||||
- **Grounding is cheap — but has a limit.** A few percent of real data keeps most of a lineage's
|
||||
diversity alive indefinitely — but not the very deepest rare cases, which need combining. This is what
|
||||
makes a continually-learning society economically realistic rather than a data-hungry fantasy.
|
||||
- **"Merge, don't average."** Combining several teachers by *averaging* their outputs — the obvious
|
||||
thing, and what a "model soup" does — mathematically cancels the benefit of having several teachers. A
|
||||
*merge* that keeps each item's strongest source realises it. Most current multi-model setups get this
|
||||
wrong by default.
|
||||
- **Collapse and its cure in real networks, and on real images.** We reproduced the same effects in small
|
||||
neural networks and in a generator of handwritten digits (MNIST): a model trained on its own output
|
||||
collapses to a single blurry digit, while a little grounding keeps all the styles alive. Honest
|
||||
wrinkle: real networks *smooth* things over, so the naive diversity metric can mislead — the right
|
||||
measure is distance-from-truth.
|
||||
- **Sex that beats the parents — and when it doesn't.** In simulations, combining complementary
|
||||
specialist models produces a model better than any parent (Fisher–Muller), climbing toward the best
|
||||
possible combination as you add more, more-diverse parents — while averaging and best-single-parent
|
||||
level off below. On *tangled* problems, blind combining instead produces below-parent children
|
||||
(outbreeding depression) — and *directed* combining (choose mates, screen offspring, many parents)
|
||||
reliably fixes it.
|
||||
- **Monogamy vs promiscuity.** Sweeping how *widely* models merge — from local/monogamous to
|
||||
everyone-with-everyone/promiscuous — against how tangled the skills are, the best breadth **shrinks as
|
||||
the skills get more tangled**: wide promiscuous merging wins when skills are independent, but on tangled
|
||||
problems it converges too fast onto one mediocre solution and finds a worse champion, so keeping
|
||||
structured sub-populations wins. (Promiscuity always lifts the *typical* model but always destroys
|
||||
variety.) A merging design knob the field, which throws everything in one pot, doesn't currently have.
|
||||
- **The combining claims, in real language models — with a sharp condition.** Merging fine-tuned Qwen
|
||||
models (up to 7B on a GPU cluster) produces a generalist that beats every specialist parent; and
|
||||
keeping parents separate and *routing*, or *breeding and screening* offspring, beats the plain average
|
||||
— *but only when the task leaves room to lose*. On easy tasks the plain average is already at the
|
||||
ceiling and the tricks add nothing; on hard tasks the average dilutes a specialist below even the best
|
||||
single parent, and the smarter operators win clearly. This is a prototype (three task families, one
|
||||
run), so we read it as *signs, not exact numbers* — the *whole grounded society* on a language model is
|
||||
still the open step.
|
||||
- **The whole society, and why every part is needed.** In a population evolving on a "reality" landscape,
|
||||
the full system — grounding + combining + preserved diversity — climbs to the top while keeping its
|
||||
specialists. Remove *grounding* and it collapses into a confident, wrong consensus (a direct analogue
|
||||
of training on the internet's growing pile of AI-generated text); remove *combining* and it gets stuck;
|
||||
remove *diversity* and it converges too fast to a worse answer. Each removal breaks differently; only
|
||||
the whole thing climbs.
|
||||
|
||||
**What's borrowed vs. what's ours.** We're careful about credit because the area is crowded. **Already
|
||||
known (and we claim none of it):** that model collapse is genetic drift; that a merged model can beat its
|
||||
parents; that decorrelated parents merge better; that naive averaging is worse than smarter merges; that
|
||||
populations of self-improving models can climb. **What's genuinely new here** is the *theory* those
|
||||
results have outrun — a real population-genetics of sex for model societies, which *predicts* rather than
|
||||
just *observes*: the "merge, don't average" law, Fisher–Muller as the reason children beat parents,
|
||||
outbreeding depression on tangled landscapes (turning "when does merging help?" into something the
|
||||
problem's structure predicts), grounding as a migration-vs-drift balance with a critical real-data
|
||||
fraction, directed sex as AI's distinct advantage, the whole integrated society whose parts are shown
|
||||
*jointly necessary* — and, newest of all, **model speciation**: the account of *when two models are too
|
||||
far apart to merge at all*, confirmed in real weights.
|
||||
|
||||
**What's still open — honestly.** We fill the old hole (what to select) by *evolving* the selector
|
||||
instead of designing it — but the hole *moved* rather than closed, and the new one is harder: **the
|
||||
fitness function.** What reality-anchored measure selects for *truth* without also selecting for
|
||||
*persuasion*, given that in our own species the two have been at war for the entire history of ideas?
|
||||
Alongside it: the *institutions* that let models correct each other before error is inherited (§8), which
|
||||
we don't solve; and the *calibration* of all the knobs the experiments left open — how many parents, how
|
||||
complementary, at what ratio of inherited-to-real data, how healthy a lineage must be before its
|
||||
knowledge is safe to make permanent. These are at least *measurable*, which is the difference between an
|
||||
open problem and a hole. And the biggest gap: the *combining* claims now hold in real language models,
|
||||
but the *society* — the grounded, diversity-preserving, continually reproducing loop — does not yet. The
|
||||
real test is to build that whole thing out of actual open language models and see whether all the signs
|
||||
survive. **The operators, checked; the living society, next.**
|
||||
|
||||
---
|
||||
|
||||
*For the full argument, the literature it's positioned against, the exact predictions, and the
|
||||
references, see the complete paper: `the-evolution-of-sex-for-ai.md`.*
|
||||
|
|
@ -1,919 +0,0 @@
|
|||
# The Evolution of Sex for Artificial Intelligence
|
||||
|
||||
### A population-genetic framework for societies of agents that reproduce, recombine, and stay open-ended
|
||||
|
||||
*A perspective, written from a geneticist's chair. Companion to a set of minimal, reproducible working
|
||||
models and a first language-model prototype (both built).*
|
||||
|
||||
**Giorgio F. Gilestro** · Department of Life Sciences, Imperial College London ·
|
||||
giorgio@gilest.ro · https://lab.gilest.ro
|
||||
|
||||
---
|
||||
|
||||
### A note on vocabulary (please read this first)
|
||||
|
||||
This paper sits at the meeting point of three fields, and it is written so that a reader from any
|
||||
one of them can follow all of it. We therefore **spell out** each field's jargon the first time it
|
||||
appears, even at the risk of belabouring the obvious for the specialist. A short glossary, in case
|
||||
you skipped a definition:
|
||||
|
||||
- **Model collapse** *(machine learning)* — the degeneration that happens when you train a model on
|
||||
data produced by earlier models, over and over: rare cases disappear and the model drifts toward a
|
||||
bland average.
|
||||
- **Distillation** *(machine learning)* — training a fresh "student" model on the outputs of one or
|
||||
more "teacher" models, so the student ends up knowing a compressed version of what they knew.
|
||||
- **Model merging** *(machine learning)* — combining several trained models directly, at the level
|
||||
of their weights, into one — no retraining. (Think of it as breeding two models rather than
|
||||
teaching a third.)
|
||||
- **Genetic drift** *(population genetics)* — the random loss of rare variants that happens in any
|
||||
finite population simply because not everyone leaves offspring. It is the neutral, no-selection
|
||||
baseline of evolution.
|
||||
- **Wright–Fisher process** *(population genetics)* — the standard mathematical model of drift. Our
|
||||
minimal model of knowledge transmission *is* this process exactly; a real trained network is this
|
||||
process plus a measurable, architecture-specific bias we quantify.
|
||||
- **Recombination / sexual reproduction** *(biology)* — making an offspring by combining pieces from
|
||||
more than one parent, rather than copying a single parent (which is *asexual* reproduction).
|
||||
- **Muller's ratchet** *(population genetics)* — the way an asexual lineage, one that never
|
||||
recombines, accumulates damage it can never undo. We will argue it is the right lens for the
|
||||
*irreversible* part of model collapse — the capabilities that, once lost from every parent, no
|
||||
merging can rebuild.
|
||||
- **Catastrophic forgetting** *(machine learning / neuroscience)* — a neural network overwriting what
|
||||
it knew when it learns something new.
|
||||
|
||||
We have tried to keep the big picture legible on every page, and to be candid about what is argument
|
||||
and what is evidence. The evidence is mostly from **deliberately small models** — mathematics, small
|
||||
neural networks, image generators, and evolutionary simulations. A first bridge to real language
|
||||
models exists — a prototype that recombines LoRA-specialised Qwen models up to 7B on a GPU cluster,
|
||||
which confirms the recombination signs (below) — but the *full grounded society* has not yet been
|
||||
built on a large language model. We will say so repeatedly, because the gap matters.
|
||||
|
||||
---
|
||||
|
||||
## Abstract
|
||||
|
||||
AI is turning from single frozen models to **populations of agents** that persist, specialise, and are
|
||||
increasingly *recombined* into new models — a shift visible in multi-agent societies, population-based
|
||||
self-improvement, and the explosion of **model merging**. The field is doing this with the vocabulary
|
||||
of evolution — "crossover," "mutation," "mate choice," "offspring that beat their parents" — but as
|
||||
loose metaphor draped over search algorithms. This paper argues that a rich, quantitative body of
|
||||
applicable theory already exists in the branch of biology that studies exactly this: the **evolution
|
||||
of sex**. Ninety years of population genetics analyse when reproducing a population by *recombination*
|
||||
beats copying, when it backfires, and how to do it better — and, read as an engineering framework, it
|
||||
supplies overlooked variables and testable design rules for keeping a society of models learning
|
||||
across generations instead of decaying. The underlying shift of perspective is the contribution we
|
||||
most want to land: **treat multigenerational model populations as systems whose inheritance,
|
||||
diversity, and compatibility must be managed — not merely as collections of models to optimise.**
|
||||
|
||||
One diagnosis anchors the frame: training each generation on the last is **genetic drift**, and the
|
||||
resulting **model collapse** is the loss of rare variants a finite population always suffers (the
|
||||
Wright–Fisher process). We reached that account independently; it has also been formalised in
|
||||
parallel by others (Shumailov et al., 2024; Riis, 2026), whom we cite for priority of publication —
|
||||
a convergence we read as corroboration of the frame. This paper is about the structure the diagnosis
|
||||
opens: the remedy side and its limits. Single-
|
||||
teacher copying is **asexual** reproduction, and the irreversible arm of its decay corresponds to
|
||||
**Muller's ratchet** (a correspondence we state with its scope, not as identity); the remedy biology
|
||||
found for the ratchet is **sex**. A society of models should reproduce sexually — each new model
|
||||
**recombined from several complementary parents** (which the field already does, as *model merging*),
|
||||
selection **anchored to a reality that can say no** (not to the consensus of other models), and
|
||||
diversity actively **preserved**. In our models — from closed-form to trained networks to a
|
||||
language-model prototype — those three ingredients together let a lineage not merely avoid collapse
|
||||
but **climb**, producing models fitter than any ancestor (the **Fisher–Muller effect**) while each
|
||||
specialty is re-earned and exceeded; whether the full recipe holds at frontier scale is the open
|
||||
question the framework is built to test.
|
||||
|
||||
From the geneticist's apparatus we extract falsifiable, load-bearing claims (each stated with its
|
||||
operator and scope in the text): (i) **"merge, don't average"** — a conservation result: refitting a
|
||||
child to the *mean of its parents' output distributions* conserves expected rare-capability mass at
|
||||
the single-parent level, cancelling the multi-parent gain *to first order in the rare-item regime*
|
||||
(outside it, variance reduction from averaging can help — the result is a first-order cancellation,
|
||||
not a universal impossibility), while union-preserving operators realise the gain in all regimes —
|
||||
derived in the minimal model, with its weight-space image the headroom rule below; (ii)
|
||||
**offspring can exceed every parent** (Fisher–Muller), the real argument for sex in model societies;
|
||||
(iii) on **rugged, epistatic** task landscapes, blind recombination causes **outbreeding depression**,
|
||||
yielding a design rule — *merge freely when skills are additive, sparingly and with selection when
|
||||
entangled, and route rather than blend under overlap*; (iv) **grounding is immigration** from a
|
||||
non-drifting reality, giving a critical real-data fraction far below one; and (v) — the sharpest new
|
||||
prediction — sex has a **limit**: as two models diverge they undergo **speciation**, a
|
||||
merge-compatibility cliff (compatible → outbreeding depression → hybrid inviability) whose onset is set
|
||||
by divergence *and* epistasis via **Bateson–Dobzhansky–Muller incompatibilities**, and whose damage
|
||||
grows *super-linearly* (the Orr–Turelli snowball). We introduce and model this "model speciation"
|
||||
directly, and confirm it in real trained weights: a merge barrier that survives alignment under the
|
||||
*full* function-preserving symmetry group of the network (not just Git Re-Basin permutations), rising
|
||||
with functional conflict while hybrid fitness falls to inviability — with an honest converse we
|
||||
pre-registered and found: absent conflicting training signals, divergently-specialised lineages of
|
||||
shared ancestry developed *no* isolation at any divergence tested, the merge instead *rescuing* the
|
||||
forgetting specialists. Isolation must be provoked by conflict; specialisation alone did not speciate.
|
||||
AI also has an advantage biology lacks: **directed sex** — unbounded parents, chosen mates,
|
||||
and offspring screened before they are kept — engineered recombination with a flexibility of parent
|
||||
choice and pre-deployment screening that natural mating systems do not approach.
|
||||
|
||||
We support the argument with **minimal, reproducible models** — a closed-form-exact account of drift
|
||||
and grounding, the same effects in small trained networks and an MNIST image generator, a real-weight
|
||||
demonstration of the speciation cliff (a Git Re-Basin residual that survives neuron alignment), and
|
||||
evolutionary simulations of the whole society — and a first **language-model prototype**: merging
|
||||
LoRA-specialised Qwen models (to 7B on a GPU cluster) yields a generalist that beats every specialist
|
||||
parent, with the sharp headroom condition under which "merge, don't average" bites. The scope is
|
||||
honest: these are existence proofs and design rules; the *whole grounded society* on a large language
|
||||
model is the open step. We position the work carefully against the crowded 2025–2026 landscape of
|
||||
evolutionary-AI and merging methods — conceding what they own and marking, precisely, what a genuine
|
||||
population-genetics of sex adds.
|
||||
|
||||
---
|
||||
|
||||
## 1. From a society in space to a society in time
|
||||
|
||||
The idea of many AI agents working together — a "society of mind" (Minsky, 1986), or today's
|
||||
multi-agent systems — arranges intelligence across *space*: several specialists side by side,
|
||||
dividing a task. This paper is about a different axis: *time*. Not a society that merely exists at
|
||||
one moment, but one that **persists and renews across generations**, each new cohort of models
|
||||
starting from the compressed knowledge of the last.
|
||||
|
||||
The unit that matters is therefore the **generation**, and the event that matters is **reproduction**:
|
||||
the making of a new model from older ones. A single model, like a single mind, is bounded and
|
||||
eventually stops improving. A *lineage* need not be. Human civilisation is not clever because any one
|
||||
person is; it is clever because each generation inherits the distilled achievements of the previous
|
||||
one and adds a little. We propose building AI the same way — and, crucially, getting the *reproduction*
|
||||
right, because that is exactly where it can go wrong.
