E13: real-weight model speciation — the Git Re-Basin residual confirms E12

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>

results/speciation_real/README.md

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+# 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 on `independent`, 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.

results/speciation_real/manifest.json

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+{
+  "experiment": "speciation_real",
+  "master_seed": 13,
+  "git_commit": "56f642e7f9ae01fe01d863bdffe98b226b9dbb7b",
+  "python": "3.14.5",
+  "libraries": {
+    "numpy": "2.5.0",
+    "scipy": "1.18.0",
+    "pandas": "3.0.3",
+    "pyarrow": "24.0.0",
+    "torch": "2.12.1",
+    "torchvision": "0.27.1"
+  },
+  "rows": 45,
+  "results_sha256": "14b15c16ea8a43523fdc929641b8ad5741445435203d1511ecb698097da0a806",
+  "layer": "1.5",
+  "tier": "speciation_real"
+}

results/speciation_real/resolved_config.yaml

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+experiment: speciation_real
+seed: 13
+n_replicates: 3
+source_config:
+  experiment: speciation_real
+  kind: speciation_real
+  seed: 13
+  n_replicates: 3
+  speciation_real:
+    sizes:
+    - 784
+    - 512
+    - 512
+    - 10
+    conditions:
+    - shared
+    - independent
+    - conflict
+    t_div:
+    - 100
+    - 200
+    - 400
+    - 800
+    - 1600
+    base_steps: 500
+    lr: 0.05
+    batch: 128
+    n_eval: 2000
+    data_root: data
+  output:
+    dir: results/speciation_real