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Manuscript revision and pending experiment work, snapshot before restructuring

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Clarity pass over the main text (36-item audit), Discussion rewrite and cut,
acknowledgements, Souly et al. as ref 62, lettered SI panels, model section
moved under Results; plus the untracked curriculum/society/compose/smol
configs, runners, figures, stats and tests that the SI already cites.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Y64o8FKP7rCuXzC48pxpMm
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@ -1,4 +1,10 @@
# SI Appendix — The evolution of sex for artificial intelligence
# Supplementary Information — The evolution of sex for artificial intelligence
## Contents
SI Text S1–S4, SI Tables S1–S2, SI Methods M1–M7, SI Statistics, SI Figures S1–S16, and a separate
Appendix 1, *The figures explained* (`figure_legends_for_students.pdf`), which restates every main and
supplementary figure with a plain-language account of the experiment behind it, for readers from biology.
## Reproducibility
@ -61,7 +67,7 @@ experiment measures. The measured answer is that it does not. In the conflict co
unchanged by permutation alignment (the `residual` readout) and by alignment modulo the full
permutation-and-positive-rescaling group (the `residual_scale` readout), while the very same aligner
removes almost all of the barrier between independently initialised networks, the positive control.
Work on richer symmetry groups for transformers (41) strengthens the removable side of the
Work on richer symmetry groups for transformers (83) strengthens the removable side of the
decomposition and is therefore complementary to this result: the more barrier a larger group can
remove for *compatible* models, the sharper the meaning of the barrier that survives for
*incompatible* ones. Proposition 2 caps what any of these methods could ever achieve on the conflict
@ -89,7 +95,7 @@ Both readings were registered before the run. If the residual barrier grows with
model speciation is emergent in real weights, and the trajectory seen in the analytic speciation model
is realised. If the residual stays at the level of the `shared` control, then within this regime
trained networks are more merge-compatible than the biological analogy predicts. The second reading
would be an honest bound on the analogy, and a useful design result in its own right: merging is safe
would bound the analogy, and be a useful design result in its own right: merging is safe
whenever there is no functional conflict.
**Outcome.** Four replicates, with divergence up to 3,200 steps — up to 6.4× the shared base training
@ -100,16 +106,119 @@ while the merged model holds approximately 0.955 at every divergence tested. Thi
Fisher–Muller rescue at zero barrier. Within this regime, reproductive isolation in real weights
required functional conflict. The same question at language-model scale is answered by the duration
arm of the language-model speciation experiment, which likewise found no isolation from over-training
alone (1 to 12 epochs); whether still longer horizons erode mergeability (cf. 43) remains open.
alone (1 to 12 epochs); whether still longer horizons erode mergeability (cf. 83) remains open.
## SI Text S3. Compatible loci and conflicting alleles in a multigenerational population
**The two kinds of new knowledge.** A *locus* is a position in the genome, and *alleles* are the
alternative versions that can occupy it: one blood-group locus, three alleles A, B and O, of which any
one chromosome carries exactly one. In a model population a locus is a slot for a capability ("how to
answer a two-way question") and alleles are the incompatible conventions that could fill it ("yes/no",
"true/false", "1/2"). A skill that conflicts with nothing a lineage already holds occupies a new locus
and is simply added; a skill that demands a different convention for a question shape the lineage
already answers is a competing allele, and a single model, like a single chromosome, carries one.
Proposition S2 gives the cost: when two parents' conventions disagree on a share `μ(S)` of inputs, any
merged child errs against at least one parent on at least `μ(S)/2` of them. In the six-generation
population a lineage obliged to merge at generation `t` pays that floor against its partner's
conflicting conventions; because the child continues the lineage, the loss is inherited, and the next
generation's conflict adds to it. Under the Latin-square curriculum `μ_t(S)` is zero while partners are
complementary (their skills occupy disjoint loci) and becomes positive once a partner carries a
differently conventioned version of a skill the lineage already holds. Two of the six families —
yes/no questions and two-way pronoun resolution — have the most idiosyncratic conventions and were
measured in calibration at 0.00–0.04 accuracy on every other family, so they carry the largest `μ(S)`
against every partner; the generation at which the curriculum hands them to a lineage's partner fixes
when that lineage's collapse begins.