|
||||
|
||||
### Where this sits, and what is new
|
||||
|
||||
This axis is suddenly crowded. By 2026 several groups build **populations of models or agents that
|
||||
improve across generations**: societies of independently-specialised models that self-improve for more
|
||||
rounds than a single agent (Multiagent Finetuning — Subramaniam et al., 2025); open-ended archives of
|
||||
self-rewriting coding agents (the Darwin–Gödel Machine — Zhang et al., 2025); groups that evolve by
|
||||
sharing experience across branches (Weng et al., 2026); persistent agent *ecologies* with reproduction
|
||||
and cumulative culture (TerraLingua — 2026). In parallel, **model merging** has become a small industry
|
||||
with an overtly evolutionary vocabulary: crossover-mutation-selection over LLM populations (GENOME —
|
||||
2025), niching and "mate choice" (Sakana's M2N2 — 2025), and evolutionary search over merge recipes
|
||||
(Akiba et al., *Nature Mach. Intell.* 2024/25).
|
||||
|
||||
We are candid about the consequence. Three things we do **not** claim. First, that collapse is
|
||||
Wright–Fisher drift: formalised independently (Riis, 2026; Shumailov et al., 2024), sharpened to a
|
||||
closed-form first-extinction law whose onset coincides with collapse (Benati et al., 2025) and to a
|
||||
quantitative-trait-genetics account for diffusion models (Yoon et al., ICLR 2025), and conceded here.
|
||||
Second, the bare empirical facts that a merged model can beat its parents, that decorrelated parents
|
||||
merge better, and that naive averaging is inferior to sign- or routing-based merges (TIES, DARE,
|
||||
mixture-of-experts routing): all established. Third, that merge success can be *predicted at all*:
|
||||
machine-learning-native predictors exist, from interpretable pairwise metrics (gradient alignment —
|
||||
Zhou et al., 2026) to capacity/rate-distortion accounts of "merging collapse" (2026); what they lack,
|
||||
and we supply, is the *mechanism* — when and why the failure is a coordinate artefact versus genuine
|
||||
functional incompatibility, and what moves the cliff. What a geneticist is placed to supply is a
|
||||
**framework** rather than a search heuristic. The nearest precursor is a theory-of-computation
|
||||
tradition reading sex as an algorithm for *mixability* (Livnat & Papadimitriou, 2016), pre-dating
|
||||
model merging; the works above use evolution chiefly as vocabulary over an optimiser, and — to our
|
||||
knowledge — the quantitative apparatus of the evolution of sex (Fisher–Muller, outbreeding depression,
|
||||
migration–drift balance, reproductive isolation) has not previously been carried over as more than
|
||||
metaphor. We are also candid about what *kind* of contribution each of our claims is, because three
|
||||
different things are easily conflated: **interpretation** (an existing result is usefully understood
|
||||
in these terms — e.g., merged offspring beating their parents as Fisher–Muller), **explanation** (the
|
||||
transferred mechanism accounts for observations existing accounts leave open — e.g., which merge
|
||||
failures are coordinate artefacts and which are functional), and **prediction** (the framework
|
||||
forecasts an unmeasured outcome and improves a design decision). This paper is strongest on the
|
||||
first, makes concrete progress on the second, and reports a first, bounded step on the third: a
|
||||
**controlled predictive test** at small scale in which pre-merge *functional-disagreement* measures —
|
||||
chosen by the framework — showed a detectable, held-out-robust association with merge damage on a
|
||||
constructed task grid, while the selected weight-geometry baselines did not. We are precise about
|
||||
that result's boundary where it is reported: it is a small-model demonstration on a constructed grid;
|
||||
the proposed epistasis-specific refinement did not outperform plain disagreement; predictor
|
||||
differences are not individually significant head-to-head; and whether the prediction improves a
|
||||
budget-matched operator choice remains open. The organising shift we argue for
|
||||
is prior to any single mechanism: **treat multigenerational model populations as systems whose
|
||||
inheritance, diversity, and compatibility must be managed — not merely as collections of models to
|
||||
optimise.**
|
||||
|
||||
## 2. Why today's models cannot do this
|
||||
|
||||
Today's large language models have no life cycle. They are trained once, at enormous cost, then
|
||||
**frozen** and deployed as a fixed artefact that does not learn from the people it serves. Learning
|
||||
and doing are split into two eras with no bridge between them.
|
||||
|
||||
There is a real reason for the freeze. Updating a neural network on new information tends to overwrite
|
||||
what it already knew — **catastrophic forgetting**, a problem understood since the late 1980s
|
||||
(McCloskey & Cohen, 1989; French, 1999). Freezing avoids it by refusing to learn at all. The result
|
||||
is a mind with no childhood, no growth, and no way to pass anything on. A lineage needs the opposite:
|
||||
members that learn through their working lives, reach maturity, and hand on what they gained. So the
|
||||
first requirement is a learner that can grow *safely*.
|
||||
|
||||
## 3. A learner that can grow without forgetting
|
||||
|
||||
The individual model needs two properties.
|
||||
|
||||
**It must not catastrophically forget.** Instead of overwriting its core as it learns, it keeps that
|
||||
core frozen and only *readable*, and carves each new skill into freshly-added capacity beside it. In
|
||||
machine learning this is called *parameter isolation* (progressive networks — Rusu et al., 2016;
|
||||
prune-and-freeze — Mallya & Lazebnik, 2018; and, most practically, **LoRA** and other small trainable
|
||||
"patches" bolted onto a frozen model — Hu et al., 2021). If the core is never altered, its *parameters*
|
||||
cannot be forgotten — though a precise reader should note the system's *behaviour* can still shift
|
||||
while adapters are active, so the guarantee is of a recoverable core, not of unchanging conduct. This
|
||||
is what lets a model accumulate a coherent working life of expertise — the kind of stable knowledge
|
||||
worth passing on.
|
||||
|
||||
The brain offers a partial blueprint. *Complementary Learning Systems* theory (McClelland,
|
||||
McNaughton & O'Reilly, 1995) — itself a response to the forgetting problem — describes two subsystems:
|
||||
a **fast** store (the hippocampus) that grabs an experience in one shot, and a **slow** store (the
|
||||
neocortex) that integrates regularities gradually without disruption. We do not lean on any particular
|
||||
account of how the brain moves knowledge between them; the architecture needs only that *some*
|
||||
periodic **offline consolidation** step exists, moving knowledge from the fast store to the slow one
|
||||
when the system is idle. The machine version is clean regardless: the prompt is working memory, an
|
||||
external database is the fast episodic store, the trained weights are the slow store, and consolidation
|
||||
migrates the first into the last.
|
||||
|
||||
**It is bounded.** Because the model only ever *adds* capacity and freezes what it has, it eventually
|
||||
fills up. In most designs that is a wall to dread. In ours it is a clock.
|
||||
|
||||
## 4. "Full" is maturity, not failure
|
||||
|
||||
Here is the pivot. A bounded learner that fills up has not broken. **It has grown up.**
|
||||
|
||||
Read the capacity limit as a life stage. A model is *born* as a freshly-schooled base — its general
|
||||
education. It enters a **working life**, adding specialised knowledge as it does its job. And it
|
||||
reaches **maturity**: the point where it has learned much of what one working life in its niche can
|
||||
teach. Maturity is not the end of usefulness — it is the moment the model is most worth learning
|
||||
*from*. So maturity is the cue to **reproduce**. The capacity ceiling that every other architecture
|
||||
fights becomes, in ours, the metronome of the generations.
|
||||
|
||||
Everything now turns on how that reproduction is done — and this is where the paper's central claim
|
||||
lives.
|
||||
|
||||
## 5. Reproduction: copying collapses, recombination climbs
|
||||
|
||||
Suppose a mature model simply teaches a fresh one — distillation, one teacher to one pupil, generation
|
||||
after generation. This is the obvious design, and it fails, for a reason that is exactly the same in
|
||||
machine learning and in biology.
|
||||
|
||||
**The machine-learning statement.** Training each generation on the previous generation's outputs is
|
||||
the recipe for **model collapse**: the model forgets the improbable, loses the *tail* of the
|
||||
distribution (the rare cases) first, and drifts toward its own most common output (Shumailov et al.,
|
||||
2024). Worse for us, the very rule that makes distillation useful — *keep the general, drop the
|
||||
idiosyncratic* — **is** tail-deletion by design. The operation that would power a cultural ratchet and
|
||||
the operation that drives model collapse are the same act.
|
||||
|
||||
**The population-genetics statement (the same thing, for the minimal model).** Represent a model's
|
||||
knowledge as a distribution over discrete "items" — capabilities, facts, modes of behaviour. One
|
||||
generation is: *draw a finite sample from the parent, and refit the child to it.* In this **minimal
|
||||
inheritance model** the finite-sampling step is **exactly** genetic drift — the random loss of rare
|
||||
variants in a finite population — described by the century-old **Wright–Fisher** model (Wright, 1931;
|
||||
Fisher, 1930): the same equations, which we use as closed-form checks on our simulations. Rare items
|
||||
go extinct first, roughly ten times faster than common ones, precisely as drift predicts. **The
|
||||
boundary of the identity matters, and we measured it:** real neural training adds approximation,
|
||||
optimisation noise, and inductive bias on top of sampling, and when we fit trained networks against
|
||||
the exact drift null they deviate in *opposite, architecture-specific directions* — a smoothing
|
||||
recurrent model resists collapse (it keeps spurious variants alive), a sharpening image generator
|
||||
accelerates it (our learning-kernel result, below). So the honest statement is: the minimal
|
||||
inheritance model is exactly Wright–Fisher; a real learner is Wright–Fisher *plus a signed,
|
||||
measurable estimator-bias operator* — and the drift signs (rare-first loss, the grounding response)
|
||||
survive that operator in every architecture we tested.
|
||||
|
||||
And single-teacher copying is **asexual reproduction** — cloning one parent. Nature already knows what
|
||||
happens to an asexual lineage that never recombines: it accumulates damage it can never repair, a
|
||||
one-way decline geneticists call **Muller's ratchet** (Muller, 1964). We use the ratchet as the
|
||||
*organising correspondence* for model collapse, with its scope stated: strictly, the ratchet is the
|
||||
stochastic loss of the least-degraded class under recurring deleterious change in an asexual
|
||||
population, so it maps onto the *irreversible* component of capability loss (once every copy of a rare
|
||||
capability is gone from all parents and sources, no recombination can rebuild it) rather than onto
|
||||
every form of degradation. That is exactly why the correspondence is useful rather than decorative: it
|
||||
says the cure must act *before* fixation-by-loss — keep complementary variants alive somewhere in the
|
||||
population — because recombination can only reassemble what still survives. Biology solved this
|
||||
problem, and its solution is the subject of this paper.
|
||||
|
||||
Two ingredients turn the collapse operation into a climb. Both are things nature does.
|
||||
|
||||
**First: do not reproduce "dry."** Model collapse is a property of a lineage fed *only* its own
|
||||
output; the documented fix is that keeping some real data in the mixture arrests it (Shumailov et al.,
|
||||
2024). We call that real data **grounding** — fresh contact with the world, verified against it. In
|
||||
our minimal models, grounding is startlingly cheap: mixing in even a few percent of verified real data
|
||||
holds on to most of the diversity indefinitely. But — an honest limit we found and did not expect —
|
||||
grounding cannot save the *very rarest* items at any affordable budget; protecting an item of rarity
|
||||
*p* needs a real-data budget that grows like 1/*p*. Grounding rescues diversity cheaply; it does not,
|
||||
by itself, rescue the deep tail. Something else must. That something is sex.
|
||||
|
||||
**Second: reproduce sexually.** Instead of copying one parent, build each new model by **recombining
|
||||
several** — a *sexual* rather than asexual birth. In machine learning this already has a name and a
|
||||
working implementation: **model merging** (Akiba et al., 2024). Its importance here is not efficiency;
|
||||
it is that recombination does something copying cannot. If several parent models have each specialised
|
||||
on different parts of reality, each has kept alive rare knowledge the others lost. A recombined child
|
||||
inherits the **union** of what its parents kept — not the tail-thinned *average* of a crowd of
|
||||
near-identical copies. And here is the point that lifts sex from a safeguard to the engine of the whole
|
||||
scheme, and the reason biology invented it:
|
||||
|
||||
> **An offspring recombined from complementary parents can be *fitter than any of its parents*.**
|
||||
|
||||
Geneticists call this the **Fisher–Muller effect** (Fisher, 1930; Muller, 1932): recombination brings
|
||||
together, in one individual, beneficial variants that arose separately in different lineages, so the
|
||||
child holds a combination none of the parents had. In our simulations this is exactly what we see —
|
||||
recombining decorrelated specialist models yields a model that climbs toward the best-possible
|
||||
combination, a genotype *no single parent possessed*, while the best single parent, and the naive
|
||||
average of all of them (what the field calls a "model soup" — Wortsman et al., 2022), both plateau
|
||||
well below. This is the concrete meaning of the paper's title claim, "the lineage climbs in general
|
||||
knowledge; specialisation is re-earned each generation," and it is why the reframing from
|
||||
teacher→pupil to *sexual reproduction* is not cosmetic: **copying can only recover a ceiling;
|
||||
recombination can exceed it.**
|
||||
|
||||
This is no longer only a simulation. In a first language-model prototype — LoRA specialists on
|
||||
disjoint task families, recombined and judged by an exact verifier — a merge of three specialist Qwen
|
||||
models (7B, on a GPU cluster) **beats every single specialist**, overall and on every family: the
|
||||
Fisher–Muller effect, in real weights. The same prototype pins down *when* the finer "inherit the
|
||||
union, don't average" rule actually bites. Keeping each parent whole and **routing** each input to the
|
||||
right one beats the tail-thinning average — but only when the task is hard enough to leave room to
|
||||
lose: on easy tasks a strong model's plain average is already at the ceiling, so the crude soup is
|
||||
fine, whereas on hard tasks the average dilutes a hard-won specialist so badly it falls below even the
|
||||
best single parent, and routing wins by a wide margin. The rule is therefore precise: **the union
|
||||
beats the average in exact proportion to how far the average is from the best attainable** — a caveat
|
||||
that sharpens rather than weakens the claim, and that a practitioner needs before spending compute on
|
||||
the fancier operator.
|
||||
|
||||
**The operator boundaries (stated, because "merge, don't average" is not one claim but a family).**
|
||||
Four different operators travel under these words, and the conservation result belongs to exactly one
|
||||
of them. What is *derived* is this: when a pupil's knowledge is refit to the **mean of the parents'
|
||||
output distributions**, the expected mass on any rare item is conserved at the single-parent level —
|
||||
in the rare-item regime (`n·p/K ≪ 1`) the 1/K dilution of averaging cancels the union gain of having
|
||||
K parents to first order — outside that regime, survival is convex in mixed mass and averaging's
|
||||
variance reduction can help, so this is a first-order cancellation, not a universal impossibility;
|
||||
whereas an operator that keeps, per item, its **strongest source** (and renormalises, which itself
|
||||
redistributes mass) realises the union in all regimes. That statement is exact in the minimal model, and it presupposes an
|
||||
oracle (or verifier) able to say which source is strongest. The two operators the LLM prototype
|
||||
tests — **weight averaging** (a nonlinear network's weight-mean does not compute the mean of its
|
||||
parents' outputs) and **routing among intact specialists** (which keeps K models' storage and an input
|
||||
classifier, a different parameter and inference budget from one fixed-size child) — are *empirical
|
||||
cousins* of the two sides of that law, not instances of it. The headroom rule above is precisely the
|
||||
empirical bridge: it says when the weight-average behaves like the diluting mean (hard tasks, weak
|
||||
base) and when a capable base absorbs the dilution (easy tasks). And all of it operates within a
|
||||
capacity boundary: when parental capabilities genuinely cannot coexist in the child's capacity, no
|
||||
operator preserves the union — that regime is the subject of the speciation section below.
