From d6a5c5cacde5544a39305eef34925a4fb35b8a19 Mon Sep 17 00:00:00 2001 From: Giorgio Gilestro Date: Sun, 6 Sep 2026 12:49:52 +0100 Subject: [PATCH] paper (Phase 2): fold hardened E13 into both versions, citation refresh, arXiv package MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Speciation section rewritten around the hardened results: alignment modulo the full function-preserving symmetry group (answers 2606.23607 preemptively), the hybrid-fitness cliff (0.97 -> 0.03), the mu(S)/2 floor, and the pre-registered emergent converse (no isolation without functional conflict; the merge rescues forgetting specialists) — in the abstract, §5, §13 ledger, and the accessible version. Citation refresh (author names verified via arXiv API): concede First-Extinction Law (Benati 2509.20101) and quantitative-trait collapse (Yoon 2407.17493) alongside Riis; add verifier-injection (Yi 2510.16657), Livnat & Papadimitriou (CACM 2016) as the sex-as-computation precursor, and the adjacent 2024-26 merge/LMC/multi-agent literature (Ainsworth, Pari, Zhou, Cao, Sharma, Hu, Kozodoi, Li & Shen, Harris, Chen, Tanaka). arXiv package (paper/arxiv/): md2tex.py — a small block-based Markdown->LaTeX converter keeping the Markdown as source of truth — main.tex, generated body.tex, 3 vector figures; builds clean under tectonic (20 pp; pdflatex hint guarded for arXiv); ARXIV-SUBMISSION.md carries categories, license note, and a <=1,920-char abstract. 149 tests green. Co-Authored-By: Claude Fable 5 Claude-Session: https://claude.ai/code/session_01BkRLcc18rwT2Lysu6PbG7v --- paper/arxiv/ARXIV-SUBMISSION.md | 42 +++ paper/arxiv/body.tex | 316 ++++++++++++++++++ paper/arxiv/figs/E12.pdf | Bin 0 -> 27149 bytes paper/arxiv/figs/E14.pdf | Bin 0 -> 32236 bytes paper/arxiv/figs/speciation_real.pdf | Bin 0 -> 28131 bytes paper/arxiv/main.pdf | Bin 0 -> 197812 bytes paper/arxiv/main.tex | 35 ++ paper/arxiv/md2tex.py | 159 +++++++++ .../the-evolution-of-sex-for-ai-accessible.md | 23 +- paper/the-evolution-of-sex-for-ai.md | 129 +++++-- tasks/workorder-pnas-submission.md | 11 +- 11 files changed, 671 insertions(+), 44 deletions(-) create mode 100644 paper/arxiv/ARXIV-SUBMISSION.md create mode 100644 paper/arxiv/body.tex create mode 100644 paper/arxiv/figs/E12.pdf create mode 100644 paper/arxiv/figs/E14.pdf create mode 100644 paper/arxiv/figs/speciation_real.pdf create mode 100644 paper/arxiv/main.pdf create mode 100644 paper/arxiv/main.tex create mode 100644 paper/arxiv/md2tex.py diff --git a/paper/arxiv/ARXIV-SUBMISSION.md b/paper/arxiv/ARXIV-SUBMISSION.md new file mode 100644 index 0000000..762e4a5 --- /dev/null +++ b/paper/arxiv/ARXIV-SUBMISSION.md @@ -0,0 +1,42 @@ +# arXiv submission notes (Phase 2 of the PNAS work order) + +**What to upload.** The source package: `main.tex`, `body.tex`, `figs/` (three PDFs). arXiv rejects +TeX-produced PDF-only uploads, so upload source; all packages are standard and `\pdfoutput=1` is set, +so arXiv's pdflatex builds it (verified locally with tectonic; `main.pdf` in this directory is the +reference build, 20 pp). To rebuild after editing the Markdown source of truth: +`python paper/arxiv/md2tex.py && (cd paper/arxiv && tectonic main.tex)`. + +**Categories.** Primary: `q-bio.PE` (Populations and Evolution). Cross-list: `cs.LG` and `cs.NE`. +If arXiv asks for an endorsement for q-bio.PE (first submission to the archive), either request it +(an evolutionary-biology colleague with q-bio postings can endorse in one click) or flip primary to +`cs.NE` with `q-bio.PE` as cross-list — the paper is defensible either way; q-bio.PE primary is +preferred for the PNAS audience trail. + +**License.** arXiv non-exclusive license (default) is fine for PNAS. Do not pick CC-BY unless you +want it — PNAS permits preprints under any license, but the default keeps options open. + +**Abstract for the arXiv field** (plain text, ~1,750 chars — the field caps at 1,920; the paper's +long abstract stays in the PDF): + +> AI is shifting from single frozen models to populations of agents that persist, specialise, and are +> recombined into new models. The field describes this with evolutionary vocabulary — crossover, mate +> choice, offspring — but as metaphor over search. We argue the right theory already exists: the +> population genetics of the evolution of sex. Training each generation on the last is genetic drift, +> and model collapse is Muller's ratchet, the decay of an asexual lineage (we take the +> collapse-is-drift diagnosis as settled and cite it). The cure is sexual: ground every generation in +> data from a non-drifting reality (immigration, with a critical real-data fraction far below one); +> recombine many complementary parents (model merging — where recombination preserves the union of +> what the parents kept, while averaging cancels the benefit); and preserve diversity. Offspring then +> exceed every parent (the Fisher-Muller effect, shown in merged language models up to 7B). Sex has a +> limit: as models diverge they can speciate — a merge-compatibility cliff governed by epistasis +> (Bateson-Dobzhansky-Muller incompatibilities) whose damage snowballs. We model this and confirm it +> in real weights: a merge barrier survives alignment under the full function-preserving symmetry +> group of the network, rising with functional conflict while hybrid fitness falls to inviability — +> yet absent conflicting training signals, divergently-specialised lineages developed no isolation, +> the merge instead rescuing the forgetting specialists. AI can also do what biology cannot — +> directed sex: unbounded parents, chosen mates, offspring screened before they are kept. We support +> the argument with closed-form-validated simulations, trained networks, an image generator, and LLM +> prototypes, and position it against the 2025-26 evolutionary-AI landscape. + +**After posting.** Record the arXiv id in `tasks/workorder-pnas-submission.md`; sync v2 with the +PNAS-submitted text at Phase 5. PNAS permits preprints. diff --git a/paper/arxiv/body.tex b/paper/arxiv/body.tex new file mode 100644 index 0000000..0760f4f --- /dev/null +++ b/paper/arxiv/body.tex @@ -0,0 +1,316 @@ +\subsection*{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 \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: + +\begin{itemize} +\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. +\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. +\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.) +\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. +\item \textbf{Wright--Fisher process} \emph{(population genetics)} --- the standard mathematical model of drift. We will claim, and show, that generational model-training \emph{is} this process, not merely like it. +\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). +\item \textbf{Muller's ratchet} \emph{(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. +\item \textbf{Catastrophic forgetting} \emph{(machine learning / neuroscience)} --- a neural network overwriting what it knew when it learns something new. +\end{itemize} + +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. + +\medskip\hrule\medskip + +\section*{Abstract} + +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 the right theory is already written, in the branch of biology that studies exactly this: the \textbf{evolution of sex}. Ninety years of population genetics say precisely when reproducing a population by \emph{recombination} beats copying, when it backfires, and how to do it better --- and, read as a control theory, it tells an engineer how to keep a society of models learning across generations instead of decaying. + +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 the other half --- the \textbf{cure}, and its assembly into a theory with predictions. Single-teacher copying is \textbf{asexual} reproduction, and asexual lineages decay by \textbf{Muller's ratchet}, which \emph{is} model collapse; the remedy nature found 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}. With those three ingredients a lineage does not merely avoid collapse; it \textbf{climbs} --- producing models fitter than any ancestor (the \textbf{Fisher--Muller effect}) while each specialty is re-earned and exceeded. + +From the geneticist's apparatus we extract falsifiable, load-bearing claims the merging literature has not: (i) \textbf{``merge, don't average''} --- recombination preserves the union of what parents kept, while averaging (a ``model soup'') is \emph{blending inheritance} that mathematically cancels the benefit; (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 --- which converts recombination from a gamble into a reliable engine and has no biological analogue. + +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. + +\medskip\hrule\medskip + +\section*{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 \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. + +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. + +\subsection*{Where this sits, and what is new} + +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). + +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 is genuinely unoccupied --- and what a geneticist