**Negative controls that isolate convention conflict.** Three alternative explanations of the
obligate arm's collapse were tested directly and refuted. (i) *A destructive skill spreading through
merges.* A single 50/50 merge of two clean single-skill adapters (science questions 0.838 / yes-no
0.000; yes-no 0.800 / science 0.300) scored 0.863 and 0.787, mean 0.825 against 0.550 for the better
parent: one merge is protective, not destructive. (ii) *Geometric dilution of an adapter's signal
under repeated averaging.* Five chained convex merges left the first skill's accuracy unchanged even
though its nominal weight fell to 1/32; but a scaling control showed the adapter alone delivers
nothing at 1/32 (0.000; full effect down to 1/8), so what propagated through the chain was the answer
format supplied by whichever partner carried enough weight, not the skill. Dilution is refuted, and
the transmitted quantity is identified as the convention. (iii) *Continued training on merged
weights.* Merging then training on the incoming family beat merging alone on the tracked skill in four
of five rounds and on the incoming skill in all five, and absorbed the one format shock that dropped
the merge-only chain (0.567 → 0.883). With capacity ruled out by the lifelong-editing benchmark (80)
at three orders of magnitude more content, convention conflict is the mechanism that remains — the one
the framework predicts, and the one single-model studies report (81, 82).
**Neutral and functional variation.** Three adapters trained on the same family, differing only in
seed and data draw, were near-orthogonal in weight space (pairwise cosine +0.006) and disagreed on 24%
of answers, yet merging two of them gave 0.887 against 0.800 for the better one — exactly the fraction
of questions on which either was right (0.887). Decomposing the weight change across seeds, roughly
85% of a LoRA delta is run-specific: shared signal power 6.2 (after correcting the finite-sample mean
for its own noise) against noise power 35. That is why raw weight distance predicted nothing in the
main text's controlled test: most of what it measures is the counterpart of *synonymous substitution*
— sequence change without functional change — which averages out when adapters for the same skill
are combined, while the fraction that conflicts lives in the answer conventions. Averaging same-skill
adapters before crossing them with a different skill improved the cross modestly (0.825 → 0.850) while
leaving each single skill unchanged, the inbred-line pattern: averaging within a line does not improve
the line, it makes it cleaner to cross.
**Attenuation and the effectiveness cliff.** Scaling an adapter's weights down does not degrade its
skill gracefully. Each skill holds full accuracy to a skill-specific fraction (1/8 for science
questions, 1/4 for reading-comprehension spans, 1/2 for commonsense completion, 1/4 for yes/no) and
then loses nearly everything within one further halving. Four of six adapters scored higher when
attenuated (inference 0.40 → 0.68 at 1/4; completion 0.75 → 0.82 at 1/2; spans 0.72 → 0.78 at 1/4;
science 0.87 → 0.92 at 1/8): they were over-trained at full strength — the effect reported for
merging experts (84, 85) — and recoverable here by one scalar per adapter with no retraining (six
separate specialists 0.678 → 0.755). Denoising across seeds does not move the cliff, so the limit is
signal magnitude rather than signal-to-noise. Choosing per-skill merge weights from these solo curves
failed (0.686–0.689 against 0.708 for uniform weights): in a six-way merge a skill's effective
strength is its weight relative to the others — six conventions competing for one output — so raising
one starves the rest.
## SI Text S4. Proof of the blending-inheritance proposition
**Setting.** `K` parents; each independently retains a given rare item with probability `q`, and a
parent that retains it assigns it mass `p`. The child draws `n` samples from a *source distribution*
and keeps the item if at least one draw is that item. Two sources are compared: (A) one parent chosen
uniformly at random; (B) the mean of the `K` parents' distributions.
**Expected mass is conserved.** Let `J ~ Binomial(K, q)` be the number of parents retaining the
item. Under (A) the source mass of the item is `p` with probability `q` and 0 otherwise, so its
expectation is `pq`. Under (B) the source mass is `pJ/K`, whose expectation is `p·E[J]/K = pq`. The
expected number of copies in the child's sample, `n` times the source mass, is therefore `npq` under
both schemes (linearity of expectation).
**Survival agrees to first order.** Write `f(x) = 1 − (1 − x)^n` for the probability that at least one
of `n` draws hits an item of source mass `x`; `f` is increasing and concave, with `f(x) = nx + O((nx)²)`.
Survival is `E[f(M)]` with `M` the (random) source mass. Under (A), `E[f(M)] = q·f(p)`; under (B),
`E[f(M)] = E[f(pJ/K)]`. When `n·p ≪ 1`, every realised mass satisfies `nM ≤ np ≪ 1`, so `f(M) ≈ nM`
and both expectations reduce to `n·E[M] = npq`: the `1/K` dilution of scheme (B) is cancelled exactly
by the item being present in the mixture whenever any of the `K` parents holds it. (Equivalently, in
this regime the child's copy count is approximately Poisson with mean `nM`, and Poisson thinning by
`1/K` composed with a `K`-fold union preserves the mean.)