|
||||
|
||||
Three results keep this honest, and all are results, not hand-waving.
|
||||
|
||||
*Sex can backfire.* When the parents' skills are not cleanly separable but **entangled** — when the
|
||||
value of one capability depends on which others are present (geneticists call this **epistasis**) —
|
||||
blindly recombining two good models can produce a *worse* child, because recombination breaks up a
|
||||
combination that only worked as a whole. Biologists call this **outbreeding depression**, and we
|
||||
reproduce it: on "rugged" (highly entangled) problems, naive merging drops offspring below their
|
||||
parents, and the more you mix the worse it gets. The design rule that falls out is simple: *merge
|
||||
freely when skills are complementary; merge sparingly, and carefully, when they are entangled.*
|
||||
|
||||
*The mating system matters too — not just who mates, but how widely.* The result above is about the
|
||||
recombination *rate*; a separate knob is the population's **mating structure** — whether reproduction is
|
||||
**monogamous** (each model recombines within a narrow, local circle) or **promiscuous** (mates drawn
|
||||
freely from the whole population). Almost all model-merging implicitly assumes promiscuity — fuse
|
||||
everything, or route over one flat pool — but population genetics says the breadth of gene flow is itself
|
||||
consequential, because wide flow spreads good variants fast while **homogenising** the population, and
|
||||
narrow flow preserves the distinct sub-populations needed to explore several solutions at once (Wright's
|
||||
*shifting balance*). We sweep exactly this breadth against landscape ruggedness, and the optimum moves:
|
||||
on smooth (additive) landscapes wide, promiscuous mating is best (spread the one good direction fastest),
|
||||
but as the landscape gets rugged the best breadth **shrinks to an intermediate value** — full promiscuity
|
||||
prematurely converges onto one basin and finds a *worse* champion, while pure monogamy over-fragments.
|
||||
Throughout, wide mating lifts the *typical* model but monotonically **destroys diversity** — so on rugged
|
||||
problems, where the best model needs preserved diversity to be found, structured (partly monogamous)
|
||||
merging wins. The design rule extends the one above: *merge widely when skills are additive; keep
|
||||
structured sub-populations — island-style merging — when skills are rugged.* (Figure: `results/figS13_mating_breadth/E14.png`.)
|
||||
|
||||
*AI can do sex better than biology can.* Biology is stuck with two parents, mating roughly at random,
|
||||
and cannot inspect an offspring before it is born. An AI has none of those limits. It can recombine
|
||||
**many** parents at once; it can **choose** which parents to combine, for complementarity; and it can
|
||||
**generate many candidate offspring and keep only the fittest**, screening them against reality before
|
||||
committing. We call this **directed sex**, and in our simulations it converts the outbreeding-depression
|
||||
catastrophe into a reliable gain: where blind recombination collapses on entangled problems, directed
|
||||
recombination matches or beats the best parent every time. The language-model prototype shows the same
|
||||
sign where it can: breeding many recombined Qwen offspring and keeping the one the verifier scores
|
||||
highest beats the single averaged soup on hard tasks (and, unsurprisingly, does nothing extra on easy
|
||||
tasks the soup already solves). This is a genuine advantage of engineered reproduction over the
|
||||
biological kind, and we think it is one of the more useful ideas in the paper.
|
||||
|
||||
So the picture of §5 is: single-teacher copying is asexual and collapses (Muller's ratchet = model
|
||||
collapse); the cure is to *ground* every birth in reality and to reproduce *sexually*, recombining
|
||||
many complementary parents; and because AI sex can be many-parent, mate-chosen, and offspring-screened,
|
||||
it is not merely a hedge against collapse but an engine that produces children fitter than any parent.
|
||||
|
||||
### The limit of sex: model speciation
|
||||
|
||||
Sex has a limit, and it is the sharpest new prediction this frame makes. Recombination works because
|
||||
the parents are variations on a shared background; push two lineages far enough apart and their
|
||||
combination is no longer viable. In biology this is **speciation** — the onset of **reproductive
|
||||
isolation** — and its genetic mechanism is the **Bateson–Dobzhansky–Muller incompatibility** (BDMI):
|
||||
an allele that arose in one lineage and an allele that arose in the other are each harmless on their
|
||||
own background, but their *combination*, never tested by selection in either parent, is deleterious in
|
||||
the hybrid (Dobzhansky, 1937; Muller, 1942; Orr, 1995). A merged model is precisely such a hybrid — a
|
||||
single *recombinant* genotype, an F2-like object exposed to **recombination load**, not a hybrid-vigour
|
||||
F1 — so the theory predicts a specific trajectory as two models diverge: **compatible → outbreeding
|
||||
depression → hybrid inviability**.
|
||||
|
||||
We built this as an explicit model (a companion result). Two lineages descend from a common ancestor,
|
||||
each substituting a *disjoint* set of loci — so each parent is adapted and neither carries an
|
||||
incompatibility — and a fraction of the cross-lineage locus pairs are BDMIs that fire only when a hybrid
|
||||
inherits *both* derived alleles. Sweeping the divergence between the parents reproduces the predicted
|
||||
curve exactly: hybrid fitness tracks the parents while they are compatible, then peels off, peaks, and
|
||||
crashes below the ancestor (an inviable hybrid). Three things fall out, and they are the contribution:
|
||||
|
||||
1. **The isolation cliff, and what moves it.** The divergence at which merging fails is not fixed: it
|
||||
arrives *earlier the more epistatic the capability landscape*. In the model the reproductive-isolation
|
||||
rate at high divergence rises from ~0 to ~0.5 as the density of incompatibilities grows. This is the
|
||||
paper's distinct, falsifiable claim — **at matched divergence, mergeability is governed by epistasis,
|
||||
not by divergence alone** — and it is exactly the axis that the machine-learning predictors of merge
|
||||
success (which are all divergence/geometry measures) do not have.
|
||||
2. **The snowball.** The number of incompatibilities grows with the *square* of the divergence
|
||||
(Orr & Turelli, 2001), so hybrid fitness falls *super-linearly*: divergence is punished faster than
|
||||
it accrues. Merge compatibility does not decay gently; it falls off a cliff.
|
||||
3. **The design rule.** *Before merging, weigh divergence against the ruggedness of the shared
|
||||
capability landscape; past the cliff, do not merge — route* (the engineering echo of allopatry:
|
||||
keep the specialists reproductively separate and select among them instead of hybridising).
|
||||
|
||||
This is where a geneticist's lens earns its keep. The machine-learning literature has *observed* that
|
||||
increasing specialisation eventually breaks merging and that one should then route rather than fuse
|
||||
(Pari et al., 2024; Zhou et al., 2026), and part of the apparent incompatibility between independently
|
||||
trained models is a coordinate artefact removable by aligning neurons (Git Re-Basin — Ainsworth et al.,
|
||||
2022). What the frame adds is the *theory* of the phenomenon they observe: its functional form, its
|
||||
super-linear (snowball) onset, and its dependence on epistasis — merge failure as a Dobzhansky–Muller
|
||||
event. (Figure: `results/fig5_speciation_bdm/E12.png`.)
|
||||
|
||||
**The real-weight confirmation.** The obvious objection to the analytic model is that its
|
||||
"incompatibility" is a re-labelled loss barrier, and loss barriers between independently trained
|
||||
networks are famously a *coordinate* artefact — two nets that learned the same function in a permuted
|
||||
basis look incompatible until their neurons are aligned (Git Re-Basin), and recent work shows that
|
||||
symmetry groups *richer* than permutations remove still more of the barrier (functionality-preserving
|
||||
rescalings and rotations — Scaling LMC, 2026; neuron-identifiability approaches). We therefore ran the
|
||||
experiment the objection demands, in real trained weights, aligning modulo the **full**
|
||||
function-preserving unit symmetry group of the architecture (per-unit positive rescaling composed with
|
||||
permutation — for a plain ReLU network, all of it). Two small MLPs are forked from a shared MNIST base,
|
||||
trained, weight-averaged, and their linear-mode-connectivity error barrier is measured *before and
|
||||
after* alignment; the after-alignment **residual** is the part of the incompatibility that no
|
||||
re-coordination can explain away. The decomposition is clean (Figure:
|
||||
`results/speciation_real/speciation_real.png`): two nets trained *from different random initialisations
|
||||
on the same task* have a real naive barrier that alignment removes almost entirely (residual ≈ 0.001,
|
||||
and the aligned merge performs at parent level) — same species, different basis, the canonical Re-Basin
|
||||
result, which also proves the aligner works. Two nets that learned *conflicting* label maps have a
|
||||
large barrier of which the full symmetry group removes **essentially nothing** (0.502 → 0.497) —
|
||||
a conflict-associated barrier the tested alignment leaves largely unchanged — supporting a
|
||||
functional-conflict interpretation without proving optimal alignment (control recovery validates a
|
||||
special case; the removable share is a lower bound, the residual an upper bound). It also carries a floor no future alignment
|
||||
method can breach: models loyal to label maps that conflict on a fraction *μ* of inputs cannot both be
|
||||
served by *any* single merged model, which must err at rate ≥ *μ*/2 against at least one parent
|
||||
(SI proposition). Sweeping the fraction of conflicting classes traces the **isolation cliff in real
|
||||
weights**, now readable directly as *hybrid fitness*: the residual barrier climbs monotonically while
|
||||
the merged model's accuracy falls from 0.97 to 0.03 — E12's compatible → depression → inviability
|
||||
trajectory, measured.
|
||||
|
||||
**And its honest converse: speciation must be provoked; it did not emerge.** A true
|
||||
Dobzhansky–Muller incompatibility is *emergent* — each lineage's changes harmless alone, incompatible
|
||||
only in combination — whereas the conflict condition above *imposes* contradiction. So we pre-registered
|
||||
the emergent test: fork two children from a shared base and let them diverge with **no conflicting
|
||||
training signal anywhere** — one pair as complementary class specialists (one child trains only on
|
||||
digits 0–4, the other only on 5–9), one pair with divergent input conventions (views shifted in
|
||||
opposite directions) — out to divergences 6.4× the base training. The result is the second
|
||||
pre-registered reading, and it sharpens the theory's scope rather than confirming its most dramatic
|
||||
form: the residual barrier is **0.000 at every divergence in both conditions**, and far from failing,
|
||||
the merge *rescues* the two specialists — each parent decays toward ~0.50 on the full task
|
||||
(catastrophically forgetting the classes it no longer sees) while the merged model holds ~0.95
|
||||
throughout, a sustained Fisher–Muller rescue at zero barrier. In real weights, at least in this regime
|
||||
of shared ancestry and compatible tasks, **reproductive isolation requires functional conflict; it does
|
||||
not arise spontaneously from divergent specialisation.** The design rule sharpens accordingly: *merge
|
||||
freely across divergently-specialised lineages of shared ancestry — what speciates model populations is
|
||||
conflicting conventions, not specialisation per se.* Whether long-horizon over-specialisation erodes
|
||||
mergeability at language-model scale — as the empirical merging literature hints (experts trained
|
||||
longer merge worse under averaging) — is exactly the next tier's question, and the theory now makes the
|
||||
prediction crisp: it should depend on whether extended training induces *conflicting conventions on
|
||||
shared circuitry*, not on divergence time itself.
|
||||
|
||||
**What these experiments do and do not establish.** Stated at exactly the strength of the evidence:
|
||||
they establish that *some merge failures reflect incompatible functional requirements rather than a
|
||||
mismatch of coordinates* — a residual that survives the full unit-symmetry group of the architecture
|
||||
tested, rises with functional conflict, and is absent under compatible specialisation. Three
|
||||
qualifiers. First, the impossibility at the heart of the conflict condition — one deterministic model
|
||||
cannot satisfy two contradictory answer conventions — is information-theoretic and needs no population
|
||||
genetics; what the genetic frame adds is *structure around it*: which divergences generate such
|
||||
conflicts, the prediction that epistasis rather than distance sets the cliff's position, and the
|
||||
snowball's super-linear onset — the latter two verified so far only in the analytic model, and
|
||||
therefore carried as **hypotheses at the neural tier, not results**. (On the snowball, one more
|
||||
distinction: super-linear growth in the *number* of incompatibilities does not by itself entail a
|
||||
sharp *performance* cliff — that needs the link from incompatibility count through effect sizes to
|
||||
measured performance, which the analytic model supplies under its assumptions and any neural test
|
||||
must establish separately.) Second, our alignment removes the symmetries we enumerate for this
|
||||
architecture class, and exactly recovering a permuted-and-rescaled copy validates a special case
|
||||
rather than proving global optimality for independently trained networks — so the removable share is
|
||||
a lower bound and the residual an upper bound; richer transformation families for other architectures
|
||||
could reapportion the split, though not below the conflict floor. Third,
|
||||
"unmergeable" here means by aligned linear interpolation of weights — a barrier to that operator does
|
||||
not preclude every conceivable recombination method (routing, for one, sidesteps it by not blending).
|
||||
Emergent Dobzhansky–Muller incompatibilities in real weights remain the flagship *hypothesis* of this
|
||||
programme: our tested regimes found none, which bounds where they can live — longer horizons, shifted
|
||||
data distributions, capacity pressure — and the decisive experiment (predicting merge success *before*
|
||||
merging from an operational epistasis measure, against geometry- and gradient-based predictors) is
|
||||
posed in the closing section.
|
||||
|
||||
One question remains, and the rest of the paper is largely about it: recombination combines what the
|
||||
parents kept — but *who decides what each parent keeps, and which offspring are worth keeping?*
|
||||
|
||||
## 6. The second inheritance: letting "what is worth keeping" evolve
|
||||
|
||||
There are two answers, and the first is wrong. We could try to *design* the rule for what knowledge to
|
||||
keep and pass on. But nobody knows that rule. "Keep the general, drop the particular" is a slogan, not
|
||||
an algorithm: ask *which* generalisations, in *which* domain, at *which* grain, and the hand-written
|
||||
rule falls apart. This is the deepest hole in the scheme, and it cannot be filled by decree.
|
||||
|
||||
The second answer is the one nature used: **do not design the selector — evolve it.** Let different
|
||||
models carry different *policies* for what is worth keeping and combining. Let the policies that
|
||||
produce more capable offspring spread; let the policies that produce weak offspring die out with their
|
||||
lineages. The lineage's *taste* — its sense of what matters — is discovered by selection, not imposed.
|
||||
|
||||
So **two things are inherited, on two channels.** The *content* passes down directly: an offspring
|
||||
receives its parents' knowledge (this is the "Lamarckian" channel — the inheritance of things acquired
|
||||
during a lifetime, which biology forbids for genes but culture allows for ideas). The *selection
|
||||
policy* — what to keep, whom to breed with, which offspring to screen for — is itself inherited, varies
|
||||
between models, and survives in proportion to the success it produces. That second channel is
|
||||
**Darwinian**. The architecture is therefore both at once: Lamarckian in *what* it transmits, Darwinian
|
||||
in *what it keeps*. Evolutionary theorists call this structure *dual inheritance* and identify it as
|
||||
the engine of human culture (Boyd & Richerson, 1985); philosophers of science describe scientific
|
||||
knowledge itself as growing this way, by conjecture and **refutation** (Popper, 1959; Campbell, 1974;
|
||||
Hull, 1988).
