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compose-audit

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license: apache-2.0
tags:
  - model-merging
  - alignment
  - polypythia
  - goldfish
  - multilingual

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