**Boundary 1 (common items).** Away from the first-order regime the comparison is settled by
Jensen's inequality. Both schemes give `M` the same mean `pq`; scheme (A) puts all its variance in
the two-point distribution `{0, p}`, and scheme (B) has strictly smaller variance for `K > 1`. Since
`f` is concave, `E[f(M)]` is larger for the less variable `M`, so averaging never lowers expected
survival, and raises it once `np` is not small. The extinction probability `1 − f` is convex, which is
the form in which the main text states this boundary. The proposition is thus a statement about rare
items, where survival is linear in mass; it does not claim averaging is harmful in general.
**Boundary 2 (union operator).** Let the child instead draw from the distribution that assigns each
item the largest mass any parent gives it, renormalised. The item's source mass is then `p` whenever
`J ≥ 1`, an event of probability `1 − (1 − q)^K`, increasing in `K` for every `q ∈ (0, 1)`. Expected
survival `(1 − (1 − q)^K)·f(p)` therefore rises with `K` in every regime, without a first-order
restriction. The operator needs an oracle (a verifier) to say which parent holds each item most
strongly, which is what routing supplies in the language-model tier.
Both statements are confirmed by simulation in Fig. S8, where mean-mixture survival is flat in `K`
and the item-wise maximum rises with it.
## SI Table S1: the claims ledger (status / assumptions / evidence / limits)
| Claim | Status | Key assumptions | Evidence | Known limits |
|---|---|---|---|---|
| Population collapse in the biological model is Wright–Fisher drift | Closed form; the diagnosis itself is due to prior work | Knowledge is a categorical distribution; refitting means resampling | Closed forms reproduced to <0.5% | Real learners add a signed, architecture-specific estimator bias (measured) |
| Population collapse in the inheritance model is Wright–Fisher drift | Closed form; the diagnosis itself is due to prior work | Knowledge is a categorical distribution; refitting means resampling | Closed forms reproduced to <0.5% | Real learners add a signed, architecture-specific estimator bias (measured) |
| Grounding behaves like immigration, and the critical real-data fraction is far below one | Closed form, plus the sign confirmed empirically | Fresh samples from a fixed, non-drifting truth | Exact `H_eq`; `g*≈0.048`; sign holds in RNN/MLP/VAE and on MNIST | Deepest tail unrescuable at feasible budgets (`m ∼ 1/p`); sharp threshold softens in trained nets |
| "Merge, don't average" conservation | Exact **for the output-mean operator** | Rare-item regime; an oracle/verifier identifies the strongest source | E4 closed form + simulation; neural reproduction | Weight-averaging and routing are empirical cousins, not instances; budgets differ; bridge = the headroom rule |
| Offspring exceed every parent (Fisher–Muller) | Interpretation + empirical | Complementary (decorrelated) parents; verifiable fitness | E8 (biological model); 7B LoRA merge beats every specialist on every family | LLM tier: 3 lexically-distinct families; replicated over five training seeds at 0.5B |
| Offspring exceed every parent (Fisher–Muller) | Interpretation + empirical | Complementary (decorrelated) parents; verifiable fitness | E8 (inheritance model); LoRA merges beat the best specialist overall in every seed at 0.5B (5 seeds) and 7B (3 seeds) | LLM tier: 3 lexically-distinct families |
| Outbreeding depression on rugged landscapes; operator design rule | Biological-model result; hypothesis at LLM scale | NK epistasis stands in for skill entanglement | E9–E10; directed selection rescues | Not yet mapped onto a real task-entanglement measure |
| Optimal mate-pool breadth shrinks with ruggedness | Biological-model result; hypothesis for merging populations | Ring population, local selection | E14 | Phenomenon known to island-model evolutionary computation; the contribution here is the mapping and the diversity/mean decomposition |
| Merge failure decomposes into a coordinate artefact plus a functional residual | Empirical at the trained-network and language-model tiers | Alignment enumerates the architecture's unit symmetries | Full-symmetry residual ≈ 0 for compatible parents versus ≈ the naive barrier under conflict; a cliff in hybrid fitness; function-specific breakdown at the LLM tier | Scoped to aligned linear interpolation; conflict floor is information-theoretic, not genetic |
@ -118,7 +227,10 @@ alone (1 to 12 epochs); whether still longer horizons erode mergeability (cf. 43