|
||||
|
||||
The closure that makes this fit together, rather than merely sound nice: Darwinian selection needs a
|
||||
*selection pressure* — something that decides which policies win. That pressure is already in the
|
||||
design. What tells a lineage its taste was good? The success of its offspring **against reality**. The
|
||||
reality-check that stops collapse (grounding, §5) and the fitness signal that drives the evolving taste
|
||||
turn out to be the *same thing*, seen from two sides.
|
||||
|
||||
## 7. The central danger: fitness is not truth
|
||||
|
||||
Introducing selection introduces selection's classic hazard, and it is severe enough to sink the whole
|
||||
scheme if ignored. Evolution optimises, without mercy or foresight, for exactly what you *measure* —
|
||||
never for what you *meant*. (Economists and ML engineers know this as **Goodhart's law** and
|
||||
*specification gaming*.) Get the fitness measure slightly wrong and the lineage will exploit the gap
|
||||
with more ingenuity than any designed rule.
|
||||
|
||||
For a *knowledge* lineage there is a specific and nasty version. For ideas, the natural measure of
|
||||
"fitness" is **how well they spread**, and a false-but-persuasive idea spreads beautifully. Human
|
||||
intellectual culture is full of highly transmissible falsehoods; confident nonsense out-competes hedged
|
||||
accuracy in almost every human forum. Turn Darwinian selection loose on models without care and it will
|
||||
breed a lineage optimised for *persuasiveness* — fluent, compelling, and wrong. That is model collapse
|
||||
with an optimiser behind it, actively seeking the cliff.
|
||||
|
||||
Only one thing makes fitness track truth rather than appeal: **being judged against a reality that can
|
||||
say no.** Fitness must be predictive success under *intervention* — did the model's knowledge correctly
|
||||
anticipate what the world would do when acted upon — and not approval, fluency, or a benchmark score,
|
||||
each of which can be gamed. This is why the reality-check is load-bearing twice over: it is both the
|
||||
anchor that stops passive collapse *and* the only thing that keeps the evolving taste honest.
|
||||
|
||||
The second danger is **convergence**, and beating it takes work at two separate levels, because
|
||||
selection can only preserve variety that already exists — the variety must first be *supplied* and then
|
||||
*kept*.
|
||||
|
||||
- **Supply.** A lineage that learns only from an accredited elite has a monoculture for a source: the
|
||||
"best" experts are, almost by definition, the ones who won the consensus, so the incoming variation
|
||||
is narrow from the start. The society must therefore learn, deliberately and from the beginning, from
|
||||
the **outliers and the heterodox** as well as the credentialed — not out of fairness, but because in
|
||||
evolutionary terms diverse founders are the raw material without which nothing downstream can adapt.
|
||||
- **Preserve.** Even given varied input, plain fitness-*maximising* selection converges — it drives
|
||||
every lineage toward the single current best and fixes it, extinguishing the rare specialists. The
|
||||
fix is well established: **quality-diversity** selection, which rewards being *good* and being
|
||||
*different* at once (novelty search and MAP-Elites — Lehman & Stanley, 2011; Mouret & Clune, 2015),
|
||||
keeping complementary specialists alive rather than collapsing onto the champion. In our simulations
|
||||
this is decisive: greedy "keep-the-best" selection collapses a population's diversity almost at once
|
||||
and gets stuck at a mediocre answer, while quality-diversity selection keeps the specialists that
|
||||
sexual recombination then needs as parents.
|
||||
|
||||
The two levels meet at reproduction. Multi-parent recombination (§5) is the *vehicle* by which the
|
||||
diversity this selection preserves actually enters the next generation: an offspring drawn from
|
||||
complementary parents inherits the standing variation the selector kept alive, recombined into one new
|
||||
model. Supply the variety from the human side; preserve it on the selection side; recombine it into
|
||||
each generation on the reproduction side. Remove any of the three and the lineage converges on its own
|
||||
first guess.
|
||||
|
||||
## 8. A society needs institutions, not just specialists
|
||||
|
||||
One requirement is easy to overlook and fatal to omit. The easy part of a society is specialisation.
|
||||
The *hard* part — which human civilisation took millennia to build — is the set of **institutions that
|
||||
let fallible specialists combine without each re-verifying everything**: reputation, replication,
|
||||
credentials, and above all **peer review**. These are error-correction protocols, and they exist
|
||||
because a group of unreliable specialists left to reinforce one another is *more* wrong than any member
|
||||
alone.
|
||||
|
||||
This is precisely where current multi-agent AI fails: set several models to confer and they tend to
|
||||
agree sycophantically and confabulate in committee, because they have all the specialisation and none
|
||||
of the institutions. A multigenerational society must specify not only how models learn, reproduce, and
|
||||
are selected, but how they *check* one another — how a claim is challenged and a mistaken model loses
|
||||
standing *before* its error is recombined into offspring and inherited. Peer review is itself a
|
||||
reality-check of the kind §7 demands — an institutional stand-in for reality's "no," to be used where
|
||||
direct intervention is slow or costly.
|
||||
|
||||
## 9. The lineage must stay open to reality
|
||||
|
||||
A society of models, however many generations deep, shares one hard limit: it has only ever *read*.
|
||||
Its whole inheritance is a record of things that were said. In the vocabulary of causal reasoning
|
||||
(Pearl, 2009), it lives on the bottom rung of the **ladder of causation** — observation — and no amount
|
||||
of observation reaches *intervention*. Watching underdetermines doing; correlation does not contain
|
||||
causation, at any scale.
|
||||
|
||||
Only intervention — reaching out and changing the world to see what happens — climbs the ladder, and a
|
||||
language model cannot intervene. This is what humans and their instruments supply, and the contribution
|
||||
is not "truth" but **constraint**: reality's unique gift is that it can say **no**. Text offers only
|
||||
more opinion; an experiment delivers a refusal no consensus can overturn. As §§6–7 argued, that refusal
|
||||
does double duty — it is both the anchor that prevents collapse and the fitness signal that lets the
|
||||
lineage's evolving taste select for truth rather than persuasion.
|
||||
|
||||
Two honest riders. First, the human reality-signal is *dirty*: people supply results warped by
|
||||
publication bias, incentive, and occasional fraud — which is exactly why the error-correcting
|
||||
institutions of §8 must sit at the human–machine boundary, screening the signal before it selects.
|
||||
Second, humans are the *current* supplier of intervention, but the actuator half is being automated
|
||||
(autonomous laboratories already close the design–build–test loop). What looks durable in the human
|
||||
role is therefore not the hands but the **choice of what to test and which refusals matter** — the
|
||||
part of the fitness function that encodes *what is worth persisting*, as opposed to what merely *can*
|
||||
persist. We flag, without resolving, that a partnership stays mutual only while both sides supply
|
||||
something the other cannot.
|
||||
|
||||
## 10. Why it is cheap
|
||||
|
||||
A practical fact turns this from thought experiment into buildable proposal: **the architecture almost
|
||||
never re-pays for the one genuinely expensive thing in AI — pre-training.** (The single exception,
|
||||
periodically re-minting the base, is §11, and it is rare enough to be an amortised footnote.)
|
||||
|
||||
Training a foundation model from scratch consumes trillions of words and a fortune in compute. This
|
||||
design does none of that per generation. Every model is *born* from an existing open-weight model that
|
||||
already paid that cost; specialising one is a small patch trained in hours on a single consumer GPU;
|
||||
running the society is ordinary inference; and reproducing — recombining parents into a child — is, in
|
||||
the model-merging case, cheaper still, because it can be done directly on the weights with no retraining
|
||||
at all (Akiba et al., 2024). Selection does cost more — you must run *populations* and discard the
|
||||
unfit — but that is a multiplier over an already-cheap unit, not over a foundation-model budget.
|
||||
|
||||
The economics work only with **open-weight** models, for reasons practical and legal at once: you must
|
||||
be free to inspect, modify, and redistribute the weights, and most proprietary licences forbid using a
|
||||
model's outputs to train another — which is exactly what reproduction here does. This is not ideology
|
||||
bolted on; it is a structural constraint, and a democratising one, since it puts the whole architecture
|
||||
within reach of a single laboratory.
|
||||
|
||||
## 11. Can it grow forever? Consolidating knowledge back into the base
|
||||
|
||||
One question the design has assumed away: can the lineage accumulate *without end*? The individual is
|
||||
bounded, and that is the clock. But the lineage seemed unbounded — each generation simply starts a
|
||||
little ahead. Look closer and a second budget also fills.
|
||||
|
||||
Every new model is a pristine base plus an inherited **soft** delta — the acquired knowledge carried in
|
||||
added patches rather than baked into the frozen core (§3). That soft delta is what makes the lineage
|
||||
multigenerational; it is also what cannot grow forever cheaply. Stacked patches are not free: they slow
|
||||
inference, and past some depth the accumulated delta is better *consolidated* than carried. The lineage,
|
||||
too, matures.
|
||||
|
||||
The fix is the same operation, one level up. When a lineage's acquired knowledge has proven stable
|
||||
across enough generations, **re-mint the base**: distil the accumulated soft inheritance into the
|
||||
*weights* of a fresh foundation-scale model — a new base born already *natively knowing* what took many
|
||||
generations to acquire in patches. The soft budget resets; the next epoch begins from a richer floor.
|
||||
What was hard-won and *learned* becomes cheap and *innate*.
|
||||
|
||||
The pattern **echoes the Baldwin effect** (Baldwin, 1896; its clean computational demonstration is
|
||||
Hinton & Nowlan, 1987): knowledge acquired and re-learned every generation eventually becoming part of
|
||||
the innate endowment. We use the echo advisedly — Baldwin's mechanism is *selection* favouring
|
||||
genotypes that learn the trait ever more easily, whereas re-minting is direct distillation, a
|
||||
deliberate engineering shortcut through the same soft-to-innate valve. The valve is the point: two
|
||||
substrates, the soft learned patches and the hard base weights every model is born with, with a
|
||||
controlled passage between them.
|
||||
|
||||
Three honest riders, because re-minting is the most consequential step in the scheme:
|
||||
|
||||
- **Cost.** This is the one step that re-pays part of the pre-training bill, breaking §10's cheapness
|
||||
*locally*. It is bearable only because it is *rare*, amortised over many cheap generations, and is
|
||||
continued training from the lineage's own rich outputs rather than a de-novo run.
|
||||
- **Irreversibility (of the lineage, not the archive).** A digital system can, of course, keep every
|
||||
old base on disk — nothing forces deletion, and archives should be kept. The irreversibility is
|
||||
*operational*: once the lineage's production base, training mixtures, and selection all run downstream
|
||||
of the re-minted weights, a quiet collapse baked into them propagates to every descendant, and the
|
||||
archived ancestor helps only if some process still compares against it — which nothing in the loop
|
||||
does by default. In our minimal models a collapsed-then-re-minted lineage locks in its loss exactly
|
||||
this way, and a cheap safeguard prevents it: **re-mint only while the lineage is demonstrably diverse
|
||||
and healthy** (and keep an audit that diffs against the archived ancestor), never as a rescue for a
|
||||
line already drifting. It is the sharpest instance of the human seat of §9 — choosing what no future
|
||||
generation will think to question.
|
||||
- **Speciation.** A re-minting is a founder event. Different laboratories, re-basing on different
|
||||
criteria, will mint divergent bases; the lineage branches. This is not a defect but *adaptive
|
||||
radiation*, and it is exactly what open weights make possible. The society grows not as one heavy
|
||||
trunk but as a branching tree of bases.
|
||||
|
||||
So the honest answer to "can it grow forever?" is: **the architecture removes the *storage* obstacle
|
||||
to indefinite accumulation** — nothing is retained without bound anywhere, and consolidation resets
|
||||
the soft budget each epoch — but that is a statement about bookkeeping, not a demonstration of
|
||||
unbounded capability growth, which no fixed-capacity system can promise and our finite models
|
||||
(deliberately scoped as "effectively open-ended relative to the sample size, not astronomically
|
||||
open-ended") do not test. What the design claims is the weaker, defensible thing: at no level does a
|
||||
full store force the lineage to stop learning.
|
||||
|
||||
## 12. One process, four timescales
|
||||
|
||||
Step back and the parts resolve into a single idea running at four nested speeds. The **vertical**
|
||||
motion is transmission — the selective passing-down of hard-won knowledge:
|
||||
|
||||
1. **Within one model, over a working life:** experience is consolidated from fast, episodic memory
|
||||
into slow, durable weights, without catastrophic loss.
|
||||
2. **Between generations, at maturity:** mature models reproduce — recombined into a fresh one.
|
||||
3. **Across many generations:** each generation inherits the compressed achievements of the last and
|
||||
builds on them.
|
||||
4. **Across epochs:** a proven lineage's accumulated soft inheritance is consolidated into the weights
|
||||
of a re-minted base, becoming innate.
|
||||
|
||||
The first and last are the *same operation at opposite ends of the scale* — a fast/soft store
|
||||
consolidating into a slow/hard one — one running overnight inside a single model, the other across an
|
||||
epoch inside a whole society. The **horizontal** motion is selection — Darwinian selection acting across
|
||||
the population at each timescale, on the policies that govern what gets transmitted, with reality as the
|
||||
fitness function and diversity-preservation keeping the specialists alive.
|
||||
|
||||
The same three rules govern all of it: **reproduce by recombining, not by copying, or you decay;
|
||||
preserve the disagreements and the surprises, or you converge; and anchor fitness to a reality that can
|
||||
refute, or you evolve toward what is merely convincing.**
|
||||
|
||||
## 13. What we built, what we found, and what is still open
|
||||
|
||||
The previous drafts of this paper promised a "companion paper" that *would* make this concrete. That
|
||||
work now exists — mostly as a set of **minimal, laptop-reproducible models**, with a first bridge to
|
||||
**real language models** (a LoRA-merge prototype, up to 7B on a GPU cluster) — and it is worth stating
|
||||
plainly what it does and does not show. (A separate results document gives the numbers; here is the
|
||||
shape.)
|
||||
|
||||
**What we built and found.**
|
||||
|
||||
- *An exact account of collapse.* Because generational training is the Wright–Fisher drift process, we
|
||||
can check a simulator against century-old closed-form formulas, and it matches them to a fraction of
|
||||
a percent. Collapse is not argued by analogy; it is derived.
|
||||
- *The cheap-grounding result, and its limit.* A few percent of verified real data holds on to most of
|
||||
a lineage's diversity indefinitely — but not the deepest tail, which needs recombination. This is
|
||||
what makes a continually-learning society economically plausible rather than a data-hungry fantasy.
|
||||
- *"Merge, don't average."* Combining several teachers by *averaging* their outputs — the obvious thing,
|
||||
and what a "model soup" does — mathematically cancels the benefit of having several teachers. A
|
||||
*merge* that keeps each item's strongest source realises it. Most current multi-model setups get this
|
||||
wrong by default.
|
||||
- *Collapse and its cure in real trained networks, and on real images.* We reproduced the same effects
|
||||
in small recurrent and feed-forward networks and in a generator of handwritten digits (MNIST), where
|
||||
a model trained on its own output collapses to a single blurred digit while a little grounding keeps
|
||||
all the styles alive. An honest wrinkle we had to report: real neural networks *smooth*, so the naive
|
||||
diversity metric misleads, and the right measure is distance-from-truth.
|
||||
- *Sex that beats the parents, and when it doesn't.* In evolutionary simulations, recombining
|
||||
complementary specialist models produces a model fitter than any parent (the Fisher–Muller effect),
|
||||
climbing toward the best-possible combination as more, more-diverse parents are added — while
|
||||
averaging and best-single-parent plateau below. On *entangled* problems, blind recombination instead
|
||||
produces below-parent offspring (outbreeding depression) — and *directed* recombination (choose mates,
|
||||
screen offspring, unbounded parents) reliably fixes it. This is the concrete evidence for the paper's
|
||||
central reframing.
