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+# Compose-audit: putting the alignment map and the merging payoff on the SAME real models
+
+_Generated 2026-08-26 20:16 UTC · training-free · code: `/root/compose-audit` · operators/aligners/metrics imported unmodified from `mergeschool.core` (`/root/mergeability`, treated as read-only)._
+
+## Read this first: what substrate, and what metric
+
+| | SET 1 | SET 4 |
+|---|---|---|
+| **Substrate** | `EleutherAI/pythia-{14m,70m,160m}-seed{1..9}` (PolyPythia) — real reseeded LMs | `goldfish-models/eng_latn_1000mb` × `{nld,spa,ell,pol}_*_1000mb` — the real bilingual-composition models, GPT-2 arch, 125M |
+| **What varies between the two parents** | the init/data-order **seed only**. Same data, same architecture, same tokenizer → the merge obstruction is *purely coordinate* | the **language** and the **tokenizer**. Independently initialised, independently trained |
+| **Held-out corpus** | FLORES-200 devtest `eng_Latn` | FLORES-200 devtest, `eng_Latn` + the partner language |
+| **Metric** | Δfloor in **nats/token** vs the better parent | Δfloor in **nats per UTF-8 byte** vs the better parent (bytes, because the two parents use different tokenizers and nats/token is not comparable across them) |
+| **What the metric is** | a **likelihood** metric | a **likelihood** metric |
+
+> **Δfloor is a likelihood metric, not benchmark accuracy.** Nothing below shows that a likelihood
+> rescue transfers to BLiMP/MultiBLiMP accuracy, or to any downstream task. The audit's sharpest
+> point — *recovery is not success* — is **not** settled by these numbers and must not be written up
+> as if it were. No accuracy benchmark was run inside this window (see Coverage).
+
+
+## SET 1 · PolyPythia seed-merge (the pure-coordinate ceiling)
+
+C(9,2) = 36 seed pairs per size. Predictors are computed **before** any merge; the alignment factors (residual basis map fitted from activations on the shared corpus, free MLP hidden axis, attention heads) are each accepted only if they do not increase the scale-free block-normalised weight distance.
+
+
+### pythia-14m — 36 seed pairs · mean parent floor **4.375** nats/token · uniform-over-vocabulary reference **10.826** nats/token
+
+| rung | n | mean nats/tok | mean Δfloor | median Δfloor | best Δfloor | beats naive | % of naive Δfloor removed |
+|---|---|---|---|---|---|---|---|
+| M0_naive_avg | 36 | 36.80 | 32.43 | 30.89 | 23.07 | 0/36 | 0.0% |
+| M1_perm_avg | 36 | 13.98 | 9.61 | 9.01 | 5.27 | 36/36 | 69.9% |
+| M1_orth_avg | 36 | 20.38 | 16.01 | 14.07 | 6.63 | 35/36 | 50.5% |
+| M2_task_arith | 36 | 151.17 | 146.80 | 141.85 | 93.41 | 0/36 | -358.6% |
+| M3_ties | 36 | 245.90 | 241.52 | 236.11 | 126.48 | 0/36 | -651.2% |
+
+Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **34.14**, permutation-aligned **10.18** nats/token.
+
+
+### pythia-70m — 13 seed pairs · mean parent floor **3.606** nats/token · uniform-over-vocabulary reference **10.826** nats/token
+
+| rung | n | mean nats/tok | mean Δfloor | median Δfloor | best Δfloor | beats naive | % of naive Δfloor removed |
+|---|---|---|---|---|---|---|---|
+| M0_naive_avg | 13 | 22.30 | 18.69 | 18.42 | 13.88 | 0/13 | 0.0% |
+| M1_perm_avg | 13 | 18.58 | 14.97 | 15.43 | 8.29 | 8/13 | 19.8% |
+| M1_orth_avg | 13 | 14.10 | 10.49 | 10.52 | 6.30 | 13/13 | 42.6% |
+| M2_task_arith | 13 | 83.87 | 80.27 | 80.48 | 45.14 | 0/13 | -331.8% |
+| M3_ties | 13 | 147.02 | 143.42 | 138.19 | 121.09 | 0/13 | -687.4% |
+
+Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **18.72**, permutation-aligned **14.95** nats/token.