| Confidence weighting improves rank prediction over raw disagreement | Not supported (pre-registered internal prediction) | — | Paired contrast over the same bootstrap resamples: Δ\|ρ\| = −0.021, CI [−0.130, +0.059] | The weighting does sharpen the conflict-versus-compatible level contrast, so it is not useless — only no better as a rank predictor |
| The predictor improves budget-matched operator choice | **Open** | — | Soup-vs-route gap readout noise-dominated at 0.5B | The practical payoff; untested |
| Emergent speciation without label conflict | Not observed (pre-registered) | Shared ancestry; compatible tasks; the divergences tested | Residual 0.000 to 6.4× base training; the merge rescues the specialists | Bounds the hypothesis; longer horizons/distribution shift/capacity pressure untested |
| Grounding, recombination, and diversity preservation make complementary contributions | Biological-model result; hypothesis at LLM scale | Conformity stands in for self-consumption | E11 four-arm ablation; each arm fails in a distinct way | General joint necessity is not established; the full grounded LLM society is unbuilt |
| Grounding, recombination, and diversity preservation make complementary contributions | Biological-model result; hypothesis at LLM scale | Conformity stands in for self-consumption | E11 four-arm ablation; each arm fails in a distinct way | General joint necessity is not established; the language-model population (Fig. 4B–C) lacks differential reproduction between lineages |
| Obligate recombination collapses once partners carry conflicting conventions | Empirical (1.5B base, 3 lineages × 6 generations, 3 seeds) | Latin-square curriculum; replay present; linear merge; no culling of lineages | Best lineage 0.269 vs 0.796 never merging; onset at complementarity < 0.8; own-ancestor merge 0.663; three alternative mechanisms refuted (SI Text S3) | Six generations; one base; the arrival order of conflicting families is set by the curriculum |
| A declinable merge reverts the population to asexual accumulation without advance knowledge of when to stop | Empirical (same population, plus two controls, 3 seeds each) | "Keep the parent" scored as one candidate on validation data | Fraction declined 0.44 → 1.00 across generations; finishes 0.792 vs 0.796 never merging. Forced stop after generation 2 finishes 0.793 (veto − stop3 per seed −0.008/−0.006/+0.011). Under a decorrelated curriculum (complementarity 0.00 → 0.70 → 0.00) declines still rise 0.44 → 0.89; pooled partial ρ(declined, complementarity \| generation) = −0.07, CI (−0.21, +0.09); partial ρ with generation +0.31 | The reduction-principle reading (declines track complementarity) is **not supported**; declines track generation, which here confounds adapter age, skill count and the arrival of conflicting conventions. Modifier set by evaluation, not evolved |
| Recombination's net benefit across six generations is an early lead, not a final gain | Empirical (same population); consistent with the inheritance model's speed advantage (E7) | Every skill reaches every lineage by the curriculum regardless | +0.08 at generation 0; −0.005 at generation 5 (per-seed −0.03/+0.01/+0.01) | Replay present, so forgetting was not a live pressure; a curriculum that withholds skills from some lineages is untested |
## SI Table S2: headline quantitative results
@ -127,14 +239,21 @@ per-experiment tables and falsifier status in the per-experiment documentation).
| Result | Setting / n | Outcome definition | Headline |
|---|---|---|---|
| Closed-form validation | Biological model; standing tests | Simulated vs closed-form H-decay, immigration equilibrium, multi-teacher union | Agreement < 0.5% |
| Grounding retention | Biological model (E2); 100 lineages per grounding level | Fraction of equilibrium diversity retained at grounding `g` (operational threshold) | `g ≈ 0.05` retains ≥95% in the tested setting; smooth in `g` |
| Closed-form validation | Inheritance model; standing tests | Simulated vs closed-form H-decay, immigration equilibrium, multi-parent union | Agreement < 0.5% |
| Grounding retention | Inheritance model (E2); 100 lineages per grounding level | Fraction of equilibrium diversity retained at grounding `g` (operational threshold) | `g ≈ 0.05` retains ≥95% in the tested setting; smooth in `g` |
| MNIST collapse & rescue | Conv-VAE, 4 replicates; frozen oracle (98.5% mode acc.) | Mode support / forward-KL over generations | Dry: 30→1 modes; 10% grounding: 30/30 held |
| Fisher–Muller in LLMs | 5 seeds (0.5B), fixed tests; single 7B run | Merged vs best-specialist accuracy (overall; worst family) | Ties 0.647±0.027 vs 0.592±0.009; 7B 0.87 vs 0.77 |