is placed to supply --- is a \textbf{theory} 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 and never applied to it. Every one of the works above uses evolution as \emph{metaphor over an optimiser}; none imports the predictive apparatus of the evolution of sex. Nobody has stated the \textbf{``merge, don't average'' conservation law}, derived \textbf{offspring-exceed-parents as Fisher--Muller}, predicted \textbf{outbreeding depression on rugged task landscapes}, framed \textbf{grounding as migration--drift balance} with a critical fraction, or connected \textbf{reproductive isolation} to when two models can be merged at all. An evolutionary algorithm that \emph{finds} a super-parent is evidence for the theory, not a substitute for it --- the way CMA-ES existing does not make fitness-landscape theory redundant. This paper supplies the theory the tinkering has outrun, and states what it predicts and where it would fail. + +\section*{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 \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. + +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}. + +\section*{3. A learner that can grow without forgetting} + +The individual model needs two properties. + +\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, 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. \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. + +\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. + +\section*{4. ``Full'' is maturity, not failure} + +Here is the pivot. A bounded learner that fills up has not broken. \textbf{It has grown up.} + +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. + +Everything now turns on how that reproduction is done --- and this is where the paper's central claim lives. + +\section*{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. + +\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. + +\textbf{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: \emph{draw a finite sample from the parent, and refit the child to it.} That finite-sampling step is \textbf{mathematically identical} to \textbf{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). 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 \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). \emph{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. + +\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. + +\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: + +\begin{quote}*\emph{An offspring recombined from complementary parents can be }fitter than any of its parents\emph{.}*\end{quote} + +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.} + +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. + +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) --- genuine reproductive isolation, not a missed symmetry, and it cannot be dismissed as a failure to align because the very same aligner erased the same-task barrier. 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. + +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}. + +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 \textbf{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: + +\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.} 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 \emph{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: \textbf{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. +\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 answer to ``can it grow forever?'' is \textbf{yes --- but only because it forgets and consolidates at every level, including the base.} Nothing is retained without bound anywhere; unbounded growth of \emph{capability} is bought by \emph{bounded} storage plus periodic consolidation. + +\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} + +\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 theory those results have outrun: a \textbf{population-genetics of sex} applied to model societies, which is \emph{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 four operators are shown \emph{jointly necessary}. 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).} + diff --git a/paper/arxiv/figs/E12.pdf b/paper/arxiv/figs/E12.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8e8778c0a6849d5bd3a6fe83c98926dee850848a GIT binary patch literal 27149 zcmc$`1yojB)HX_YOXo{U^TJDaBi#+sozf{CD%~QWbayBnf+*6R0#X7ZAgR>9K|ROs z9PW4g#~pXv!Fbud)?9O~HP@W;dG@ANk(6d(XXQkpEt?0GHleVCz#u16TNFV-5Sxa# zvjvDv!oTCs3Fxi0_BAVvdeZ zz!CfPlWHh`>*o6MFJ&rNI9j<`gV=uxAZ=q0G#|t!Z4c-~(!$Ki+~T?wu5KFlhkb<7v9UXPuyk&9d$q&`=^+CSQS_|WJ43r*qf-o^|~0r3Ad zO(EO<#*FOJ=7g-AnPq+^HpUR!6RVvy`xej1Wr7?