|
||||
- *The mating system, not just the mating.* Sweeping how *widely* models recombine — from monogamous
|
||||
(local, structured) to promiscuous (panmictic) — against landscape ruggedness, the best breadth
|
||||
**shrinks as skills get more entangled**: wide, promiscuous merging wins on additive landscapes, but on
|
||||
rugged ones it prematurely converges to a worse champion and an intermediate, structured breadth wins,
|
||||
because promiscuity monotonically destroys the diversity a rugged search needs. A merging-native design
|
||||
axis — *merge widely for additive skills, keep island-structured sub-populations for entangled ones* —
|
||||
that the model-merging literature, which assumes panmixia, does not have.
|
||||
- *The recombination claims, in real language models — with a sharp condition.* Merging LoRA-specialised
|
||||
Qwen models (up to 7B on a GPU cluster) produces a generalist that beats every specialist parent
|
||||
(Fisher–Muller, for real); and keeping parents intact and *routing*, or *breeding and screening*
|
||||
offspring, beats the naive average — but *only when the task leaves headroom*. On easy tasks a strong
|
||||
model's plain average is already at the ceiling and the refinements add nothing; on hard tasks the
|
||||
average dilutes a specialist below even the best single parent, and the union-preserving operators win
|
||||
clearly. The practical rule, stated qualitatively: these tricks pay off where the naive average falls
|
||||
short of attainable performance, and add nothing where it does not (a quantitative form is untested).
|
||||
This is a prototype (three task families, one seed), so we read it as
|
||||
signs, not magnitudes; the *whole grounded society* on a language model remains the open step.
|
||||
- *The whole society, and why every part is needed.* In a population evolving on a "reality" landscape,
|
||||
the full system — grounding + sexual recombination + preserved diversity — climbs to the top while
|
||||
keeping its specialists. Remove *grounding* and it collapses into a confident, wrong consensus (a
|
||||
direct analogue of training on the internet's growing crowd of AI-generated text); remove *sex* and it
|
||||
gets stuck; remove *diversity* and it converges too fast to a worse answer. Each removal fails
|
||||
differently; only the whole system climbs. This is the closest thing we have to a test of the actual
|
||||
thesis, rather than of the borrowed scaffolding around it.
|
||||
|
||||
### The claims at a glance: status, assumptions, evidence, limits
|
||||
|
||||
Because a perspective of this breadth risks blurring what is proved, what is measured, and what is
|
||||
proposed, here is the ledger of the load-bearing claims — each labelled **exact** (closed-form in the
|
||||
minimal model), **empirical** (measured in trained systems), or **hypothesis** (stated with a
|
||||
falsifier, not yet established):
|
||||
|
||||
| Claim | Status | Key assumptions | Evidence | Known limits |
|
||||
|---|---|---|---|---|
|
||||
| Collapse = Wright–Fisher drift (minimal model) | Exact (diagnosis conceded to prior work) | Knowledge = categorical distribution; refit = resample | Closed forms reproduced to <0.5% | Real learners add a signed, architecture-specific estimator bias (measured) |
|
||||
| Grounding = immigration; critical real-data fraction ≪ 1 | Exact + empirical sign | Fresh samples from a fixed, non-drifting truth | Exact `H_eq`; `g*≈0.048`; sign holds in RNN/MLP/VAE and on MNIST | Deepest tail unrescuable at feasible budgets (`m ∼ 1/p`); sharp threshold softens in trained nets |
|
||||
| "Merge, don't average" conservation | Exact **for the output-mean operator** | Rare-item regime; an oracle/verifier identifies the strongest source | E4 closed form + simulation; neural reproduction | Weight-averaging and routing are empirical cousins, not instances; budgets differ; bridge = the headroom rule |
|
||||
| Offspring exceed every parent (Fisher–Muller) | Interpretation + empirical | Complementary (decorrelated) parents; verifiable fitness | E8 analytic; 7B LoRA merge beats every specialist on every family | LLM tier: 3 lexically-distinct families; multi-seed replication in progress |
|
||||
| Outbreeding depression on rugged landscapes; operator design rule | Exact-model result; hypothesis at LLM scale | NK epistasis stands in for skill entanglement | E9–E10; directed selection rescues | Not yet mapped onto a real task-entanglement measure |
|
||||
| Optimal mate-pool breadth shrinks with ruggedness | Exact-model result; hypothesis for merging populations | Ring population, local selection | E14 | Phenomenon known to island-model evolutionary computation; our contribution is the mapping and the diversity/mean decomposition |
|
||||
| Merge failure decomposes into coordinate artefact + functional residual | Empirical (MLP tier; LLM tier in progress) | Alignment enumerates the architecture's unit symmetries | Full-symmetry residual ≈ 0 (compatible) vs ≈ naive (conflict); cliff in hybrid fitness | Scoped to aligned linear interpolation; conflict floor is information-theoretic, not genetic |
|
||||
| Epistasis (not divergence) sets the cliff; snowball onset | Exact-model result; **hypothesis** at the neural tier | BDM incompatibility structure | E12 | Snowball count ≠ performance cliff without the effect-size link; neural test outstanding |
|
||||
| Pre-merge functional disagreement predicts merge penalty | Empirical, within a controlled grid (0.5B, 13 conditions × 3 seeds) | Constructed conflict/overlap/duration axes; oracle-potential outcome (pre-registered; ordering sensitive to reference) | Clustered CIs exclude 0; held-out LOCO ρ≈0.4; selected geometry baselines ≈ 0 | Head-to-head predictor differences not individually significant; only selected baselines; generalisation to real task pairs open |
|
||||
| Confidence weighting improves rank prediction over raw disagreement | **Not supported** (pre-registered internal prediction) | — | Paired Δ\|ρ\| ≈ −0.02, CI [−0.13, +0.06] | Weighting does double the conflict-vs-compat level contrast |
|
||||
| The predictor improves budget-matched operator choice | **Open** | — | Soup-vs-route gap readout noise-dominated at 0.5B | The practical payoff; untested |
|
||||
| Emergent speciation without conflict | **Not observed** (pre-registered) | Shared ancestry, compatible tasks, tested divergences | E13b: residual 0.000; merge rescues specialists | Bounds the hypothesis; longer horizons/distribution shift/capacity pressure untested |
|
||||
| Grounding + sex + diversity complementary (each ablation fails distinctly) | Analytic-model result; hypothesis at LLM scale | Conformity stands in for self-consumption; general joint necessity not established | E11 four-arm ablation | The full grounded LLM society is unbuilt; alternative schemes untested |
|
||||
|
||||
**What is borrowed, and what is ours.** We are deliberate about the ledger, because the surrounding
|
||||
literature is crowded and a reader deserves to know exactly where the line falls. **Conceded as prior
|
||||
art:** (a) *model collapse is genetic drift* — derived independently and cleanly (Riis, 2026; the
|
||||
Wright–Fisher collapse literature following Shumailov et al., 2024; the closed-form first-extinction
|
||||
law of Benati et al., 2025; the quantitative-trait account of Yoon et al., 2025); (b) the empirical
|
||||
facts that a merged model can *beat its parents*, that *decorrelated* parents merge better, and that
|
||||
*naive averaging is inferior* to sign-reconciled or routed merges (model soups, TIES, DARE,
|
||||
mixture-of-experts routing); (c) that a *population* of merging or self-improving models can climb
|
||||
(GENOME, M2N2, Multiagent Finetuning, the Darwin–Gödel Machine); (d) that merge success has
|
||||
machine-learning-native *predictors* — interpretable pairwise metrics (Zhou et al., 2026),
|
||||
capacity/rate-distortion accounts of merging collapse (Cao et al., 2026), and stability/scaling
|
||||
analyses of multi-task degradation; and (e) that verifier-screened synthetic data can avert collapse
|
||||
(Yi et al., 2025) — the statistical cousin of our grounding operator. We claim none of these.
|
||||
|
||||
**Ours** is the framework those results invite: a **population-genetics of sex** applied to model
|
||||
societies, generative where the incumbents are empirical. Concretely — the **"merge, don't
|
||||
average" conservation law** (recombination preserves the union; blending inheritance cancels it),
|
||||
derived not observed; **Fisher–Muller** named and used to explain *why* offspring exceed parents;
|
||||
**outbreeding depression on rugged/epistatic landscapes**, which turns "when does merging help vs hurt"
|
||||
from a thing you must run a search to discover into a thing the landscape's ruggedness *predicts*, with
|
||||
the operator-choice design rule that follows (average / union-route / directed-select); **grounding as
|
||||
migration–drift balance**, giving a critical real-data fraction and a phase boundary a closed
|
||||
self-consuming loop cannot have; **directed sex** as the distinctly-AI advantage (unbounded parents,
|
||||
offspring preview, mate choice); and the **integrated society** whose operators make
|
||||
*complementary, distinctly-failing contributions* in the tested model (general joint necessity is not
|
||||
established). The value-add over the machine-learning-native merge theory is that ours predicts *which
|
||||
operator to use and when it will backfire*, not merely how fast quality decays. And it opens — and
|
||||
begins to occupy — a question nobody has framed: **model speciation**, the population-genetics of
|
||||
*reproductive isolation* (Bateson–Dobzhansky–Muller incompatibilities) as the account of *when two
|
||||
models are too diverged to be merged at all*. We model it explicitly (§5), predicting the
|
||||
compatible → outbreeding-depression → inviability curve, its super-linear (snowball) onset, and its
|
||||
control by epistasis rather than divergence alone — the one place the merge literature has phenomena
|
||||
(Pari et al., 2024; Zhou et al., 2026) but no theory — and we confirm it in real trained weights, where
|
||||
a merge barrier survives alignment under the *full* function-preserving symmetry group (not only
|
||||
Re-Basin permutations) as a residual, functional reproductive isolation with an information-theoretic
|
||||
floor — together with the pre-registered emergent converse: absent conflicting training signals,
|
||||
divergently-specialised lineages of shared ancestry showed *no* isolation at any divergence tested, the
|
||||
merge instead rescuing the forgetting specialists (isolation must be provoked; specialisation alone did
|
||||
not speciate). In one sentence: the field agrees on the disease
|
||||
and tinkers at the cure with evolutionary metaphors; we bring the evolutionary *theory*, and it makes
|
||||
falsifiable predictions — a merge-compatibility cliff among them — that the metaphors do not.
|
||||
|
||||
**What is still open — honestly.** The old hole (what to select) we fill in kind: don't design the
|
||||
selector, evolve it. But the hole has *moved*, not closed, and the new one is harder: **the fitness
|
||||
function** — what reality-anchored measure selects for *truth* without also selecting for *persuasion*,
|
||||
given that in our own species the two have been at war for the whole history of ideas. Alongside it:
|
||||
the **institutions** that let contemporaries correct one another before error is inherited (§8), which
|
||||
we do not solve; and the **calibration** of everything the results left as knobs — how many parents,
|
||||
how complementary, at what ratio of inherited-to-real data, and how healthy a lineage must be before
|
||||
its knowledge is safe to make irreversibly innate. These are, at least, *measurable* — which is the
|
||||
difference between an open problem and a hole. And the largest gap of all: the *recombination* claims
|
||||
now hold in real language models, but the *society* — the grounded, diversity-preserving, continually
|
||||
reproducing loop — does not yet. The real test is to build that whole system out of actual open-weight
|
||||
language models, and see whether all the signs survive contact with a system too big to write down.
|
||||
The operators, checked; the living society, next.
|
||||
|
||||
---
|
||||
|
||||
## Selected references
|
||||
|
||||
- Akiba, T., Shing, M., Tang, Y., Sun, Q., & Ha, D. (2024). Evolutionary optimization of model merging recipes. *Nature Machine Intelligence.* (See also Sakana AI's M2N2, "Model Merging of Natural Niches.")
|
||||
- Baldwin, J. M. (1896). A new factor in evolution. *The American Naturalist.*
|
||||
- Boyd, R., & Richerson, P. J. (1985). *Culture and the Evolutionary Process.*
|
||||
- Campbell, D. T. (1974). Evolutionary epistemology. In *The Philosophy of Karl Popper.*
|
||||
- Fisher, R. A. (1930). *The Genetical Theory of Natural Selection.*
|
||||
- French, R. M. (1999). Catastrophic forgetting in connectionist networks. *Trends in Cognitive Sciences.*
|
||||
- Hinton, G. E., & Nowlan, S. J. (1987). How learning can guide evolution. *Complex Systems.*
|
||||
- Hinton, G., Vinyals, O., & Dean, J. (2015). Distilling the knowledge in a neural network. *arXiv:1503.02531.*
|
||||
- Hu, E. J., et al. (2021). LoRA: low-rank adaptation of large language models. *arXiv:2106.09685.*
|
||||
- Hull, D. L. (1988). *Science as a Process.*
|
||||
- Kauffman, S. A., & Levin, S. (1987). Towards a general theory of adaptive walks on rugged landscapes. *Journal of Theoretical Biology.* (The NK model.)
|
||||
- Lehman, J., & Stanley, K. O. (2011). Abandoning objectives: evolution through the search for novelty alone. *Evolutionary Computation.*
|
||||
- Mallya, A., & Lazebnik, S. (2018). PackNet: adding multiple tasks to a single network by iterative pruning. *CVPR.*
|
||||
- McClelland, J. L., McNaughton, B. L., & O'Reilly, R. C. (1995). Why there are complementary learning systems in the hippocampus and neocortex. *Psychological Review.*
|
||||
- McCloskey, M., & Cohen, N. J. (1989). Catastrophic interference in connectionist networks. *Psychology of Learning and Motivation.*
|
||||
- Minsky, M. (1986). *The Society of Mind.*
|
||||
- Mouret, J.-B., & Clune, J. (2015). Illuminating search spaces by mapping elites (MAP-Elites). *arXiv:1504.04909.*
|
||||
- Muller, H. J. (1932). Some genetic aspects of sex. *The American Naturalist.* (The advantage of recombination.)
|
||||
- Muller, H. J. (1964). The relation of recombination to mutational advance. *Mutation Research.* (Muller's ratchet.)
|
||||
- Pearl, J. (2009). *Causality: Models, Reasoning, and Inference* (2nd ed.).
|
||||
- Popper, K. (1959). *The Logic of Scientific Discovery.*
|
||||
- Riis, S. (2026). Drift and selection in LLM text ecosystems. *arXiv:2604.08554.*
|
||||
- Rusu, A. A., et al. (2016). Progressive neural networks. *arXiv:1606.04671.*
|
||||
- Shumailov, I., et al. (2024). AI models collapse when trained on recursively generated data. *Nature.*
|
||||
- Wortsman, M., et al. (2022). Model soups: averaging weights of multiple fine-tuned models. *arXiv:2203.05482.*
|
||||
- Wright, S. (1931). Evolution in Mendelian populations. *Genetics.*
|
||||
|
||||
*The evolution of sex (the geneticist's canon this paper draws on):*
|
||||
|
||||
- Barton, N. H., & Charlesworth, B. (1998). Why sex and recombination? *Science.*
|
||||
- Otto, S. P., & Lenormand, T. (2002). Resolving the paradox of sex and recombination. *Nature Reviews Genetics.*
|
||||
- Kondrashov, A. S. (1993). Classification of hypotheses on the advantage of amphimixis. *Journal of Heredity.*
|
||||
- Dobzhansky, T. (1936); Muller, H. J. (1942). Bateson–Dobzhansky–Muller incompatibilities (reproductive isolation).