| Union vs blend (headroom) | 3 seeds (0.5B hard); single 7B-hard run | Paired per-seed ordering, routing vs weight-average | Routing > blend in 3/3 seeds; one catastrophic blend failure avoided |
| Fisher–Muller in LLMs | 5 seeds (0.5B) and 3 seeds (7B), fixed tests | Merged vs best-specialist accuracy (overall; worst family); ±: 95% CI over seeds | 0.5B ties 0.647±0.027 vs 0.592±0.009; 7B soup 0.873±0.004 vs 0.807±0.038 (soup − best +0.066±0.036, 3/3 seeds) |
| Union vs blend (headroom) | 3 seeds (0.5B hard); 3 seeds (7B hard) | Paired per-seed ordering, routing vs weight-average | 0.5B: routing > blend in 3/3 seeds, one catastrophic blend failure avoided. 7B: routing 0.503±0.007 vs soup 0.408±0.021 (+0.094±0.015, 3/3); soup vs best specialist +0.001±0.041 (the seed-1 'soup below best parent' did not replicate). Directed − soup +0.073±0.031 (3/3) |
| Speciation decomposition | MLPs, 3 replicates | LMC error barrier residual after permutation+rescaling alignment | Same-task 0.001; conflict 0.497 (naive 0.502) |
| Emergent isolation | MLPs 4 reps to 6.4× base training; LLM 1→12 epochs | Residual barrier; merged vs parent accuracy | 0.000 everywhere; merge rescues parents (≈0.955 vs ≈0.50) |
| LLM speciation, seeds | 0.5B; 3 training seeds; fixed test prompts | Conflict cliff: merge best-convention accuracy vs parents' own at full conflict. Duration null: merged private-task accuracy, 1 → 12 epochs | Cliff in 3/3 seeds (merge 0.02/0.12/0.16 vs parents 0.23–0.25); merged coherence over the sweep 0.147±0.013 → 0.100±0.082. No isolation in 3/3 (0.760±0.075 → 0.950±0.010) |
| Predictive test | 13 conditions × 3 seeds (0.5B) | Merge penalty vs oracle parent potential (pre-registered; ±: clustered 95% CI) | Functional ρ +0.45/+0.46, CI excl. 0; LOCO ρ ≈ 0.4; geometry n.s.; paired differences n.s. |
| Predictive test, seed sensitivity | Same; per-seed and leave-one-seed-out | Spearman ρ vs merge penalty within each seed alone (n = 13 conditions) | Functional +0.37 to +0.53 in every seed; weight geometry ≈ 0 in every seed; gradient alignment seed-unstable (−0.11 to −0.55) |
| Six-generation population | 1.5B base; 3 lineages × 6 generations; 3 training seeds; fixed tests (60 per family) | Best-lineage accuracy over six families at the final generation (mean of seeds; per-seed contrasts) | Never merge 0.796; declinable merge 0.792 (Δ −0.03/+0.01/+0.01); forced stop after generation 2: 0.793 (declinable − stop −0.008/−0.006/+0.011); obligate merge 0.269 (declinable − obligate +0.57/+0.54/+0.45); own-ancestor merge 0.663; single model 0.802 |
| Conflict-arrival curricula | Conflict-early / conflict-late (boolq + winogrande in generations 1–2 or 5–6); isolated, declinable and obligate arms; 3 seeds each | Decline rate and obligate-arm accuracy per generation; partial Spearman of declines on a conflict-present indicator controlling for generation (seed-clustered bootstrap) | Declines 0.56 → 0.78 (early), 0.44 → 0.89 (late); partial ρ(conflict | generation) −0.09, CI (−0.45, 0.15); ρ(generation | conflict) +0.45; pooled over four curricula −0.04, CI (−0.30, 0.15). Obligate final 0.280 / 0.386 vs isolated 0.796 / 0.781 (3/3 seeds); declinable 0.777 / 0.791 |
| Differential reproduction | Latin square; truncation selection (worst lineage re-founded from the best each generation); isolated and declinable arms; 3 seeds | Final best-lineage accuracy; per-seed contrasts against the unselected arms | Never merge + selection 0.804, declinable + selection 0.793 (declinable − never merge −0.011±0.003, below in 3/3); unselected 0.796 / 0.792; selection − no selection +0.007±0.030 |
| Second base lineage | SmolLM2-1.7B-Instruct; Fisher–Muller 5 seeds, headroom (hard) 3 seeds; fixed tests | Same contrasts as the Qwen rows | Soup − best specialist +0.049±0.022, TIES − best +0.097±0.020 (5/5 each; worst family +0.19 / +0.20). Routing − soup +0.162±0.036 (3/3); soup − best specialist −0.029±0.017 (below in 3/3) |
| Declinable-merge acceptance | Latin-square and decorrelated curricula; 9 merge decisions per generation; 3 seeds each | Fraction of proposed merges declined vs partner complementarity, with generation controlled (partial Spearman, seed-clustered bootstrap CI) | Latin square: 0.44 → 1.00 (raw ρ with complementarity −0.57, n = 18). Decorrelated curriculum (complementarity 0.00, 0.67, 0.70, 0.58, 0.33, 0.00): 0.44 → 0.89. Pooled (n = 36): partial ρ with complementarity −0.07, CI (−0.21, +0.09); partial ρ with generation +0.31 |
## SI Methods: experimental procedures
@ -154,12 +273,12 @@ instrument can still return the answer "no". A costlier tier is entered only whe
discriminating test rather than a replication — which is why several cells of the programme (Fig. 1A)
are deliberately empty.