+
+
+### pythia-160m — 4 seed pairs · mean parent floor **3.260** nats/token · uniform-over-vocabulary reference **10.826** nats/token
+
+| rung | n | mean nats/tok | mean Δfloor | median Δfloor | best Δfloor | beats naive | % of naive Δfloor removed |
+|---|---|---|---|---|---|---|---|
+| M0_naive_avg | 4 | 11.34 | 8.08 | 8.09 | 7.68 | 0/4 | 0.0% |
+| M1_perm_avg | 4 | 9.70 | 6.44 | 6.28 | 6.06 | 4/4 | 20.1% |
+| M1_orth_avg | 4 | 9.28 | 6.02 | 6.16 | 5.35 | 4/4 | 25.4% |
+| M2_task_arith | 4 | 31.20 | 27.94 | 27.65 | 22.30 | 0/4 | -245.3% |
+| M3_ties | 4 | 59.34 | 56.08 | 56.34 | 50.64 | 0/4 | -596.6% |
+
+Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **8.07**, permutation-aligned **6.43** nats/token.
+
+
+**What this says.**
+
+1. **Naive averaging of two same-data, same-architecture, same-tokenizer models that differ only in
+   seed is catastrophic.** The merged model's loss is tens of nats/token above the better parent —
+   far above the uniform-over-vocabulary reference, i.e. the merge is not a degraded model, it is a
+   destroyed one. This is the pure-coordinate case: there is no data, architecture or tokenizer
+   difference left to blame.
+2. **Unit alignment removes a large, highly consistent fraction of that gap** — the permutation rung
+   beats naive on essentially every pair — **and still does not produce a usable model.** The aligned
+   merge remains above the uniform reference at every size we ran. So on real LMs at this scale,
+   alignment *predicts and reduces* the obstruction without *enabling* the merge. Reporting the
+   reduction as "merging works once you align" would be wrong.
+3. **Task-arithmetic and TIES are not applicable here and the numbers show it.** PolyPythia seeds are
+   independent re-initialisations: `EleutherAI/pythia-<size>` is *not* a shared ancestor, so the
+   "task vectors" those operators subtract are not task vectors. Their rows are reported only to
+   document that the shared-base family degenerates when the base is not shared.
+4. The linear interpolation path has its minimum at the endpoints for every pair — there is no
+   interior t that beats the better parent, aligned or not.
+
+
+## SET 4 · Goldfish monolingual → bilingual merge (the real composition models)
+
+Uniform-over-vocabulary reference (a model that has learned nothing), mean over the two languages, in the same units: **eng-nld_Latn** 3.093 nats/byte.
+
+**Δfloor vs the better parent, mean over the two languages, nats/UTF-8 byte** (lower is better; 0 would mean the merge matches the better parent):
+
+| pair | vocab overlap | floor eng | floor X | M0_naive_avg | M1a_vocab_avg | M1b_vocab_perm_avg | M1c_vocab_orth_avg | M1d_vocab_perm_forced | M1e_vocab_orth_forced | M1f_perm_novocab |
+|---|---|---|---|---|---|---|---|---|---|---|
+| eng–nld_Latn | 27.8% | 0.811 | 0.792 | 1.689 | 1.763 | 1.766 | 1.766 | 2.004 | 1.601 | 1.691 |
+
+**Split by language, and Δ vs naive:**
+
+| pair | rung | Δfloor eng | Δfloor X | Δ vs naive (mean) |
+|---|---|---|---|---|
+| eng–nld_Latn | M0_naive_avg | 0.889 | 2.489 | 0.000 |
+| eng–nld_Latn | M1a_vocab_avg | 1.056 | 2.471 | 0.074 |
+| eng–nld_Latn | M1b_vocab_perm_avg | 1.058 | 2.474 | 0.077 |
+| eng–nld_Latn | M1c_vocab_orth_avg | 1.058 | 2.474 | 0.077 |
+| eng–nld_Latn | M1d_vocab_perm_forced | 1.167 | 2.840 | 0.314 |
+| eng–nld_Latn | M1e_vocab_orth_forced | 0.990 | 2.211 | -0.089 |
+| eng–nld_Latn | M1f_perm_novocab | 0.891 | 2.491 | 0.002 |
+
+**Rungs.** `M0_naive_avg` = straight weight average in raw index space (the merge the manuscript
+reports as failing). `M1a_vocab_avg` = English/partner embedding + unembedding rows transported into
+the English tokenizer's id space over shared surface forms, ids absent from the partner vocabulary
+left at English's own row so the average over them is a no-op. `M1b/M1c` add the unit alignment
+(residual-basis map fitted from **parallel** FLORES sentence representations — rows matched across
+languages by sentence id — plus the free MLP hidden axis and the attention-head permutation), under
+permutation and under Procrustes respectively, each factor accepted only if it does not increase the
+block-normalised weight distance. `M1d/M1e` force the residual factor in regardless of that test.
