MachineSex/results/speciation_real/README.md

E13 — Real-weight model speciation (the alignment residual, now modulo the full symmetry group)

Claim tested. E12 predicts model speciation analytically: as two lineages diverge, recombination (merging) fails, via Bateson–Dobzhansky–Muller incompatibilities. E13 confirms it in real trained weights, separating the part of the merge barrier that is a mere coordinate artefact (removable by re-coordinating hidden units) from the residual that no alignment can remove — the true reproductive-isolation signal.

E13c hardening (2026 PNAS campaign). Recent work shows symmetry groups richer than permutations remove more of the barrier between independently trained transformers (arXiv:2606.23607; neuron-identifiability LMC). We therefore align modulo the full function-preserving unit symmetry group of a plain ReLU MLP — per-unit positive rescaling (scale canonicalisation, exact) composed with Git Re-Basin permutation matching (neural/rebasin.py; the sanity gate recovers a permuted and rescaled copy to exact weight identity). Both residuals are reported: residual (permutation only) and residual_scale (full group).

Setup. No-BatchNorm MLPs (784–512–512–10) on MNIST. Children forked/trained per condition; weight-average merge; linear-mode-connectivity error barrier before/after alignment; midpoint (merged-model) accuracy recorded alongside. 3 replicates (decomposition/cliff), 4 (emergent). Statistically reproducible (seeded); the alignment itself is deterministic NumPy/scipy.

Results — the decomposition (mean over divergence, reps)

condition	naive barrier	residual (permutation)	residual (full symmetry group)	merged acc
shared (same task, shared fork)	0.000	0.000	0.000	0.964
independent (same task, different init)	0.044	0.001	0.001	0.960 (= parents)
conflict (contradictory label maps)	0.502	0.502	0.497	0.037 (inviable)

• independent: the barrier is a coordinate artefact — permutations already remove ~98%, and the full symmetry group confirms (residual 0.001). The aligned merge performs at parent level (0.960): same species, different basis.
• conflict: permutation+rescaling alignment removes essentially nothing (0.502 → 0.497), and the hybrid is functionally dead (accuracy 0.037). The tested alignment removes the same-task barrier but leaves the conflict-associated barrier largely unchanged — supporting a functional-conflict interpretation without proving optimal alignment (control recovery validates a special case; removable = lower bound, residual = upper bound).
• Formal floor (SI note S1, paper/si-notes.md): for label maps conflicting on mass μ(S), any single merged model errs at rate ≥ μ(S)/2 against at least one parent, under any alignment group and merge operator — hybrid disadvantage is information-theoretic, and endpoints/chord are invariant to all function-preserving transformations.

Results — the isolation cliff (speciation_real_cliff/)

Sweeping the fraction of conflicting classes (residual = full-symmetry alignment; t_div=800):

conflict fraction	0.0	0.2	0.4	0.6	0.8	1.0
residual barrier	0.000	0.122	0.187	0.278	0.406	0.506
merged (hybrid) accuracy	0.968	0.764	0.586	0.396	0.199	0.034

residual_scale ≈ residual at every point (±0.005): the cliff is functional isolation under the full symmetry group. Read as hybrid fitness, the merged model's accuracy falls 0.97 → 0.03 — the real-weight image of E12's compatible → outbreeding depression → hybrid inviability trajectory.

Results — emergent divergence does NOT speciate (speciation_real_emergent/, E13b)

The conflict condition imposes contradiction; a true BDM incompatibility is emergent. Two pre-registered conditions with no conflicting training signal anywhere: disjoint (child A trains only on classes 0–4, child B on 5–9) and augment (same labels, inputs rolled ±3 px), swept to t_div = 3200 (children trained 6.4× longer than the shared base):

• Residual barrier = 0.000 at every divergence, both conditions (naive barrier is 0 too — the children never leave the shared basin).
• The disjoint parents decay to 0.535/0.474 on the full task (each forgets the other's classes), while the merged model holds ≈ 0.955 at every divergence — a sustained ~40-point Fisher–Muller rescue of two catastrophically-forgetting specialists, at zero barrier. augment shows the same shape (parents 0.65/0.73, merge ≈ 0.90).

Honest conclusion (the pre-registered second reading): in this regime — shared ancestry, same architecture, compatible tasks, divergence up to 3200 steps — model speciation does not emerge spontaneously; reproductive isolation requires functional conflict. Trained networks are more merge-compatible than the biological analogy predicts, and the design rule sharpens: merge freely across divergently-specialised lineages of shared ancestry — the danger is conflicting conventions, not specialisation per se. Scope caveat: small MLPs, one fork depth; whether long-horizon over-specialisation at LLM scale erodes mergeability (as the expert-training-duration literature suggests, arXiv:2607.11997) is exactly the Phase-3 llm_speciation question.

Positioning

Git Re-Basin / Entezari (barriers as coordinate artefacts), the richer-symmetry LMC results (2606.23607 and neuron-identifiability, 2026), Frankle (fork instability), Pari 2024 (route don't fuse), Zhou 2026 / 2601.22285 (predict mergeability from divergence/geometry), 2603.09463 (merge-collapse capacity theory). E13's contribution is the synthesis they lack: a controlled decomposition where alignment — modulo the full symmetry group — cleanly partitions the merge barrier into a removable coordinate artefact and a functional reproductive-isolation residual that rises with task conflict, is absent under compatible specialisation, and carries an information-theoretic floor. Falsifiers (none triggered): alignment failing on independent (would invalidate the residual); conflict showing no residual; the richer symmetry group dissolving the conflict residual (it removed 0.005 of 0.502); emergent conditions showing residual attributable to alignment failure.