(zlZ$(zD-v|{5}yUZGxFmX}M@0 zl=ufx$n5Ma3CfOqf?8Iw@Ya|ORK#G~T6IOopaP!tIo6NYdRhk;3@Z2a@#PUDWquIO zy!7-DTDVf6&9Gdn2jy7OMrqz<*Qabv7@M;KT?w3j8|F-JkPf(XIe!nFDNL-dMWZ?e zdke@^)-`~d5dFPTMD=tYJ7N_;S+lDIygKUCEEM-EEP{KLxGYbtCUGZ8O*+aT2 zSlE`>E~U}X8F~k)ExPY~NVJ(5d9JmO-l((5HR>{1(fAvggwGu_8H4YzE=sq0fvJ 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preprint (paper-specific, not general). + +Converts `paper/the-evolution-of-sex-for-ai.md` into `body.tex`, which `main.tex` inputs. Kept +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/E14/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/E12/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("") + + out: list[str] = [] + for block in blocks: + first = block[0].strip() + if 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}") diff --git a/paper/the-evolution-of-sex-for-ai-accessible.md b/paper/the-evolution-of-sex-for-ai-accessible.md index 411e965..e9a8c3f 100644 --- a/paper/the-evolution-of-sex-for-ai-accessible.md +++ b/paper/the-evolution-of-sex-for-ai-accessible.md @@ -248,13 +248,26 @@ 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.) -- Two networks trained on **conflicting tasks**: big merge damage, and re-aligning removes **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. + 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 — confirming the prediction. So the speciation effect is real, not a relabelled artifact. +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?** diff --git a/paper/the-evolution-of-sex-for-ai.md b/paper/the-evolution-of-sex-for-ai.md index 4a7898c..6febae6 100644 --- a/paper/the-evolution-of-sex-for-ai.md +++ b/paper/the-evolution-of-sex-for-ai.md @@ -83,9 +83,13 @@ prediction — sex has a **limit**: as two models diverge they undergo **speciat 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: after permutation alignment (Git Re-Basin), a -residual, epistasis-driven merge barrier survives that alignment provably cannot remove — reproductive -isolation, not a coordinate artefact. AI also has an advantage biology lacks: **directed sex** — unbounded parents, chosen mates, +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 — which converts recombination from a gamble into a reliable engine and has no biological analogue. @@ -129,14 +133,22 @@ with an overtly evolutionary vocabulary: crossover-mutation-selection over LLM p 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. Two things we do **not** claim. First, that collapse is -Wright–Fisher drift: formalised independently (Riis, 2026; Shumailov et al., 2024) and conceded here. +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. What is genuinely unoccupied — and what a geneticist is -placed to supply — is a **theory** rather than a search heuristic. Every one of the works above uses -evolution as *metaphor over an optimiser*; none imports the predictive apparatus of the evolution of -sex. Nobody has stated the **"merge, don't average" conservation law**, derived **offspring-exceed-parents +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 is genuinely unoccupied — and what a +geneticist is placed to supply — is a **theory** 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 and never applied to it. Every one of the works above +uses evolution as *metaphor over an optimiser*; none imports the predictive apparatus of the evolution +of sex. Nobody has stated the **"merge, don't average" conservation law**, derived **offspring-exceed-parents as Fisher–Muller**, predicted **outbreeding depression on rugged task landscapes**, framed **grounding as migration–drift balance** with a critical fraction, or connected **reproductive isolation** to when two models can be merged at all. An evolutionary algorithm that *finds* a super-parent is evidence for @@ -357,22 +369,49 @@ event. (Figure: `results/E12/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). We therefore ran the experiment -that the objection demands, in real trained weights. Two small MLPs are forked from a shared MNIST base, +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* in-house Git Re-Basin permutation alignment; the after-alignment **residual** is the part of the -incompatibility that alignment provably cannot explain away. The decomposition is clean (Figure: +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 ~98 % of** (residual ≈ 0.001) — -same species, different basis, exactly the canonical Re-Basin result, which also proves our aligner -works. Two nets that learned *conflicting* label maps have a large barrier that alignment **removes