+`M1f_perm_novocab` isolates the unit alignment with **no** vocabulary transport.
+
+
+## P0-2 · Do the pre-merge predictors predict the realised rescue?
+
+Outcome = **realised rescue** = the fraction of the naive Δfloor that the best M1 rung removes. Label = above the within-size median. Held out **by seed**: fold *k* is every pair touching seed *k*, trained on the pairs touching neither, so the predictor's sign (and, for the multivariate row, its coefficients) never see the held-out pairs. Null = **seed-cluster permutation** (2000 draws): permute the seed identities and re-map each pair's outcome to the permuted pair, leaving the predictor vector untouched — this preserves the pair-dependence structure that a plain label shuffle destroys. BH-corrected across the predictor family.
+
+| substrate | predictor | n | Spearman | AUROC (held out by seed) | null mean | perm p | BH q |
+|---|---|---|---|---|---|---|---|
+| pythia-14m | weight_cosine | 36 | 0.095 | 0.549 | 0.501 | 0.316 | 0.638 |
+| pythia-14m | weight_cosine_bn | 36 | 0.092 | 0.460 | 0.500 | 0.621 | 0.698 |
+| pythia-14m | d_raw | 36 | -0.072 | 0.478 | 0.499 | 0.596 | 0.692 |
+| pythia-14m | qmd_perm | 36 | 0.077 | 0.664 | 0.500 | 0.064 | 0.497 |
+| pythia-14m | coord_share_perm | 36 | -0.074 | 0.438 | 0.506 | 0.757 | 0.798 |
+| pythia-14m | qmd_orth | 36 | 0.093 | 0.676 | 0.499 | 0.040 | 0.497 |
+| pythia-14m | coord_share_orth | 36 | -0.094 | 0.457 | 0.501 | 0.674 | 0.735 |
+| pythia-14m | bnd_raw | 36 | -0.025 | 0.543 | 0.499 | 0.339 | 0.638 |
+| pythia-14m | bnd_perm | 36 | 0.012 | 0.296 | 0.499 | 0.978 | 0.978 |
+| pythia-14m | bnd_orth | 36 | 0.015 | 0.420 | 0.498 | 0.776 | 0.798 |
+| pythia-14m | coord_share_bnd_perm | 36 | -0.009 | 0.478 | 0.499 | 0.588 | 0.692 |
+| pythia-14m | coord_share_bnd_orth | 36 | -0.074 | 0.540 | 0.499 | 0.371 | 0.638 |
+| pythia-14m | cka_mean | 36 | -0.013 | 0.605 | 0.495 | 0.135 | 0.638 |
+| pythia-14m | cka_last | 36 | -0.478 | 0.651 | 0.501 | 0.069 | 0.497 |
+| pythia-14m | qmd_act_perm | 36 | -0.207 | 0.657 | 0.498 | 0.048 | 0.497 |
+| pythia-14m | qmd_act_procrustes | 36 | -0.207 | 0.657 | 0.497 | 0.046 | 0.497 |
+| pythia-14m | qmd_act_ot | 36 | -0.050 | 0.568 | 0.501 | 0.262 | 0.638 |
+| pythia-14m | task_vector_cosine | 36 | 0.131 | 0.580 | 0.500 | 0.223 | 0.638 |
+| pythia-14m | MULTIVARIATE_ridge_all | 36 | 0.254 | 0.620 | — | — | — |
+| pythia-70m | weight_cosine | 13 | 0.324 | 0.786 | 0.692 | 0.279 | 0.638 |
+| pythia-70m | weight_cosine_bn | 13 | -0.511 | 0.667 | 0.608 | 0.389 | 0.638 |
+| pythia-70m | d_raw | 13 | -0.297 | 0.619 | 0.570 | 0.400 | 0.638 |
+| pythia-70m | qmd_perm | 13 | -0.302 | 0.452 | 0.465 | 0.589 | 0.692 |
+| pythia-70m | coord_share_perm | 13 | 0.330 | 0.619 | 0.573 | 0.408 | 0.638 |
+| pythia-70m | qmd_orth | 13 | -0.604 | 0.714 | 0.635 | 0.357 | 0.638 |
+| pythia-70m | coord_share_orth | 13 | 0.560 | 0.738 | 0.654 | 0.297 | 0.638 |
+| pythia-70m | bnd_raw | 13 | 0.297 | 0.571 | 0.549 | 0.503 | 0.692 |
+| pythia-70m | bnd_perm | 13 | 0.055 | 0.524 | 0.522 | 0.572 | 0.692 |
+| pythia-70m | bnd_orth | 13 | -0.115 | 0.548 | 0.533 | 0.532 | 0.692 |
+| pythia-70m | coord_share_bnd_perm | 13 | 0.236 | 0.524 | 0.512 | 0.567 | 0.692 |
+| pythia-70m | coord_share_bnd_orth | 13 | 0.500 | 0.714 | 0.639 | 0.355 | 0.638 |
+| pythia-70m | cka_mean | 13 | 0.659 | 0.762 | 0.670 | 0.291 | 0.638 |
+| pythia-70m | cka_last | 13 | 0.500 | 0.762 | 0.674 | 0.311 | 0.638 |
+| pythia-70m | qmd_act_perm | 13 | -0.709 | 0.786 | 0.689 | 0.282 | 0.638 |
