# 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.