*Match the precision of the claim to the precision of the instrument.* The biological model is exact,
*Match the precision of the claim to the precision of the instrument.* The inheritance model is exact,
so it carries the paper's quantitative statements. Trained systems add optimisation noise and
inductive bias, so at those tiers I claim signs and orderings, never magnitudes.
*Make reality able to refuse.* Every tier has an oracle that is independent of the model being
measured: a fixed true distribution in the biological model, a lossless identity code or a frozen
measured: a fixed true distribution in the inheritance model, a lossless identity code or a frozen
classifier in the neural tier, an exact-match verifier over procedurally generated tasks in the
language-model tier.
@ -172,7 +291,7 @@ reported as failures in the main text.
A replicate means something different at each tier, and conflating the three would misstate what the
error bars cover.
In the biological model a replicate is an independent lineage: a fresh random stream driving the same
In the inheritance model a replicate is an independent lineage: a fresh random stream driving the same
resolved config, with sub-seeds derived from the master seed by `SeedSequence.spawn`. Because drift
*is* the object of study, the spread across replicates is signal rather than nuisance, and replicate
counts are set so that the confidence interval on the summary statistic is small relative to the
@ -199,7 +318,7 @@ Replicate counts, and why each is what it is:
| E12, E12_nk | 15 | Each point already averages 500 (E12) or 200 (E12_nk) offspring |
| E14 | 20 | Breadth × ruggedness grid, 60 generations per cell |
| kernel_sharpen, kernel_smooth | 24 | Two-parameter kernel fits against neural reference endpoints |
| bridge | 60 | The harness gate: must detect *any* departure from the biological model, so the most replicated neural run |
| bridge | 60 | The harness gate: must detect *any* departure from the inheritance model, so the most replicated neural run |
| grounding | 18 | Nine-point grounding sweep with per-generation network retraining |
| collapse, architectures | 5 | Sign-level demonstrations across architectures; each lineage retrains a network 22–25 times |
| recombination | 8 | Operator contrast in trained weights |
@ -208,13 +327,18 @@ Replicate counts, and why each is what it is:
| speciation_real_emergent | 4 | A null: replicates are spent on longer divergence horizons rather than more repeats |
| llm_merge_seeds | 5 training seeds | The Fisher–Muller signature, the most-replicated language-model claim |
| llm_moe_hard_seeds, llm_directed_hard_seeds, llm_epistasis(+compat), llm_speciation_add | 3 training seeds | Per-seed orderings reported individually rather than averaged |
| 7B runs, llm_speciation | 1 | Single-run confirmations at a scale where each run costs GPU-hours; reported as sign-level and labelled as single runs |
| 7B runs (llm_merge_hpc, llm_moe_hard_hpc, llm_directed_hard_hpc) | 3 training seeds | Seeds 2–3 added 2026-09-11 (`hpc/llm_7b_seeds.pbs`, ~33 min per seed on one L40S); per-seed contrasts in `figures/stats_llm_7b_seeds.py` |
| llm_curriculum_v5_{early,late}(_obl) | 3 training seeds each | Conflict-arrival curricula; per-seed contrasts and the pooled partial-correlation test |
| llm_curriculum_v5_cull | 3 training seeds | Differential reproduction; per-seed contrasts against the unselected arms |
| llm_merge_seeds_smol, llm_moe_hard_seeds_smol | 5 and 3 training seeds | Second base lineage; per-seed orderings as for the Qwen runs |
| llm_speciation | 3 training seeds | Conflict cliff and duration null checked seed by seed (`figures/stats_llm_speciation_seeds.py`); seeds 2–3 added 2026-09-12 |
| llm_curriculum_v5, llm_curriculum_v5_veto, llm_curriculum_v5_stop3, llm_curriculum_v5_decor | 3 training seeds | The six-generation population; arm separations (≈0.5) far exceed seed spread (≈0.02), and the declinable-vs-never contrast is reported per seed because its mean is near zero |
The asymmetry is deliberate: replicates are cheap exactly where the quantitative claims live, and the
expensive tiers are asked only for the sign of an effect the cheap tier has already quantified. Where
a single run is all there is, the manuscript says so.
### M3. The biological-model tier
### M3. The inheritance-model tier
Knowledge is a distribution over `K` discrete items; reality is a fixed Zipf-tailed distribution
`p*`; one generation resamples `n` draws from the parent, optionally mixes in `m` verified draws from
@ -228,14 +352,14 @@ reading. Horizons of 400–600 generations were chosen so that ungrounded lineag
grounded ones reach stationarity within the run, which the trajectories confirm.
