narrative revision: substantiated premise, continual-learning positioning, convergence framing

Per GG's directive: (1) the model-societies premise is no longer asserted
— the Introduction opens with the verified evidence base (3M-model
ecosystem with phylogenetic lineage-mapping literature, >98%-synthetic
alignment pipelines, machine-generated web share, the human-data
ceiling, mainstream merging tooling, agent economies; refs 31-44, all
identifiers verified by the literature scan). (2) The findings are
contextualised in CONTINUAL LEARNING, where they land hardest: a new
Introduction block maps the CL canon onto the operators — replay <->
grounding, with the field's measured replay fractions (1%/5%/25%)
sitting on our theorized g*~0.05; pseudo-rehearsal/generative replay as
precisely our ungrounded null; parameter isolation; CLS consolidation;
merging-for-CL vs cross-lineage recombination; tail-first forgetting <->
tail-allele extinction; CF-vs-collapse mechanism distinction kept
explicit — plus a Discussion block with five CL impact points (replay-
ratio theory testable against published sweeps; a failure theory for
generative replay; pre-merge interference prediction with a mechanism; a
consolidate-vs-modular decision rule; tail monitoring, engaging the
latent-vs-extinct objection). The scan verified the bridge is open: no
prior work carries pop-gen formalism into CL. (3) Downplaying replaced
by convergence framing: the diagnosis was reached independently and is
corroborated by parallel arrivals (Riis; Benati; Yoon; and Crutchfield &
Whalen 2012, pre-deep-learning) — cited for priority of publication, the
full arc owned as one framework. References 30 -> 65; Significance
carries the CL frame; 20-pp rebuild; 151 tests green.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01BkRLcc18rwT2Lysu6PbG7v

paper/pnas/main.md

@@ -12,10 +12,11 @@ on their own output, model lineages degenerate — a process already recognised
 genetic drift. This paper imports the other half of population genetics: the biology of sexual
 reproduction. It treats model merging as recombination, real data as immigration, and merge failure as
 reproductive isolation, and tests each correspondence in simulations, small neural networks, and
-language models. The framework yields design rules — when to average models, when to keep them
-separate, how much real data suffices — and a controlled small-model test in which pre-merge
-functional disagreement predicted merge damage, motivating further comparison with weight-space
-measures.
+language models. The framework recasts machine learning's oldest problem — continual learning without
+forgetting — at the population scale, and yields design rules: when to average models, when to keep
+them separate, how much real data suffices (a theory for the field's empirical replay fractions), and
+a controlled small-model test in which pre-merge functional disagreement predicted merge damage,
+motivating further comparison with weight-space measures.
 
 ## Abstract
 
@@ -23,7 +24,10 @@ AI development increasingly resembles a population process: models are specialis
 output, and recombined by weight merging, with an openly evolutionary vocabulary but little use of
 evolutionary theory. Here we treat multigenerational model populations as systems whose inheritance,
 diversity, and compatibility must be managed, and transfer the quantitative apparatus of the evolution
-of sex. We take as settled that training on model output is genetic drift (model collapse). In a
+of sex. Its entry point — training on model output is genetic drift, and model collapse is its
+signature — we developed independently, and parallel work has now formalised the same diagnosis from
+several directions, a convergence we read as evidence for the frame rather than as a shared discovery
+to be divided. In a
 minimal inheritance model that is exactly Wright–Fisher — and measurably Wright–Fisher-plus-bias in
 trained networks — we derive and test the remedies: grounding as immigration, where a real-data
 fraction far below one retained most equilibrium diversity in the tested settings, with a
@@ -44,27 +48,71 @@ association. We state precisely what is exact, what is measured, and what remain
 