none -of** (residual ≈ 0.50) — genuine reproductive isolation, not a coordinate artefact, and it cannot be -dismissed as a failure to align because the very same aligner erased the same-task barrier. Sweeping the -fraction of conflicting classes traces the **isolation cliff in real weights**: the residual (after -alignment) barrier climbs monotonically from 0 to ~0.49 with task conflict — the real-weight image of -E12's analytic cliff, and the direct answer to "isn't this just a permutation artefact?" It is not: the -part that survives alignment is real speciation, and it rises with the functional conflict between the -lineages exactly as the Dobzhansky–Muller frame predicts. +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) — +genuine reproductive isolation, not a missed symmetry, and it cannot be dismissed as a failure to align +because the very same aligner erased the same-task barrier. 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. 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?* @@ -641,14 +680,17 @@ shape.) **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; and the -Wright–Fisher collapse literature following Shumailov et al., 2024); (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); and (d) that even the *magnitude* of multi-task merge degradation -has a machine-learning-native predictive account (recent stability/scaling analyses). We claim none of -these. +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 theory those results have outrun: a **population-genetics of sex** applied to model societies, which is *generative* where the incumbents are empirical. Concretely — the **"merge, don't @@ -668,8 +710,12 @@ models are too diverged to be merged at all*. We model it explicitly (§5), pred 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 permutation alignment (Git Re-Basin) as a residual, epistasis-driven -reproductive isolation that the coordinate-artefact account cannot explain away. In one sentence: the field agrees on the disease +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. @@ -724,6 +770,7 @@ The operators, checked; the living society, next. - 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:* @@ -735,5 +782,19 @@ The operators, checked; the living society, next. - 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: the machine-learning-native theory of merge degradation with task count; tacit knowledge (Polanyi) and human capital (Becker).* +*Still to engage in a full version: tacit knowledge (Polanyi) and human capital (Becker).* diff --git a/tasks/workorder-pnas-submission.md b/tasks/workorder-pnas-submission.md index 177ebb7..a76f886 100644 --- a/tasks/workorder-pnas-submission.md +++ b/tasks/workorder-pnas-submission.md @@ -64,17 +64,18 @@ barriers). Patch before the preprint goes up. ## Phase 2 — arXiv preprint (priority stake) — end of Week 1 -- [ ] Citation refresh in `paper/the-evolution-of-sex-for-ai.md`: **new concessions** — +- [x] Citation refresh in `paper/the-evolution-of-sex-for-ai.md` *(done 2026-08-11; author names verified against arXiv API)*: **new concessions** — First-Extinction Law (2509.20101), quantitative-trait collapse (2407.17493), verifier-injection (2510.16657); **precursor** — Livnat & Papadimitriou, *Sex as an algorithm* (CACM 2016); **adjacent-to-differentiate** — merge-collapse theory (2603.09463), mergeability prediction (2601.22285), non-local merging (2410.12766), model kinship (2410.12613), expert-duration (2607.11997), symmetry-scaling (2606.23607), Harris (2604.05142), in-context diversity collapse (2604.18005, 2603.24676). -- [ ] Fold E13b/c results into the speciation section (whatever they show — honestly). -- [ ] LaTeX conversion of the full v6 (article class is fine for arXiv; keep figures as-is), - build with tectonic, proof-read pass. -- [ ] Post to arXiv: q-bio.PE primary, cs.LG (or cs.NE) cross-list. PNAS permits preprints. +- [x] Fold E13b/c results into the speciation section (whatever they show — honestly). *(Done: full-symmetry residual + hybrid-fitness cliff + the emergent converse, in abstract, §5, §13 and the accessible version.)* +- [x] LaTeX conversion: `paper/arxiv/` (md2tex.py block-based converter from the Markdown source of + truth; main.tex; 3 figures; builds clean under tectonic, 20 pp; arXiv pdflatex hint guarded). +- [ ] **Post to arXiv (GG action — package ready):** upload `paper/arxiv/{main.tex,body.tex,figs/}`; + categories, license note, and a ≤1,920-char abstract are prepared in `paper/arxiv/ARXIV-SUBMISSION.md`. ## Phase 3 — New experiments for impact & robustness — Weeks 2–3