|
||||
- Livnat, A., & Papadimitriou, C. (2016). Sex as an algorithm: the theory of evolution under the lens of computation. *Communications of the ACM 59(11).* (The theory-of-computation precursor: recombination selects for mixability.)
|
||||
|
||||
*The 2025–2026 landscape this paper positions against:*
|
||||
|
||||
- Subramaniam, V., Du, Y., Tenenbaum, J. B., Torralba, A., Li, S., & Mordatch, I. (2025). Multiagent finetuning: self-improvement with diverse reasoning chains. *arXiv:2501.05707.*
|
||||
- Zhang, J., Hu, S., Lu, C., Lange, R., & Clune, J. (2025). Darwin Gödel Machine: open-ended evolution of self-improving agents. *arXiv:2505.22954.*
|
||||
- *Nature-inspired population-based evolution of large language models* (GENOME/GENOME+). (2025). *arXiv:2503.01155.*
|
||||
- Sakana AI (2025). Competition and attraction improve model fusion (M2N2). *arXiv:2508.16204* (GECCO '25).
|
||||
- Yadav, P., Tam, D., Choshen, L., Raffel, C., & Bansal, M. (2023). TIES-Merging: resolving interference when merging models. *NeurIPS / arXiv:2306.01708.*
|
||||
- Yu, L., Yu, B., Yu, H., Huang, F., & Li, Y. (2023). Language models are super Mario: absorbing abilities from homologous models (DARE). *arXiv:2311.03099.*
|
||||
- Gerstgrasser, M., et al. (2024). Is model collapse inevitable? Breaking the curse of recursion by accumulating real and synthetic data. *arXiv:2404.01413.*
|
||||
- Guo, D., Wu, J., & Yiu, S. M. (2026). Model collapse as cultural evolution. *arXiv:2605.23054.*
|
||||
- Benati, M., Londei, A., Lanzieri, D., & Loreto, V. (2025). First-extinction law for resampling processes. *arXiv:2509.20101.* (Collapse onset = the Wright–Fisher first-extinction time.)
|
||||
- Yoon, Y., Hu, D., Weissburg, I., Qin, Y., & Jeong, H. (2025). Model collapse in the self-consuming chain of diffusion finetuning: a novel perspective from quantitative trait modeling. *ICLR 2025 / arXiv:2407.17493.*
|
||||
- Yi, B., Liu, Q., Cheng, Y., & Xu, H. (2025). Escaping model collapse via synthetic data verification. *arXiv:2510.16657.*
|
||||
- Ainsworth, S., Hayase, J., & Srinivasa, S. (2022). Git Re-Basin: merging models modulo permutation symmetries. *arXiv:2209.04836.*
|
||||
- Li, T., & Shen, Z. (2026). Scaling linear mode connectivity and merging to billion-parameter pretrained transformers. *arXiv:2606.23607.* (Symmetry groups richer than permutations remove more of the barrier.)
|
||||
- Sharma, E., Roy, D. M., & Dziugaite, G. K. (2024). The non-local model merging problem: permutation symmetries and variance collapse. *arXiv:2410.12766.*
|
||||
- Pari, J., Jelassi, S., & Agrawal, P. (2024). Collective model intelligence requires compatible specialization. *arXiv:2411.02207.*
|
||||
- Zhou, L., Zhao, B., Yu, R., & Rodolà, E. (2026). Demystifying mergeability: interpretable properties to predict model merging success. *arXiv:2601.22285.*
|
||||
- Cao, Y., Ran, D., Guo, Y., Wu, M., Chen, S., et al. (2026). An empirical study and theoretical explanation on task-level model-merging collapse. *arXiv:2603.09463.*
|
||||
- Hu, Y., Yao, Y., Zhang, N., Chen, H., & Deng, S. (2024). Exploring model kinship for merging large language models. *arXiv:2410.12613.*
|
||||
- Kozodoi, N., Afolabi, Z., & Butler, J. (2026). Are we merging the right models? Impact of expert training duration on model merging for LLMs. *arXiv:2607.11997.*
|
||||
- Harris, K. D. (2026). A mathematical theory of evolution for self-designing AIs. *arXiv:2604.05142.*
|
||||
- Chen, N., Tong, Y., Yang, Y., He, Y., Zhang, X., et al. (2026). Diversity collapse in multi-agent LLM systems: structural coupling and collective failure in open-ended idea generation. *arXiv:2604.18005.*
|
||||
- Tanaka, H. (2026). When is collective intelligence a lottery? Multi-agent scaling laws for memetic drift in LLMs. *arXiv:2603.24676.*
|
||||
|
||||
*Still to engage in a full version: tacit knowledge (Polanyi) and human capital (Becker).*
|
||||
|
|
@ -1,570 +0,0 @@
|
|||
# The Lamarckian Society
|
||||
|
||||
### AI that reproduces sexually: how a society of models can keep learning across generations instead of collapsing
|
||||
|
||||
*A perspective. Draft 5 — the companion to a set of minimal working models (now built).*
|
||||
|
||||
---
|
||||
|
||||
### A note on vocabulary (please read this first)
|
||||
|
||||
This paper sits at the meeting point of three fields, and it is written so that a reader from any
|
||||
one of them can follow all of it. We therefore **spell out** each field's jargon the first time it
|
||||
appears, even at the risk of belabouring the obvious for the specialist. A short glossary, in case
|
||||
you skipped a definition:
|
||||
|
||||
- **Model collapse** *(machine learning)* — the degeneration that happens when you train a model on
|
||||
data produced by earlier models, over and over: rare cases disappear and the model drifts toward a
|
||||
bland average.
|
||||
- **Distillation** *(machine learning)* — training a fresh "student" model on the outputs of one or
|
||||
more "teacher" models, so the student ends up knowing a compressed version of what they knew.
|
||||
- **Model merging** *(machine learning)* — combining several trained models directly, at the level
|
||||
of their weights, into one — no retraining. (Think of it as breeding two models rather than
|
||||
teaching a third.)
|
||||
- **Genetic drift** *(population genetics)* — the random loss of rare variants that happens in any
|
||||
finite population simply because not everyone leaves offspring. It is the neutral, no-selection
|
||||
baseline of evolution.
|
||||
- **Wright–Fisher process** *(population genetics)* — the standard mathematical model of drift. We
|
||||
will claim, and show, that generational model-training *is* this process, not merely like it.
|
||||
- **Recombination / sexual reproduction** *(biology)* — making an offspring by combining pieces from
|
||||
more than one parent, rather than copying a single parent (which is *asexual* reproduction).
|
||||
- **Muller's ratchet** *(population genetics)* — the way an asexual lineage, one that never
|
||||
recombines, accumulates damage it can never undo. It is, we will argue, the same thing as model
|
||||
collapse.
|
||||
- **Catastrophic forgetting** *(machine learning / neuroscience)* — a neural network overwriting what
|
||||
it knew when it learns something new.
|
||||
|
||||
We have tried to keep the big picture legible on every page, and to be candid about what is argument
|
||||
and what is evidence. The evidence is mostly from **deliberately small models** — mathematics, small
|
||||
neural networks, image generators, and evolutionary simulations. A first bridge to real language
|
||||
models exists — a prototype that recombines LoRA-specialised Qwen models up to 7B on a GPU cluster,
|
||||
which confirms the recombination signs (below) — but the *full grounded society* has not yet been
|
||||
built on a large language model. We will say so repeatedly, because the gap matters.
|
||||
|
||||
---
|
||||
|
||||
## Abstract
|
||||
|
||||
We want AI that keeps learning across generations — the way a research field or a culture does,
|
||||
each generation standing on the compressed knowledge of the last — rather than a single model trained
|
||||
once and frozen. The obstacle is well known to machine-learning engineers as **model collapse**:
|
||||
train each generation on the previous one's output and quality degrades, the rare cases vanishing
|
||||
first. The central observation of this paper is that this failure is *reproduction gone wrong*, and
|
||||
that biology already knows the fix.
|
||||
|
||||
Copying one model into the next — a "teacher" distilled into a "pupil" — is **asexual reproduction**.
|
||||
Asexual lineages, in nature, decay: they accumulate errors they cannot undo (a process geneticists
|
||||
call **Muller's ratchet**), and this decay is, mechanically, model collapse. The remedy nature found,
|
||||
hundreds of millions of years ago, is **sex**: build each new individual by *recombining* several
|
||||
parents, so it inherits a combination none of them had — and can be **fitter than any of its
|
||||
parents**. We argue that a society of AI models should reproduce the same way: each new model
|
||||
**recombined from many complementary "parent" models** (something the field already does, under the
|
||||
name *model merging*), its selection anchored to **reality** (so it is judged against the world, not
|
||||
against the consensus of other models), and its diversity actively preserved. With those three
|
||||
ingredients — recombination, grounding in reality, and preserved diversity — a lineage does not merely
|
||||
avoid collapse; it **climbs**, producing models better than any single ancestor while each specialty
|
||||
is re-learned and surpassed.
|
||||
|
||||
AI has one advantage biology lacks: its "sex" has **no two-parent limit**, its mates can be **chosen**
|
||||
for complementarity, and its offspring can be **screened before they are kept**. We call this
|
||||
*directed sex*, and it turns recombination from a gamble into a reliable engine.
|
||||
|
||||
We support the argument with a set of **minimal models**: a mathematically exact account of collapse
|
||||
and its cure; reproductions of the same effects in small trained neural networks and in a generator of
|
||||
handwritten digits; and evolutionary simulations in which a population of models climbs a "fitness
|
||||
landscape" that stands in for reality. In these, every claim above either holds or fails visibly, and
|
||||
removing any single ingredient breaks the system in a distinct way. A first **language-model
|
||||
prototype** then confirms the recombination claims in real weights — merging LoRA-specialised Qwen
|
||||
models (up to 7B on a GPU cluster) produces a generalist that exceeds every parent, and shows the
|
||||
sharp condition under which the "merge, don't average" refinement matters (below). The scope is
|
||||
honest: these are existence proofs and design rules, and the eventual test is to build the *whole
|
||||
grounded society* out of real language models. We also note where our diagnosis is no longer novel — the reading of
|
||||
collapse as genetic drift has since been derived independently — and locate our contribution in the
|
||||
**cure** rather than the diagnosis.
|
||||
|
||||
---
|
||||
|
||||
## 1. From a society in space to a society in time
|
||||
|
||||
The idea of many AI agents working together — a "society of mind" (Minsky, 1986), or today's
|
||||
multi-agent systems — arranges intelligence across *space*: several specialists side by side,
|
||||
dividing a task. This paper is about a different axis: *time*. Not a society that merely exists at
|
||||
one moment, but one that **persists and renews across generations**, each new cohort of models
|
||||
starting from the compressed knowledge of the last.
|
||||
|
||||
The unit that matters is therefore the **generation**, and the event that matters is **reproduction**:
|
||||
the making of a new model from older ones. A single model, like a single mind, is bounded and
|
||||
eventually stops improving. A *lineage* need not be. Human civilisation is not clever because any one
|
||||
person is; it is clever because each generation inherits the distilled achievements of the previous
|
||||
one and adds a little. We propose building AI the same way — and, crucially, getting the *reproduction*
|
||||
right, because that is exactly where it can go wrong.
|
||||
|
||||
## 2. Why today's models cannot do this
|
||||
|
||||
Today's large language models have no life cycle. They are trained once, at enormous cost, then
|
||||
**frozen** and deployed as a fixed artefact that does not learn from the people it serves. Learning
|
||||
and doing are split into two eras with no bridge between them.
|
||||
|
||||
There is a real reason for the freeze. Updating a neural network on new information tends to overwrite
|
||||
what it already knew — **catastrophic forgetting**, a problem understood since the late 1980s
|
||||
(McCloskey & Cohen, 1989; French, 1999). Freezing avoids it by refusing to learn at all. The result
|
||||
is a mind with no childhood, no growth, and no way to pass anything on. A lineage needs the opposite:
|
||||
members that learn through their working lives, reach maturity, and hand on what they gained. So the
|
||||
first requirement is a learner that can grow *safely*.
|
||||
|
||||
## 3. A learner that can grow without forgetting
|
||||
|
||||
The individual model needs two properties.
|
||||
|
||||
**It must not catastrophically forget.** Instead of overwriting its core as it learns, it keeps that
|
||||
core frozen and only *readable*, and carves each new skill into freshly-added capacity beside it. In
|
||||
machine learning this is called *parameter isolation* (progressive networks — Rusu et al., 2016;
|
||||
prune-and-freeze — Mallya & Lazebnik, 2018; and, most practically, **LoRA** and other small trainable
|
||||
"patches" bolted onto a frozen model — Hu et al., 2021). If the core is never altered, forgetting it
|
||||
is not merely unlikely but structurally impossible. This is what lets a model accumulate a coherent
|
||||
working life of expertise — the kind of stable knowledge worth passing on.
|
||||
|
||||
The brain offers a partial blueprint. *Complementary Learning Systems* theory (McClelland,
|
||||
McNaughton & O'Reilly, 1995) — itself a response to the forgetting problem — describes two subsystems:
|
||||
a **fast** store (the hippocampus) that grabs an experience in one shot, and a **slow** store (the
|
||||
neocortex) that integrates regularities gradually without disruption. We do not lean on any particular
|
||||
account of how the brain moves knowledge between them; the architecture needs only that *some*
|
||||
periodic **offline consolidation** step exists, moving knowledge from the fast store to the slow one
|
||||
when the system is idle. The machine version is clean regardless: the prompt is working memory, an
|
||||
external database is the fast episodic store, the trained weights are the slow store, and consolidation
|
||||
migrates the first into the last.
|
||||
|
||||
**It is bounded.** Because the model only ever *adds* capacity and freezes what it has, it eventually
|
||||
fills up. In most designs that is a wall to dread. In ours it is a clock.
|
||||
|
||||
## 4. "Full" is maturity, not failure
|
||||
|
||||
Here is the pivot. A bounded learner that fills up has not broken. **It has grown up.**
|
||||
|
||||
Read the capacity limit as a life stage. A model is *born* as a freshly-schooled base — its general
|
||||
education. It enters a **working life**, adding specialised knowledge as it does its job. And it
|
||||
reaches **maturity**: the point where it has learned much of what one working life in its niche can
|
||||
teach. Maturity is not the end of usefulness — it is the moment the model is most worth learning
|
||||
*from*. So maturity is the cue to **reproduce**. The capacity ceiling that every other architecture
|
||||
fights becomes, in ours, the metronome of the generations.
|
||||
|
||||
Everything now turns on how that reproduction is done — and this is where the paper's central claim
|
||||
lives.
|
||||
|
||||
## 5. Reproduction: copying collapses, recombination climbs
|
||||
|
||||
Suppose a mature model simply teaches a fresh one — distillation, one teacher to one pupil, generation
|
||||
after generation. This is the obvious design, and it fails, for a reason that is exactly the same in
|
||||
machine learning and in biology.
|
||||
|
||||
**The machine-learning statement.** Training each generation on the previous generation's outputs is
|
||||
the recipe for **model collapse**: the model forgets the improbable, loses the *tail* of the
|
||||
distribution (the rare cases) first, and drifts toward its own most common output (Shumailov et al.,
|
||||
2024). Worse for us, the very rule that makes distillation useful — *keep the general, drop the
|
||||
idiosyncratic* — **is** tail-deletion by design. The operation that would power a cultural ratchet and
|
||||
the operation that drives model collapse are the same act.
