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>
54 lines
3.8 KiB
Markdown
54 lines
3.8 KiB
Markdown
# E13 — Real-weight model speciation (Git Re-Basin residual)
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**Claim tested.** E12 predicts model *speciation* analytically: as two lineages diverge, recombination
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(merging) fails, via Bateson–Dobzhansky–Muller incompatibilities. E13 confirms it in **real trained
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weights**, and — decisively — separates the part of the incompatibility that is a mere **coordinate
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artefact** (removable by permuting hidden units; Git Re-Basin, Ainsworth et al. 2022) from the
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**residual** that permutation *cannot* remove, which is the true reproductive-isolation signal. This is
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the experiment that answers the mode-connectivity reviewer: if alignment removes the barrier, it was a
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coordinate artefact; the barrier that *survives* alignment is real speciation.
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**Setup.** Small no-BatchNorm MLPs (784–512–512–10) on MNIST — the clean Re-Basin regime. Two children
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are forked from a shared base and trained independently; we weight-average them and measure the
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**linear-mode-connectivity error barrier** before (`naive`) and after (`aligned`) in-house, deterministic
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Git Re-Basin weight-matching (`neural/rebasin.py`, scipy `linear_sum_assignment`). Statistically
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reproducible (seeded torch; NumPy/scipy alignment is deterministic). 3 replicates.
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### Results — the decomposition (mean over divergence, reps)
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| condition | naive barrier | removable (coordinate) | **residual (isolation)** |
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|---|---|---|---|
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| `shared` (same task, shared fork) | 0.00 | 0.00 | **0.00** |
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| `independent` (same task, different init) | 0.056 | 0.055 | **0.001** |
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| `conflict` (conflicting label maps) | 0.496 | 0.000 | **0.496** |
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- **`independent`**: two nets trained *from different random inits* on the *same task* have a real naive
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barrier — which alignment **removes ~98%** of (residual 0.001). Same species, different basis: the
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incompatibility is a coordinate artefact. (This reproduces the canonical Git Re-Basin result and
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proves our alignment works.)
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- **`conflict`**: two nets that learned *conflicting* functions have a large barrier that alignment
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**removes none** of (residual 0.496). Different species: genuine reproductive isolation. Because
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alignment demonstrably works on `independent`, this residual cannot be dismissed as a failure to align.
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- The **residual after alignment** is therefore the clean discriminator: ~0 for compatible models (even
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independently trained), large only for functionally incompatible ones.
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### Results — the isolation cliff (`speciation_real_cliff/`)
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Sweeping the fraction of classes on which child B learns a *conflicting* label map, the residual
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(after-alignment) barrier rises monotonically — the real-weight image of E12's cliff:
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| conflict fraction | 0.0 | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 |
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|---|---|---|---|---|---|---|
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| residual barrier | 0.00 | 0.13 | 0.19 | 0.28 | 0.40 | 0.49 |
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residual = naive at every point (alignment removes nothing in the conflict condition), so the cliff is
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genuinely functional isolation, not a coordinate artefact.
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### Positioning
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The incumbents each hold one piece: Git Re-Basin / Entezari (barriers are coordinate artefacts),
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Frankle (the fork-instability protocol), Pari et al. 2024 (specialisation diverges representations,
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route don't fuse), Zhou et al. 2026 (predict mergeability from divergence metrics). E13's contribution
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is the synthesis they lack: a controlled decomposition where alignment cleanly partitions the merge
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barrier into a **removable coordinate artefact** and a **residual reproductive-isolation** term that
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rises with task conflict — the real-weight confirmation of E12's speciation prediction, and the direct
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answer to "isn't this just a loss barrier / permutation artefact?" **Falsifier (not triggered):**
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alignment failing to remove the independent-init barrier (then residual is meaningless), or conflict
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showing no residual — instead alignment removed 98% of the former and 0% of the latter.
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