+| pythia-70m | qmd_act_procrustes | 13 | -0.709 | 0.786 | 0.687 | 0.289 | 0.638 |
+| pythia-70m | qmd_act_ot | 13 | -0.555 | 0.619 | 0.579 | 0.397 | 0.638 |
+| pythia-70m | task_vector_cosine | 13 | -0.038 | 0.548 | 0.534 | 0.519 | 0.692 |
+| pythia-70m | MULTIVARIATE_ridge_all | 13 | 0.099 | 0.405 | — | — | — |
+
+## Coverage — what ran and what did not
+
+| cell | n | status | what was measured |
+|---|---|---|---|
+| SET 1 · pythia-14m | 36/36 seed pairs | complete | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; barrier for M0 and M1-perm |
+| SET 1 · pythia-70m | 13/36 seed pairs | partial | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; barrier for M0 and M1-perm |
+| SET 1 · pythia-160m | 4/36 seed pairs | partial | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; barrier for M0 and M1-perm |
+| SET 4 · goldfish eng×X | 1/4 language pairs (nld_Latn) | partial | M0 naive · M1a vocab-transport · M1b/c vocab+unit-aligned (perm/Procrustes) · M1d/e forced-residual · M1f unit-aligned only |
+| BLiMP / MultiBLiMP accuracy | 0 | **NOT RUN** | No benchmark harness was close to wired inside this window. Deliberately not built from scratch. The Δfloor results below therefore say nothing about accuracy. |
+| B-GPT joint bilingual reference | 0 | **NOT RUN** | Out of window; the merged models are not compared against a jointly-trained bilingual ceiling. |
+| Goldfish 160m/other tiers, other language pairs | 0 | NOT RUN | Only the 1000mb tier and the four audit languages. |
+
+## Threats to validity, stated plainly
+
+- **Likelihood ≠ accuracy.** Repeated because it is the single most load-bearing caveat here.
+- **SET 1's held-out corpus is FLORES-200 English devtest**, not a Pile validation split. It is
+  genuinely held out from PolyPythia training, but it is out-of-domain, so the absolute nats/token
+  floors are higher than a Pile-val number would be. Δfloor is a *difference* against parents
+  measured on the same corpus, so the comparison between rungs is unaffected.
+- **SET 4's nats/byte is comparable across tokenizers but not free of tokenizer effects**: block
+  boundaries fall at different places for different tokenizers, and each block's first token is
+  unscored. With ~30k tokens per evaluation this is a sub-1% effect.
+- **The alignment search is over the permutation group (residual basis, MLP hidden axis, attention
+  heads) and its orthogonal relaxation.** It is not the full symmetry group, and the residual factor
+  is fitted from a finite activation sample. A better aligner could raise the M1 rungs; nothing here
+  bounds how far.
+- **SET 4's n = 4 language pairs.** Any predictor claim on that substrate is descriptive.
+
+
+## Files
+
+```
+results/set1_{14m,70m,160m}.jsonl   per-pair raw records (predictors, rungs, barriers, align info)
+results/set1_pairs.csv              per-pair flat table, SET 1
+results/set4_goldfish.jsonl         per-language-pair raw records, SET 4
+results/set4_pairs.csv              per-language-pair flat table, SET 4
+results/rung_summary.csv            rung x substrate x metric summary
+results/predictor_auroc.csv         SET 1 predictor table: held-out AUROC, permutation null, BH q
+results/set4_predictors.csv         SET 4 predictor rank correlations (n=4, descriptive)
+figs/set1_dfloor_by_rung.png        Δfloor by rung, per size
+figs/set1_rescue_vs_predictor.png   realised rescue vs coordinate share / CKA
+figs/set1_roc.png                   held-out-by-seed ROC
+figs/set4_dfloor.png                Δfloor by rung, Goldfish
+```