*Sweeps.* E2 sweeps grounding `g ∈ {0, 0.005, 0.01, 0.02, 0.05, 0.1, 0.2, 0.4}`; E3 contrasts uniform
against region-matched grounding allocation; E4 crosses parent count `K_T ∈ {1,2,3,5}` with teacher
against region-matched grounding allocation; E4 crosses parent count `K_T ∈ {1,2,3,5}` with parent
correlation `ρ ∈ {0, 0.25, 0.5, 0.75, 1}` and `g ∈ {0, 0.02, 0.05}`; E5 crosses selection mode
(none / greedy / quality-diversity) with novelty weight; E6 compares four re-minting arms.
*The correlated-parent construction (E4).* Teacher correlation is constructed directly rather than
*The correlated-parent construction (E4).* Parent correlation is constructed directly rather than
obtained by tuning drift, so that `ρ` is not confounded with `n`, `m`, tail size, or generation
count. For each tail item a shared switch `z ~ Bern(ρ)`, a shared retention `s ~ Bern(q)`, and
per-teacher `u⁽ᵏ⁾ ~ Bern(q)` give teacher `k` retention `s` if `z` else `u⁽ᵏ⁾`. This yields exact
per-parent `u⁽ᵏ⁾ ~ Bern(q)` give parent `k` retention `s` if `z` else `u⁽ᵏ⁾`. This yields exact
marginal retention `q` and exact pairwise correlation `ρ`, and is exchangeable, so `ρ` is a single
scalar knob.
@ -265,18 +389,18 @@ index losslessly, so the oracle reads the mode back with zero error) followed by
uniformly at random. The style segment gives genuine within-mode entropy, so a generative model must
learn a distribution rather than memorise `K` fixed strings, while the identity segment keeps the
measurement noise-free. Mode truth comes from the same `make_true_distribution` used by the
biological model, so "mode", "region", and "tail" denote the same objects at both tiers.
inheritance model, so "mode", "region", and "tail" denote the same objects at both tiers.
*The bridge gate.* Before any trained model is interpreted, a histogram generator is run through the
identical harness; it must reproduce the biological model exactly. This separates harness bugs from
identical harness; it must reproduce the inheritance model exactly. This separates harness bugs from
model behaviour, and is why the bridge run carries 60 replicates.
*Architectures and training.* The recurrent generator is an embedding (24) → GRU (128 hidden; 192 in
*Architectures and training.* The recurrent generator is an embedding (26) → GRU (128 hidden; 192 in
the architecture-generality run) → linear readout, trained each generation from scratch with Adam,
learning rate 2×10⁻³, batch size 256, 25 epochs, and evaluated by sampling 12,000–15,000 sequences.
Feedforward and variational autoencoder generators share the harness. Retraining from scratch each
generation (rather than fine-tuning) makes the generational step a clean refit, matching the
biological model's operator.
inheritance model's operator.
*MNIST tier.* Dataset: MNIST via torchvision (60,000 training images). Modes are digit class ×
stroke-thickness bin (10 × 3 = 30 modes) with a Zipf frequency profile, so roughly eighteen modes are
@ -302,8 +426,8 @@ possible alignments, the removable share is a lower bound and the residual an up
*Base models.* Qwen2.5-Instruct at 0.5B and 7B, open weights under a permissive licence, with the
revision pinned. Using two sizes from one family makes scale the only variable that changes between
the small and large runs; the 0.5B model carries the multi-seed protocols and the 7B model the
single-run confirmations.
the small and large runs; the 0.5B model carries five-seed protocols on the easy families; the 7B
runs are replicated over three training seeds.
*Task families, and why they are procedural.* Three deliberately disjoint families — list
operations, string transformations, and small-integer arithmetic — are generated procedurally from a
@ -352,6 +476,43 @@ outcome is the merge penalty against oracle parent potential, pre-registered, an
against best-parent and mean-parent references because the predictor ordering is sensitive to that
choice.
*The six-generation population.* Base model Qwen2.5-1.5B (base weights, not the instruction-tuned
variant; 0.006 accuracy on the families untrained). Six public datasets with per-family verifiers:
natural-language inference (MNLI; label), science questions (ARC; letter), commonsense completion
(HellaSwag; letter), reading-comprehension spans (SQuAD; normalised span with aliases), yes/no
questions (BoolQ), and pronoun resolution (WinoGrande; 1/2). Each family's pool is split into disjoint
training, validation, and test items before any sampling, so validation and test never share an item.
Two further curricula, conflict-early and conflict-late, are given as explicit orders: the two families
whose answer conventions conflict (BoolQ yes/no, WinoGrande 1/2) occupy generations 1–2 or 5–6 of
every lineage and the four compatible families fill the remaining generations in rotated orders, so
adapter age and skill count rise one family per generation in both and only the arrival of conflict
differs (`configs/llm/curriculum_v5_{early,late}.yaml`; obligate arms in the `_obl` configs; three
training seeds each; `hpc/llm_curriculum_timing.pbs`). The conflict-timing readout is the partial
Spearman correlation of the per-generation decline rate with an indicator of conflict presence,
controlling for generation, with a seed-clustered percentile bootstrap (`figures/stats_llm_curriculum.py`).