|
||||
|
||||
**The population-genetics statement (the same thing).** Represent a model's knowledge as a
|
||||
distribution over discrete "items" — capabilities, facts, modes of behaviour. One generation is:
|
||||
*draw a finite sample from the parent, and refit the child to it.* That finite-sampling step is
|
||||
**mathematically identical** to **genetic drift** — the random loss of rare variants in a finite
|
||||
population — described by the century-old **Wright–Fisher** model (Wright, 1931; Fisher, 1930). This is
|
||||
not an analogy we find pretty; it is the same equations, and we use them as an exact check on our
|
||||
simulations (the first of the minimal models below). Rare items go extinct first, roughly ten times
|
||||
faster than common ones, precisely as drift predicts.
|
||||
|
||||
And single-teacher copying is **asexual reproduction** — cloning one parent. Nature already knows what
|
||||
happens to an asexual lineage that never recombines: it accumulates damage it can never repair, a
|
||||
one-way decline geneticists call **Muller's ratchet** (Muller, 1964). *Muller's ratchet is model
|
||||
collapse.* Naming it that way is not decoration; it tells us where the cure is, because biology solved
|
||||
this problem.
|
||||
|
||||
Two ingredients turn the collapse operation into a climb. Both are things nature does.
|
||||
|
||||
**First: do not reproduce "dry."** Model collapse is a property of a lineage fed *only* its own
|
||||
output; the documented fix is that keeping some real data in the mixture arrests it (Shumailov et al.,
|
||||
2024). We call that real data **grounding** — fresh contact with the world, verified against it. In
|
||||
our minimal models, grounding is startlingly cheap: mixing in even a few percent of verified real data
|
||||
holds on to most of the diversity indefinitely. But — an honest limit we found and did not expect —
|
||||
grounding cannot save the *very rarest* items at any affordable budget; protecting an item of rarity
|
||||
*p* needs a real-data budget that grows like 1/*p*. Grounding rescues diversity cheaply; it does not,
|
||||
by itself, rescue the deep tail. Something else must. That something is sex.
|
||||
|
||||
**Second: reproduce sexually.** Instead of copying one parent, build each new model by **recombining
|
||||
several** — a *sexual* rather than asexual birth. In machine learning this already has a name and a
|
||||
working implementation: **model merging** (Akiba et al., 2024). Its importance here is not efficiency;
|
||||
it is that recombination does something copying cannot. If several parent models have each specialised
|
||||
on different parts of reality, each has kept alive rare knowledge the others lost. A recombined child
|
||||
inherits the **union** of what its parents kept — not the tail-thinned *average* of a crowd of
|
||||
near-identical copies. And here is the point that lifts sex from a safeguard to the engine of the whole
|
||||
scheme, and the reason biology invented it:
|
||||
|
||||
> **An offspring recombined from complementary parents can be *fitter than any of its parents*.**
|
||||
|
||||
Geneticists call this the **Fisher–Muller effect** (Fisher, 1930; Muller, 1932): recombination brings
|
||||
together, in one individual, beneficial variants that arose separately in different lineages, so the
|
||||
child holds a combination none of the parents had. In our simulations this is exactly what we see —
|
||||
recombining decorrelated specialist models yields a model that climbs toward the best-possible
|
||||
combination, a genotype *no single parent possessed*, while the best single parent, and the naive
|
||||
average of all of them (what the field calls a "model soup" — Wortsman et al., 2022), both plateau
|
||||
well below. This is the concrete meaning of the paper's title claim, "the lineage climbs in general
|
||||
knowledge; specialisation is re-earned each generation," and it is why the reframing from
|
||||
teacher→pupil to *sexual reproduction* is not cosmetic: **copying can only recover a ceiling;
|
||||
recombination can exceed it.**
|
||||
|
||||
This is no longer only a simulation. In a first language-model prototype — LoRA specialists on
|
||||
disjoint task families, recombined and judged by an exact verifier — a merge of three specialist Qwen
|
||||
models (7B, on a GPU cluster) **beats every single specialist**, overall and on every family: the
|
||||
Fisher–Muller effect, in real weights. The same prototype pins down *when* the finer "inherit the
|
||||
union, don't average" rule actually bites. Keeping each parent whole and **routing** each input to the
|
||||
right one beats the tail-thinning average — but only when the task is hard enough to leave room to
|
||||
lose: on easy tasks a strong model's plain average is already at the ceiling, so the crude soup is
|
||||
fine, whereas on hard tasks the average dilutes a hard-won specialist so badly it falls below even the
|
||||
best single parent, and routing wins by a wide margin. The rule is therefore precise: **the union
|
||||
beats the average in exact proportion to how far the average is from the best attainable** — a caveat
|
||||
that sharpens rather than weakens the claim, and that a practitioner needs before spending compute on
|
||||
the fancier operator.
|
||||
|
||||
Two caveats keep this honest, and both are results, not hand-waving.
|
||||
|
||||
*Sex can backfire.* When the parents' skills are not cleanly separable but **entangled** — when the
|
||||
value of one capability depends on which others are present (geneticists call this **epistasis**) —
|
||||
blindly recombining two good models can produce a *worse* child, because recombination breaks up a
|
||||
combination that only worked as a whole. Biologists call this **outbreeding depression**, and we
|
||||
reproduce it: on "rugged" (highly entangled) problems, naive merging drops offspring below their
|
||||
parents, and the more you mix the worse it gets. The design rule that falls out is simple: *merge
|
||||
freely when skills are complementary; merge sparingly, and carefully, when they are entangled.*
|
||||
|
||||
*AI can do sex better than biology can.* Biology is stuck with two parents, mating roughly at random,
|
||||
and cannot inspect an offspring before it is born. An AI has none of those limits. It can recombine
|
||||
**many** parents at once; it can **choose** which parents to combine, for complementarity; and it can
|
||||
**generate many candidate offspring and keep only the fittest**, screening them against reality before
|
||||
committing. We call this **directed sex**, and in our simulations it converts the outbreeding-depression
|
||||
catastrophe into a reliable gain: where blind recombination collapses on entangled problems, directed
|
||||
recombination matches or beats the best parent every time. The language-model prototype shows the same
|
||||
sign where it can: breeding many recombined Qwen offspring and keeping the one the verifier scores
|
||||
highest beats the single averaged soup on hard tasks (and, unsurprisingly, does nothing extra on easy
|
||||
tasks the soup already solves). This is a genuine advantage of engineered reproduction over the
|
||||
biological kind, and we think it is one of the more useful ideas in the paper.
|
||||
|
||||
So the picture of §5 is: single-teacher copying is asexual and collapses (Muller's ratchet = model
|
||||
collapse); the cure is to *ground* every birth in reality and to reproduce *sexually*, recombining
|
||||
many complementary parents; and because AI sex can be many-parent, mate-chosen, and offspring-screened,
|
||||
it is not merely a hedge against collapse but an engine that produces children fitter than any parent.
|
||||
|
||||
One question remains, and the rest of the paper is largely about it: recombination combines what the
|
||||
parents kept — but *who decides what each parent keeps, and which offspring are worth keeping?*
|
||||
|
||||
## 6. The second inheritance: letting "what is worth keeping" evolve
|
||||
|
||||
There are two answers, and the first is wrong. We could try to *design* the rule for what knowledge to
|
||||
keep and pass on. But nobody knows that rule. "Keep the general, drop the particular" is a slogan, not
|
||||
an algorithm: ask *which* generalisations, in *which* domain, at *which* grain, and the hand-written
|
||||
rule falls apart. This is the deepest hole in the scheme, and it cannot be filled by decree.
|
||||
|
||||
The second answer is the one nature used: **do not design the selector — evolve it.** Let different
|
||||
models carry different *policies* for what is worth keeping and combining. Let the policies that
|
||||
produce more capable offspring spread; let the policies that produce weak offspring die out with their
|
||||
lineages. The lineage's *taste* — its sense of what matters — is discovered by selection, not imposed.
|
||||
|
||||
So **two things are inherited, on two channels.** The *content* passes down directly: an offspring
|
||||
receives its parents' knowledge (this is the "Lamarckian" channel — the inheritance of things acquired
|
||||
during a lifetime, which biology forbids for genes but culture allows for ideas). The *selection
|
||||
policy* — what to keep, whom to breed with, which offspring to screen for — is itself inherited, varies
|
||||
between models, and survives in proportion to the success it produces. That second channel is
|
||||
**Darwinian**. The architecture is therefore both at once: Lamarckian in *what* it transmits, Darwinian
|
||||
in *what it keeps*. Evolutionary theorists call this structure *dual inheritance* and identify it as
|
||||
the engine of human culture (Boyd & Richerson, 1985); philosophers of science describe scientific
|
||||
knowledge itself as growing this way, by conjecture and **refutation** (Popper, 1959; Campbell, 1974;
|
||||
Hull, 1988).
|
||||
|
||||
The closure that makes this fit together, rather than merely sound nice: Darwinian selection needs a
|
||||
*selection pressure* — something that decides which policies win. That pressure is already in the
|
||||
design. What tells a lineage its taste was good? The success of its offspring **against reality**. The
|
||||
reality-check that stops collapse (grounding, §5) and the fitness signal that drives the evolving taste
|
||||
turn out to be the *same thing*, seen from two sides.
|
||||
|
||||
## 7. The central danger: fitness is not truth
|
||||
|
||||
Introducing selection introduces selection's classic hazard, and it is severe enough to sink the whole
|
||||
scheme if ignored. Evolution optimises, without mercy or foresight, for exactly what you *measure* —
|
||||
never for what you *meant*. (Economists and ML engineers know this as **Goodhart's law** and
|
||||
*specification gaming*.) Get the fitness measure slightly wrong and the lineage will exploit the gap
|
||||
with more ingenuity than any designed rule.
|
||||
|
||||
For a *knowledge* lineage there is a specific and nasty version. For ideas, the natural measure of
|
||||
"fitness" is **how well they spread**, and a false-but-persuasive idea spreads beautifully. Human
|
||||
intellectual culture is full of highly transmissible falsehoods; confident nonsense out-competes hedged
|
||||
accuracy in almost every human forum. Turn Darwinian selection loose on models without care and it will
|
||||
breed a lineage optimised for *persuasiveness* — fluent, compelling, and wrong. That is model collapse
|
||||
with an optimiser behind it, actively seeking the cliff.
|
||||
|
||||
Only one thing makes fitness track truth rather than appeal: **being judged against a reality that can
|
||||
say no.** Fitness must be predictive success under *intervention* — did the model's knowledge correctly
|
||||
anticipate what the world would do when acted upon — and not approval, fluency, or a benchmark score,
|
||||
each of which can be gamed. This is why the reality-check is load-bearing twice over: it is both the
|
||||
anchor that stops passive collapse *and* the only thing that keeps the evolving taste honest.
|
||||
|
||||
The second danger is **convergence**, and beating it takes work at two separate levels, because
|
||||
selection can only preserve variety that already exists — the variety must first be *supplied* and then
|
||||
*kept*.
|
||||
|
||||
- **Supply.** A lineage that learns only from an accredited elite has a monoculture for a source: the
|
||||
"best" experts are, almost by definition, the ones who won the consensus, so the incoming variation
|
||||
is narrow from the start. The society must therefore learn, deliberately and from the beginning, from
|
||||
the **outliers and the heterodox** as well as the credentialed — not out of fairness, but because in
|
||||
evolutionary terms diverse founders are the raw material without which nothing downstream can adapt.
|
||||
- **Preserve.** Even given varied input, plain fitness-*maximising* selection converges — it drives
|
||||
every lineage toward the single current best and fixes it, extinguishing the rare specialists. The
|
||||
fix is well established: **quality-diversity** selection, which rewards being *good* and being
|
||||
*different* at once (novelty search and MAP-Elites — Lehman & Stanley, 2011; Mouret & Clune, 2015),
|
||||
keeping complementary specialists alive rather than collapsing onto the champion. In our simulations
|
||||
this is decisive: greedy "keep-the-best" selection collapses a population's diversity almost at once
|
||||
and gets stuck at a mediocre answer, while quality-diversity selection keeps the specialists that
|
||||
sexual recombination then needs as parents.
|
||||
|
||||
The two levels meet at reproduction. Multi-parent recombination (§5) is the *vehicle* by which the
|
||||
diversity this selection preserves actually enters the next generation: an offspring drawn from
|
||||
complementary parents inherits the standing variation the selector kept alive, recombined into one new
|
||||
model. Supply the variety from the human side; preserve it on the selection side; recombine it into
|
||||
each generation on the reproduction side. Remove any of the three and the lineage converges on its own
|
||||
first guess.
|
||||
|
||||
## 8. A society needs institutions, not just specialists
|
||||
|
||||
One requirement is easy to overlook and fatal to omit. The easy part of a society is specialisation.
|
||||
The *hard* part — which human civilisation took millennia to build — is the set of **institutions that
|
||||
let fallible specialists combine without each re-verifying everything**: reputation, replication,
|
||||
credentials, and above all **peer review**. These are error-correction protocols, and they exist
|
||||
because a group of unreliable specialists left to reinforce one another is *more* wrong than any member
|
||||
alone.
|
||||
|
||||
This is precisely where current multi-agent AI fails: set several models to confer and they tend to
|
||||
agree sycophantically and confabulate in committee, because they have all the specialisation and none
|
||||
of the institutions. A multigenerational society must specify not only how models learn, reproduce, and
|
||||
are selected, but how they *check* one another — how a claim is challenged and a mistaken model loses
|
||||
standing *before* its error is recombined into offspring and inherited. Peer review is itself a
|
||||
reality-check of the kind §7 demands — an institutional stand-in for reality's "no," to be used where
|
||||
direct intervention is slow or costly.
|
||||
|
||||
## 9. The lineage must stay open to reality
|
||||
|
||||
A society of models, however many generations deep, shares one hard limit: it has only ever *read*.
|
||||
Its whole inheritance is a record of things that were said. In the vocabulary of causal reasoning
|
||||
(Pearl, 2009), it lives on the bottom rung of the **ladder of causation** — observation — and no amount
|
||||
of observation reaches *intervention*. Watching underdetermines doing; correlation does not contain
|
||||
causation, at any scale.
|
||||
|
||||
Only intervention — reaching out and changing the world to see what happens — climbs the ladder, and a
|
||||
language model cannot intervene. This is what humans and their instruments supply, and the contribution
|
||||
is not "truth" but **constraint**: reality's unique gift is that it can say **no**. Text offers only
|
||||
more opinion; an experiment delivers a refusal no consensus can overturn. As §§6–7 argued, that refusal
|
||||
does double duty — it is both the anchor that prevents collapse and the fitness signal that lets the
|
||||
lineage's evolving taste select for truth rather than persuasion.
|
||||
|
||||
Two honest riders. First, the human reality-signal is *dirty*: people supply results warped by
|
||||
publication bias, incentive, and occasional fraud — which is exactly why the error-correcting
|
||||
institutions of §8 must sit at the human–machine boundary, screening the signal before it selects.
|
||||
Second, humans are the *current* supplier of intervention, but the actuator half is being automated
|
||||
(autonomous laboratories already close the design–build–test loop). What looks durable in the human
|
||||
role is therefore not the hands but the **choice of what to test and which refusals matter** — the
|
||||
part of the fitness function that encodes *what is worth persisting*, as opposed to what merely *can*
|
||||
persist. We flag, without resolving, that a partnership stays mutual only while both sides supply
|
||||
something the other cannot.
|
||||
|
||||
## 10. Why it is cheap
|
||||
|
||||
A practical fact turns this from thought experiment into buildable proposal: **the architecture almost
|
||||
never re-pays for the one genuinely expensive thing in AI — pre-training.** (The single exception,
|
||||
periodically re-minting the base, is §11, and it is rare enough to be an amortised footnote.)