 ## Introduction
 
-The unit of AI progress is quietly changing. Multi-agent systems arrange many models across *space* —
-specialists cooperating on a task. A newer axis is *time*: populations of models that persist across
-generations, each new model built from older ones — specialised by fine-tuning, trained on data earlier
-models generated, and, increasingly, produced by **model merging**, the direct combination of trained
-weights (1, 2). The engineering literature describes this openly in evolutionary vocabulary —
-"crossover," "mutation," "mate choice," populations of merging models that climb benchmarks (2–5) —
-but as metaphor over search algorithms. The organising claim of this paper is that the vocabulary
-deserves its mathematics: **multigenerational model populations are systems whose inheritance,
-diversity, and compatibility must be managed — not merely collections of models to optimise — and the
-branch of biology that studies exactly this problem, the population genetics of the evolution of sex,
-transfers as a quantitative framework.**
+Machine learning has quietly become a population-scale phenomenon. Public repositories now host
+millions of models — Hugging Face alone grew past three million by 2026 — and these are not
+independent creations: the overwhelming majority are fine-tunes, distillations, or merges of a small
+number of foundation models, forming sprawling family trees whose lineage structure, inherited traits,
+and mutation dynamics are already being mapped with explicitly phylogenetic methods (31–33).
+Reproduction in this population is no longer metaphorical. Weight-space **model merging** — the direct
+combination of trained parents into a new model — is mainstream community practice with standard
+tooling and thousands of hybrid checkpoints, including leaderboard-topping ones (1, 2, 37, 38), and
+the engineering literature describes it in openly evolutionary vocabulary: "crossover," "mutation,"
+"mate choice," populations of merging models that climb benchmarks (2–5).
 
-One half of the transfer is settled and is not our contribution. Training each generation of a model
-on the previous generation's output degrades it — *model collapse*: rare capabilities vanish first and
-the lineage drifts toward its own most common behaviour (6). That this is the mathematics of **genetic
-drift** in a finite population is now established from several directions (7–9); a closed-form
-first-extinction law even places collapse onset at the Wright–Fisher first-extinction time (8). We cite
-this literature as the diagnosis and build on it.
+The generations are coupled through data as well as through weights. Successive models increasingly
+learn from model output rather than from fresh human experience: frontier alignment pipelines are now
+predominantly synthetic — over 98% in documented cases (43, 44) — self-generated instruction data
+seeds whole lineages of descendants (5), a large and growing share of the public web is
+machine-generated or machine-translated text (35, 36), and the stock of human text is projected to be
+exhausted by frontier training within this decade (34). Meanwhile persistent multi-agent systems and
+emerging agent economies put many interacting models into sustained contact (39–42). A population
+whose members inherit from one another, recombine, and retransmit under these conditions is an
+evolving population in the technical sense, whatever one thinks of the metaphors. The organising claim
+of this paper is that the vocabulary deserves its mathematics: **multigenerational model populations
+are systems whose inheritance, diversity, and compatibility must be managed — not merely collections
+of models to optimise — and the branch of biology that studies exactly this problem, the population
+genetics of the evolution of sex, transfers as a quantitative framework.**
 