Differential reproduction (`cull: true`) applies truncation selection after each generation's
measurement: the lineage with the lowest all-families accuracy is re-founded from the one with the
highest (adapter, taught families, example budget and ancestry archive are copied; the slot keeps its
curriculum order; ties leave the population unchanged), recorded as `culled` and `cull_source` rows
(`configs/llm/curriculum_v5_cull.yaml`; three training seeds; `hpc/llm_cull.pbs`).
The second base lineage is `HuggingFaceTB/SmolLM2-1.7B-Instruct` (Apache-2.0; Llama architecture),
run through the unchanged `merge_seeds` and `moe_hard_seeds` protocols with its own adapter cache
(`configs/llm/{merge_seeds,moe_hard_seeds}_smol.yaml`; `hpc/llm_smol.pbs`; `figures/stats_llm_smol.py`).
Three lineages take the six families in a cyclic Latin square (each lineage's order is the previous
lineage's shifted by two), which fixes partner complementarity — the fraction of the partner's families
a lineage has not yet seen — at 1.0, 1.0, 0.8, 0.67, 0.33, 0.0 across the six generations. Each
generation a lineage draws 300 new items from its scheduled family and 150 replay items split evenly
across families already seen; the child adapter (rank 16) is initialised from the parent's and trained
for 3 epochs at learning rate 10⁻⁴ (founders from the base at 2×10⁻⁴). Recombination averages two
adapters at each weight in {0.5/0.5, 0.3/0.7, 0.7/0.3}; the winner is chosen on 20 validation items
per family seen and then trains on the generation's new family. In the declinable arm the unchanged
parent is a fourth candidate scored identically. The contemporary partner is the next lineage in the
square; the ancestor partner is the lineage's own adapter three generations earlier; the self-replay
variant draws its replay from the parent's own answers rather than from the datasets. Reporting uses
60 test items per family. Because two of the families are binary, an accuracy threshold at 0.5 is
chance, so the text reports mean accuracy over the families a lineage has been taught and the
trajectory of its first-learned family rather than a count of families above a threshold.
*The composed society.* A population of `N` LoRA agents on a shared frozen base evolves for `G`
non-overlapping generations. Each generation every agent answers a fixed validation pool (verifier
scored) and a fresh conformity pool (whose modal answer defines the population consensus); selection
@ -372,9 +533,13 @@ collapsed to ρ = +0.03 once compatible overlap was present, identifying it as a
a signal. The duration axis supplies divergence without conflict. The emergent-speciation condition
supplies divergence with no conflicting signal anywhere, and returns a null. The budget-controlled
speciation design (`conflict_mode: add`) removes the confound between conflict fraction and private
training budget. The histogram bridge is a harness control. In the biological model, `m = 0` arms and
training budget. The histogram bridge is a harness control. In the inheritance model, `m = 0` arms and
`ρ = 1` (fully correlated parents) are the null conditions against which the corresponding effects
are read.
are read. In the six-generation population, three arms are controls — a single model taught the
curriculum alone (no population), the never-merge population (no recombination), and merging with
one's own ancestor (shared conventions, partial complementarity) — and the self-replay variant of the
obligate arm controls the replay channel; SI Text S3 records the three direct tests that refuted
alternative mechanisms for the obligate arm's collapse.
### M7. Statistical procedures
@ -396,7 +561,42 @@ submission. Chronology of the predictive test (prospective / adaptive / post-hoc
## SI Figures
One per experiment, regenerated from committed artifacts: E1–E14, bridge/collapse/grounding/
architectures/recombination, kernel (sharpen/smooth), mnist_collapse (+ montage), speciation_real
(decomposition/cliff/emergent), llm_merge(_hpc/_seeds), llm_moe(_hpc/_hard_hpc/_hard_seeds),
llm_directed(_hpc/_hard_hpc/_hard_seeds), llm_speciation(_add), llm_epistasis(_compat).
Sixteen figures are cited from the main text by number. Each is the per-experiment figure
regenerated from the committed results artifact (`figures/plot_*.py`), reproduced here without
re-plotting, so panel titles still carry the experiment's working name. Five of them are
inheritance-model results with no real-model counterpart in this paper, reported here because each
reproduces an established result: blending versus union retention (Fig. S8), the Fisher–Muller
super-parent (Fig. S9), outbreeding depression on rugged landscapes (Fig. S10), directed
recombination (Fig. S11), and the mate-pool breadth optimum (Fig. S13).
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