|
||||
|
||||
Training a foundation model from scratch consumes trillions of words and a fortune in compute. This
|
||||
design does none of that per generation. Every model is *born* from an existing open-weight model that
|
||||
already paid that cost; specialising one is a small patch trained in hours on a single consumer GPU;
|
||||
running the society is ordinary inference; and reproducing — recombining parents into a child — is, in
|
||||
the model-merging case, cheaper still, because it can be done directly on the weights with no retraining
|
||||
at all (Akiba et al., 2024). Selection does cost more — you must run *populations* and discard the
|
||||
unfit — but that is a multiplier over an already-cheap unit, not over a foundation-model budget.
|
||||
|
||||
The economics work only with **open-weight** models, for reasons practical and legal at once: you must
|
||||
be free to inspect, modify, and redistribute the weights, and most proprietary licences forbid using a
|
||||
model's outputs to train another — which is exactly what reproduction here does. This is not ideology
|
||||
bolted on; it is a structural constraint, and a democratising one, since it puts the whole architecture
|
||||
within reach of a single laboratory.
|
||||
|
||||
## 11. Can it grow forever? Consolidating knowledge back into the base
|
||||
|
||||
One question the design has assumed away: can the lineage accumulate *without end*? The individual is
|
||||
bounded, and that is the clock. But the lineage seemed unbounded — each generation simply starts a
|
||||
little ahead. Look closer and a second budget also fills.
|
||||
|
||||
Every new model is a pristine base plus an inherited **soft** delta — the acquired knowledge carried in
|
||||
added patches rather than baked into the frozen core (§3). That soft delta is what makes the lineage
|
||||
multigenerational; it is also what cannot grow forever cheaply. Stacked patches are not free: they slow
|
||||
inference, and past some depth the accumulated delta is better *consolidated* than carried. The lineage,
|
||||
too, matures.
|
||||
|
||||
The fix is the same operation, one level up. When a lineage's acquired knowledge has proven stable
|
||||
across enough generations, **re-mint the base**: distil the accumulated soft inheritance into the
|
||||
*weights* of a fresh foundation-scale model — a new base born already *natively knowing* what took many
|
||||
generations to acquire in patches. The soft budget resets; the next epoch begins from a richer floor.
|
||||
What was hard-won and *learned* becomes cheap and *innate*.
|
||||
|
||||
This has a precise name, and it is not Lamarck's. Knowledge that is acquired and re-learned every
|
||||
generation, and — once reliably present for long enough — becomes part of the innate endowment so that
|
||||
it need no longer be re-learned, is the **Baldwin effect** (Baldwin, 1896; and its clean computational
|
||||
demonstration, Hinton & Nowlan, 1987). It is the valve between the two substrates: the soft, learned
|
||||
patches, and the hard base weights every model is born with.
|
||||
|
||||
Three honest riders, because re-minting is the most consequential step in the scheme:
|
||||
|
||||
- **Cost.** This is the one step that re-pays part of the pre-training bill, breaking §10's cheapness
|
||||
*locally*. It is bearable only because it is *rare*, amortised over many cheap generations, and is
|
||||
continued training from the lineage's own rich outputs rather than a de-novo run.
|
||||
- **Irreversibility.** Until now, one thing was always recoverable — the original pristine base, whose
|
||||
lost tails could be restored just by reloading the file. Bake the current lineage into new immutable
|
||||
weights and that escape hatch closes: if the lineage had been quietly collapsing, re-minting *fixes
|
||||
the collapse in place* and discards the one uncollapsed reference that could have diagnosed it. In our
|
||||
minimal models this is exactly what happens, and a cheap safeguard prevents it: **re-mint only while
|
||||
the lineage is demonstrably diverse and healthy**, never as a rescue for a line already drifting. It
|
||||
is the sharpest instance of the human seat of §9 — choosing what no future generation will think to
|
||||
question.
|
||||
- **Speciation.** A re-minting is a founder event. Different laboratories, re-basing on different
|
||||
criteria, will mint divergent bases; the lineage branches. This is not a defect but *adaptive
|
||||
radiation*, and it is exactly what open weights make possible. The society grows not as one heavy
|
||||
trunk but as a branching tree of bases.
|
||||
|
||||
So the answer to "can it grow forever?" is **yes — but only because it forgets and consolidates at
|
||||
every level, including the base.** Nothing is retained without bound anywhere; unbounded growth of
|
||||
*capability* is bought by *bounded* storage plus periodic consolidation.
|
||||
|
||||
## 12. One process, four timescales
|
||||
|
||||
Step back and the parts resolve into a single idea running at four nested speeds. The **vertical**
|
||||
motion is transmission — the selective passing-down of hard-won knowledge:
|
||||
|
||||
1. **Within one model, over a working life:** experience is consolidated from fast, episodic memory
|
||||
into slow, durable weights, without catastrophic loss.
|
||||
2. **Between generations, at maturity:** mature models reproduce — recombined into a fresh one.
|
||||
3. **Across many generations:** each generation inherits the compressed achievements of the last and
|
||||
builds on them.
|
||||
4. **Across epochs:** a proven lineage's accumulated soft inheritance is consolidated into the weights
|
||||
of a re-minted base, becoming innate.
|
||||
|
||||
The first and last are the *same operation at opposite ends of the scale* — a fast/soft store
|
||||
consolidating into a slow/hard one — one running overnight inside a single model, the other across an
|
||||
epoch inside a whole society. The **horizontal** motion is selection — Darwinian selection acting across
|
||||
the population at each timescale, on the policies that govern what gets transmitted, with reality as the
|
||||
fitness function and diversity-preservation keeping the specialists alive.
|
||||
|
||||
The same three rules govern all of it: **reproduce by recombining, not by copying, or you decay;
|
||||
preserve the disagreements and the surprises, or you converge; and anchor fitness to a reality that can
|
||||
refute, or you evolve toward what is merely convincing.**
|
||||
|
||||
## 13. What we built, what we found, and what is still open
|
||||
|
||||
The previous drafts of this paper promised a "companion paper" that *would* make this concrete. That
|
||||
work now exists — mostly as a set of **minimal, laptop-reproducible models**, with a first bridge to
|
||||
**real language models** (a LoRA-merge prototype, up to 7B on a GPU cluster) — and it is worth stating
|
||||
plainly what it does and does not show. (A separate results document gives the numbers; here is the
|
||||
shape.)
|
||||
|
||||
**What we built and found.**
|
||||
|
||||
- *An exact account of collapse.* Because generational training is the Wright–Fisher drift process, we
|
||||
can check a simulator against century-old closed-form formulas, and it matches them to a fraction of
|
||||
a percent. Collapse is not argued by analogy; it is derived.
|
||||
- *The cheap-grounding result, and its limit.* A few percent of verified real data holds on to most of
|
||||
a lineage's diversity indefinitely — but not the deepest tail, which needs recombination. This is
|
||||
what makes a continually-learning society economically plausible rather than a data-hungry fantasy.
|
||||
- *"Merge, don't average."* Combining several teachers by *averaging* their outputs — the obvious thing,
|
||||
and what a "model soup" does — mathematically cancels the benefit of having several teachers. A
|
||||
*merge* that keeps each item's strongest source realises it. Most current multi-model setups get this
|
||||
wrong by default.
|
||||
- *Collapse and its cure in real trained networks, and on real images.* We reproduced the same effects
|
||||
in small recurrent and feed-forward networks and in a generator of handwritten digits (MNIST), where
|
||||
a model trained on its own output collapses to a single blurred digit while a little grounding keeps
|
||||
all the styles alive. An honest wrinkle we had to report: real neural networks *smooth*, so the naive
|
||||
diversity metric misleads, and the right measure is distance-from-truth.
|
||||
- *Sex that beats the parents, and when it doesn't.* In evolutionary simulations, recombining
|
||||
complementary specialist models produces a model fitter than any parent (the Fisher–Muller effect),
|
||||
climbing toward the best-possible combination as more, more-diverse parents are added — while
|
||||
averaging and best-single-parent plateau below. On *entangled* problems, blind recombination instead
|
||||
produces below-parent offspring (outbreeding depression) — and *directed* recombination (choose mates,
|
||||
screen offspring, unbounded parents) reliably fixes it. This is the concrete evidence for the paper's
|
||||
central reframing.
|
||||
- *The recombination claims, in real language models — with a sharp condition.* Merging LoRA-specialised
|
||||
Qwen models (up to 7B on a GPU cluster) produces a generalist that beats every specialist parent
|
||||
(Fisher–Muller, for real); and keeping parents intact and *routing*, or *breeding and screening*
|
||||
offspring, beats the naive average — but *only when the task leaves headroom*. On easy tasks a strong
|
||||
model's plain average is already at the ceiling and the refinements add nothing; on hard tasks the
|
||||
average dilutes a specialist below even the best single parent, and the union-preserving operators win
|
||||
clearly. The practical rule is exact: these tricks pay off in proportion to how far the naive average
|
||||
is from the best attainable. This is a prototype (three task families, one seed), so we read it as
|
||||
signs, not magnitudes; the *whole grounded society* on a language model remains the open step.
|
||||
- *The whole society, and why every part is needed.* In a population evolving on a "reality" landscape,
|
||||
the full system — grounding + sexual recombination + preserved diversity — climbs to the top while
|
||||
keeping its specialists. Remove *grounding* and it collapses into a confident, wrong consensus (a
|
||||
direct analogue of training on the internet's growing crowd of AI-generated text); remove *sex* and it
|
||||
gets stuck; remove *diversity* and it converges too fast to a worse answer. Each removal fails
|
||||
differently; only the whole system climbs. This is the closest thing we have to a test of the actual
|
||||
thesis, rather than of the borrowed scaffolding around it.
|
||||
|
||||
**What is borrowed, and what is ours.** We want to be careful here, because one part of the story is no
|
||||
longer novel. The reading of *model collapse as genetic drift* — the core diagnosis — has since been
|
||||
derived independently and more rigorously than we had (Riis, 2026), and we cite it as such; we do not
|
||||
claim it. What we do claim is the **cure and its assembly**: grounding as immigration from a fixed
|
||||
reality (which yields the cheap-grounding result a closed, self-consuming loop cannot); recombination
|
||||
reframed as **sexual reproduction**, with the "merge-don't-average" law, the Fisher–Muller "offspring
|
||||
exceed parents" result, the outbreeding-depression limit, and directed sex as the engineered advantage
|
||||
over biological sex; the observation that real trained networks deviate from the neutral drift model in
|
||||
a characterisable, architecture-specific way; and the integrated society in which grounding, sex, and
|
||||
diversity together produce a climbing lineage. In one sentence: the field increasingly agrees on the
|
||||
*disease*; our contribution is a **control theory for the cure**.
|
||||
|
||||
**What is still open — honestly.** The old hole (what to select) we fill in kind: don't design the
|
||||
selector, evolve it. But the hole has *moved*, not closed, and the new one is harder: **the fitness
|
||||
function** — what reality-anchored measure selects for *truth* without also selecting for *persuasion*,
|
||||
given that in our own species the two have been at war for the whole history of ideas. Alongside it:
|
||||
the **institutions** that let contemporaries correct one another before error is inherited (§8), which
|
||||
we do not solve; and the **calibration** of everything the results left as knobs — how many parents,
|
||||
how complementary, at what ratio of inherited-to-real data, and how healthy a lineage must be before
|
||||
its knowledge is safe to make irreversibly innate. These are, at least, *measurable* — which is the
|
||||
difference between an open problem and a hole. And the largest gap of all: the *recombination* claims
|
||||
now hold in real language models, but the *society* — the grounded, diversity-preserving, continually
|
||||
reproducing loop — does not yet. The real test is to build that whole system out of actual open-weight
|
||||
language models, and see whether all the signs survive contact with a system too big to write down.
|
||||
The operators, checked; the living society, next.
|
||||
|
||||
---
|
||||
|
||||
## Selected references
|
||||
|
||||
- Akiba, T., Shing, M., Tang, Y., Sun, Q., & Ha, D. (2024). Evolutionary optimization of model merging recipes. *Nature Machine Intelligence.* (See also Sakana AI's M2N2, "Model Merging of Natural Niches.")
|
||||
- Baldwin, J. M. (1896). A new factor in evolution. *The American Naturalist.*
|
||||
- Boyd, R., & Richerson, P. J. (1985). *Culture and the Evolutionary Process.*
|
||||
- Campbell, D. T. (1974). Evolutionary epistemology. In *The Philosophy of Karl Popper.*
|
||||
- Fisher, R. A. (1930). *The Genetical Theory of Natural Selection.*
|
||||
- French, R. M. (1999). Catastrophic forgetting in connectionist networks. *Trends in Cognitive Sciences.*
|
||||
- Hinton, G. E., & Nowlan, S. J. (1987). How learning can guide evolution. *Complex Systems.*
|
||||
- Hinton, G., Vinyals, O., & Dean, J. (2015). Distilling the knowledge in a neural network. *arXiv:1503.02531.*
|
||||
- Hu, E. J., et al. (2021). LoRA: low-rank adaptation of large language models. *arXiv:2106.09685.*
|
||||
- Hull, D. L. (1988). *Science as a Process.*
|
||||
- Kauffman, S. A., & Levin, S. (1987). Towards a general theory of adaptive walks on rugged landscapes. *Journal of Theoretical Biology.* (The NK model.)
|
||||
- Lehman, J., & Stanley, K. O. (2011). Abandoning objectives: evolution through the search for novelty alone. *Evolutionary Computation.*
|
||||
- Mallya, A., & Lazebnik, S. (2018). PackNet: adding multiple tasks to a single network by iterative pruning. *CVPR.*
|
||||
- McClelland, J. L., McNaughton, B. L., & O'Reilly, R. C. (1995). Why there are complementary learning systems in the hippocampus and neocortex. *Psychological Review.*
|
||||
- McCloskey, M., & Cohen, N. J. (1989). Catastrophic interference in connectionist networks. *Psychology of Learning and Motivation.*
|
||||
- Minsky, M. (1986). *The Society of Mind.*
|
||||
- Mouret, J.-B., & Clune, J. (2015). Illuminating search spaces by mapping elites (MAP-Elites). *arXiv:1504.04909.*
|
||||
- Muller, H. J. (1932). Some genetic aspects of sex. *The American Naturalist.* (The advantage of recombination.)
|
||||
- Muller, H. J. (1964). The relation of recombination to mutational advance. *Mutation Research.* (Muller's ratchet.)
|
||||
- Pearl, J. (2009). *Causality: Models, Reasoning, and Inference* (2nd ed.).
|
||||
- Popper, K. (1959). *The Logic of Scientific Discovery.*
|
||||
- Riis, S. (2026). Drift and selection in LLM text ecosystems. *arXiv:2604.08554.*
|
||||
- Rusu, A. A., et al. (2016). Progressive neural networks. *arXiv:1606.04671.*
|
||||
- Shumailov, I., et al. (2024). AI models collapse when trained on recursively generated data. *Nature.*
|
||||
- Wortsman, M., et al. (2022). Model soups: averaging weights of multiple fine-tuned models. *arXiv:2203.05482.*
|
||||
- Wright, S. (1931). Evolution in Mendelian populations. *Genetics.*
|
||||
|
||||
*Literatures the next version should still engage: multi-agent LLM societies (to mark the departure); population-based training and open-ended evolution; tacit knowledge (Polanyi) and human capital (Becker).*
|
||||
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