-Our contribution is on the remedy side, and we are explicit about what kind of contribution each claim
-is, distinguishing **interpretation** (an existing result understood in population-genetic terms),
+The frame's entry point is the diagnosis. Training each generation of a model on the previous
+generation's output degrades it — *model collapse*: rare capabilities vanish first and the lineage
+drifts toward its own most common behaviour (6). That this is the mathematics of **genetic drift** in
+a finite population is a conclusion we reached independently in building the present framework, and
+one that has been derived in parallel from several other directions (7–9), including a closed-form
+first-extinction law placing collapse onset at the Wright–Fisher first-extinction time (8) — and that
+was anticipated, before deep learning, in an analysis of sequential inference chains as generalised
+genetic drift (63). We cite these works for priority of publication on the diagnosis and read the
+convergence — independent arrivals at the same population-genetic account by different routes and in
+different decades — as corroboration that the frame is the natural one. What none of that parallel work develops, and what this paper is about, is the
+structure the diagnosis opens: the full arc from drift through its remedies (immigration,
+recombination, selection, population structure) to its limit (reproductive isolation), carried as one
+framework from closed forms to trained networks to language models.
+
+Seen from machine learning's own history, the problem this frame addresses is the field's oldest —
+**continual learning** — reappearing one level up. Within a single network, sequential learning
+overwrites prior knowledge (catastrophic forgetting; 45, 46), and the discipline's remedies are, one
+by one, the population operators of this paper in single-model form: **rehearsal and replay** of past
+data is grounding's within-lineage counterpart, and the field's empirically settled replay fractions —
+on the order of 1% for instruction tuning (53), 5% for weak and 25% for strong distribution shift in
+continual pretraining (52) — sit exactly where the minimal model's operational grounding threshold
+lies, a correspondence for which the framework supplies the missing theory (equilibrium diversity,
+and a per-capability survival law). **Pseudo-rehearsal** — replaying the network's own generated
+samples, proposed as a cure in 1995 (47) and revived as generative replay (48) — is precisely this
+paper's ungrounded null: immigration from a drifting source, benign for one hop and compounding into
+collapse over generations, with verifier-filtering (12, 62) as what converts it back into grounding.
+**Parameter isolation** (65, and frozen-base adapters, which forget far less; 54) is the engineered
+decorrelation our specialists use; **complementary-learning-systems consolidation** (49–51) is our
+periodic adapter-into-base merge; the recent turn to **merging as a continual-learning mechanism**
+(55–58) applies recombination within one lineage over time, where we apply it across lineages; and
+the observation that **rare examples and long-tail knowledge are forgotten first** (59–61) is
+tail-allele extinction observed one model at a time. One distinction is kept explicit throughout:
+catastrophic forgetting is largely deterministic interference from shifted training, whereas collapse
+is stochastic sampling drift — the phenomena share their victims (the rare) and their remedies, not
+their mechanism. To our knowledge, no prior work carries population-genetic formalism into continual
+learning itself; that bridge — replay as immigration with a survival law, merging as recombination
+with a compatibility criterion, consolidation as the slow store of a two-speed memory — is where this
+framework may matter most.
+
+We are explicit about what kind of contribution each claim is, distinguishing **interpretation** (an existing result understood in population-genetic terms),
 **explanation** (the transferred mechanism accounts for observations existing accounts leave open),
 and **prediction** (the framework forecasts an unmeasured outcome). The paper is strongest on the
 first; makes concrete progress on the second — separating merge failures that are coordinate artefacts
@@ -350,8 +398,29 @@ tested weight-distance baselines were not; and *do not treat divergence or speci
 evidence of incompatibility* — in every regime we tested, what broke merging was conflicting
 conventions on shared circuitry, which is the thing to detect.
 
-**What is borrowed and what is ours.** The diagnosis — collapse as drift — is prior art (6–9), as are
-the empirical facts that merges can beat parents, that decorrelated parents merge better, and that
+**What this offers continual learning.** Read into the field where these results most directly land:
+(i) a first-principles account of the **replay ratio** — the folklore constants (≈1%, 5%, 25%; 52, 53)
+acquire an equilibrium theory and a sharper prediction, that the required fraction is set by the
+rarest capability one refuses to lose (the `1 − e^{−m·p}` law), not by average loss — directly
+testable against published replay sweeps; (ii) a **failure theory for generative replay**:
+self-generated rehearsal is safe for short horizons and compounds into collapse across generations
+unless verifier-filtered back into grounding (47, 48, 12, 62); (iii) **pre-merge interference
+prediction with a mechanism**: where the current state of the art fits regressions over candidate
+metrics (21), the functional-conflict measure arrives at a convergent signal from principle and comes
+with an operator prescription — when conflict is high, do not average; route or breed-and-screen;
+(iv) a candidate **decision rule for the consolidate-versus-stay-modular question** that currently
+splits the field's practice (keep adapters separate vs merge them; 54–58): union-preserving operators
+where headroom exists, fusion where the base composes, consolidation as the slow-store step; and (v)
+**tail monitoring as the leading indicator**: continual-learning evaluation that averages over
+capabilities hides exactly the losses that drift theory says come first and, past a threshold, become
+irreversible. On that last point we note the standing objection that apparent forgetting can be
+skewed task-inference over latent capability rather than erasure (64); our irreversibility results
+concern oracle-measured behavioural distributions, and distinguishing latent from extinct capability
+at language-model scale is an open and, we think, decisive experiment for both readings.
+
+**What is borrowed and what is ours.** The diagnosis — collapse as drift — was published first by
+others and we cite it so (6–9), while noting the derivations are independent and convergent; prior art
+in the strict sense are the empirical facts that merges can beat parents, that decorrelated parents merge better, and that
 naive averaging loses to interference-aware or routed merges (1, 19, 20), that model populations can
 climb (2–5), and that merge success admits ML-native predictors (21, 22). Ours is the framework-level
 synthesis — inheritance, diversity, and compatibility as managed quantities — together with: the
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