Giorgio Gilestro
01d87e504f
The real-weight image of E12, and the answer to the mode-connectivity reviewer. Small no-BN MLPs on MNIST, forked from a shared base and trained independently, are weight-averaged; we measure the linear-mode-connectivity barrier before and after in-house deterministic Git Re-Basin permutation alignment (neural/rebasin.py, scipy linear_sum_assignment), decomposing it into removable (coordinate artefact) and residual (reproductive isolation). kind: speciation_real. Result (3 reps): - shared (same task, shared fork): no barrier — trivially mergeable. - independent (same task, different init): naive 0.056, alignment removes 98% (residual 0.001) — the incompatibility is a coordinate artefact. - conflict (conflicting label maps): naive 0.496, alignment removes 0% (residual 0.496) — genuine reproductive isolation. Because alignment demonstrably works on the independent case, the conflict residual is real, not a failure to align. - Isolation cliff (speciation_real_cliff): residual rises 0.00->0.13->0.19->0.28-> 0.40->0.49 with the fraction of conflicting classes — the real-weight mirror of E12's cliff; residual==naive throughout (functional, not coordinate). rebasin.py sanity-gated (recovers a known permutation exactly). plot_speciation_real.py (2-panel), +4 pure-NumPy tests (142 green), README with honest positioning vs Git Re-Basin / Entezari / Frankle / Pari 2024 / Zhou 2026. Wired into make mnist (needs torchvision). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
3.8 KiB
E13 — Real-weight model speciation (Git Re-Basin residual)
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, and — decisively — separates the part of the incompatibility that is a mere coordinate artefact (removable by permuting hidden units; Git Re-Basin, Ainsworth et al. 2022) from the residual that permutation cannot remove, which is the true reproductive-isolation signal. This is the experiment that answers the mode-connectivity reviewer: if alignment removes the barrier, it was a coordinate artefact; the barrier that survives alignment is real speciation.
Setup. Small no-BatchNorm MLPs (784–512–512–10) on MNIST — the clean Re-Basin regime. Two children
are forked from a shared base and trained independently; we weight-average them and measure the
linear-mode-connectivity error barrier before (naive) and after (aligned) in-house, deterministic
Git Re-Basin weight-matching (neural/rebasin.py, scipy linear_sum_assignment). Statistically
reproducible (seeded torch; NumPy/scipy alignment is deterministic). 3 replicates.
Results — the decomposition (mean over divergence, reps)
| condition | naive barrier | removable (coordinate) | residual (isolation) |
|---|---|---|---|
shared (same task, shared fork) |
0.00 | 0.00 | 0.00 |
independent (same task, different init) |
0.056 | 0.055 | 0.001 |
conflict (conflicting label maps) |
0.496 | 0.000 | 0.496 |
independent: two nets trained from different random inits on the same task have a real naive barrier — which alignment removes ~98% of (residual 0.001). Same species, different basis: the incompatibility is a coordinate artefact. (This reproduces the canonical Git Re-Basin result and proves our alignment works.)conflict: two nets that learned conflicting functions have a large barrier that alignment removes none of (residual 0.496). Different species: genuine reproductive isolation. Because alignment demonstrably works onindependent, this residual cannot be dismissed as a failure to align.- The residual after alignment is therefore the clean discriminator: ~0 for compatible models (even independently trained), large only for functionally incompatible ones.
Results — the isolation cliff (speciation_real_cliff/)
Sweeping the fraction of classes on which child B learns a conflicting label map, the residual (after-alignment) barrier rises monotonically — the real-weight image of E12's cliff:
| conflict fraction | 0.0 | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 |
|---|---|---|---|---|---|---|
| residual barrier | 0.00 | 0.13 | 0.19 | 0.28 | 0.40 | 0.49 |
residual = naive at every point (alignment removes nothing in the conflict condition), so the cliff is genuinely functional isolation, not a coordinate artefact.
Positioning
The incumbents each hold one piece: Git Re-Basin / Entezari (barriers are coordinate artefacts), Frankle (the fork-instability protocol), Pari et al. 2024 (specialisation diverges representations, route don't fuse), Zhou et al. 2026 (predict mergeability from divergence metrics). E13's contribution is the synthesis they lack: a controlled decomposition where alignment cleanly partitions the merge barrier into a removable coordinate artefact and a residual reproductive-isolation term that rises with task conflict — the real-weight confirmation of E12's speciation prediction, and the direct answer to "isn't this just a loss barrier / permutation artefact?" Falsifier (not triggered): alignment failing to remove the independent-init barrier (then residual is meaningless), or conflict showing no residual — instead alignment removed 98% of the former and 0% of the latter.