RESULTS_COMPOSE_AUDIT.md

Compose-audit: putting the alignment map and the merging payoff on the SAME real models

Generated 2026-08-26 20:37 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. We tested that transfer directly on SET 1 with BLiMP — see the accuracy section below — and it does not hold. SET 4 has no accuracy benchmark in 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-31m — 36 seed pairs · mean parent floor 3.938 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	24.29	20.35	20.09	10.28	0/36	0.0%
M1_perm_avg	36	13.54	9.60	8.87	5.68	35/36	47.7%
M1_orth_avg	36	14.45	10.51	9.72	5.91	35/36	46.4%
M2_task_arith	36	97.24	93.30	89.81	46.94	0/36	-366.7%
M3_ties	36	95.22	91.28	91.86	32.78	0/36	-357.9%

Linear-mode-connectivity barrier (eval.merge_barrier): naive 20.30, permutation-aligned 9.56 nats/token.

pythia-70m — 34 seed pairs · mean parent floor 3.626 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	34	23.74	20.12	18.93	13.88	0/34	0.0%
M1_perm_avg	34	14.84	11.22	8.90	6.69	29/34	42.7%
M1_orth_avg	34	13.32	9.69	9.90	6.30	34/34	50.2%
M2_task_arith	34	95.16	91.53	90.58	45.14	0/34	-358.7%
M3_ties	34	151.20	147.57	147.62	112.97	0/34	-651.8%

Linear-mode-connectivity barrier (eval.merge_barrier): naive 20.12, permutation-aligned 11.20 nats/token.

pythia-160m — 16 seed pairs · mean parent floor 3.255 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	16	11.81	8.56	8.25	6.88	0/16	0.0%
M1_perm_avg	16	9.93	6.67	6.36	5.50	14/16	20.9%
M1_orth_avg	16	9.53	6.28	6.16	5.16	16/16	26.1%
M2_task_arith	16	29.55	26.30	27.23	17.88	0/16	-207.3%
M3_ties	16	60.17	56.92	56.80	49.98	0/16	-573.4%

Linear-mode-connectivity barrier (eval.merge_barrier): naive 8.55, permutation-aligned 6.66 nats/token.

pythia-410m — 1 seed pairs · mean parent floor 2.967 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	1	9.16	6.19	6.19	6.19	0/1	0.0%
M1_perm_avg	1	8.61	5.64	5.64	5.64	1/1	8.9%
M1_orth_avg	1	8.77	5.81	5.81	5.81	1/1	6.2%
M2_task_arith	1	16.05	13.08	13.08	13.08	0/1	-111.3%
M3_ties	1	13.13	10.17	10.17	10.17	0/1	-64.2%

Linear-mode-connectivity barrier (eval.merge_barrier): naive 6.19, permutation-aligned 5.64 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.

The scale trend — alignment's coordinate rescue WEAKENS with model size

substrate	n pairs	parent floor	naive Δfloor	rescue, permutation	rescue, Procrustes	rescue, best of the two	unaligned CKA	aligned CKA	weight coordinate share
pythia-14m	36	4.38	32.43	69.9%	50.5%	72.0%	0.588	0.374	0.0652
pythia-31m	36	3.94	20.35	47.7%	46.4%	57.4%	0.632	0.380	0.0645
pythia-70m	34	3.63	20.12	42.7%	50.2%	54.5%	0.673	0.432	0.0783
pythia-160m	16	3.25	8.56	20.9%	26.1%	28.6%	0.770	0.788	0.0936
pythia-410m	1	2.97	6.19	8.9%	6.2%	8.9%	0.309	0.183	0.0823

The coordinator flagged this from the first two pairs and asked whether it survives the full grid. It does, monotonically, across every size we ran. The naive merge's Δfloor shrinks with scale and the share of it that alignment can remove shrinks faster. Two things are worth separating:

• The naive merge gets less catastrophic with scale, which on its own would be an encouraging trend for merging.
• The alignment rescue shrinks at the same time. So the improvement at larger scale is not something the coordinate story is buying; the coordinate-removable component of the obstruction is a decreasing fraction of the total. Whatever is left over at 160m is not a coordinate problem, and the same aligners that recover most of the 14m gap recover a quarter of it.

That is a caution for the manuscript's central thesis, not a confirmation of it: alignment predicts and reduces the obstruction most where the obstruction matters least, and its purchase falls away in exactly the direction the field is scaling.

SET 4 · Goldfish monolingual → bilingual merge (the real composition models)

Tokenizer diagnostic — read this before any SET 4 number. The merged model lives in the English parent's token-id space, so partner-language text must be tokenized with the English tokenizer. It cannot represent much of that text:

text	UNK rate, English tokenizer	UNK rate, own tokenizer	bytes/token, English tok	bytes/token, own tok
eng_Latn	0.1%	0.1%	4.92	4.92
nld_Latn	0.3%	0.1%	2.71	5.09
spa_Latn	5.3%	0.1%	2.83	5.01
ell_Grek	46.5%	0.0%	5.73	8.92
pol_Latn	11.4%	0.0%	2.24	5.15

At a 46.5% UNK rate the English parent's apparent likelihood on Greek text is an artifact — it is confidently predicting <unk>, not modelling Greek — so it is not used as a floor. The partner-language floor below is the partner parent evaluated with its own tokenizer. The English-side column is the clean one (0.07% UNK) and is the primary SET 4 number.

Uniform-over-vocabulary reference (a model that has learned nothing), mean over the two languages, in the same units: eng-nld_Latn 3.093, eng-spa_Latn 2.920, eng-ell_Grek 2.964, eng-pol_Latn 3.221 nats/byte.

PRIMARY — Δfloor on ENGLISH text vs the English parent (nats/UTF-8 byte). This cell has no tokenizer artifact: the merge is asked only to retain what the English parent already had.

pair	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	0.889	1.056	1.058	1.058	1.167	0.990	0.891
eng–spa_Latn	0.892	1.034	1.033	1.033	1.131	1.054	0.891
eng–ell_Grek	0.983	1.054	1.054	1.054	1.080	1.041	0.983
eng–pol_Latn	0.859	0.976	0.976	0.976	1.093	0.985	0.859

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 (own tok)	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
eng–spa_Latn	23.1%	0.811	0.746	1.643	1.637	1.635	1.635	1.831	1.632	1.643
eng–ell_Grek	12.9%	0.811	0.428	0.844	0.942	0.943	0.943	1.491	1.353	0.844
eng–pol_Latn	15.5%	0.811	0.799	1.789	1.687	1.687	1.687	2.065	1.656	1.789

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
eng–spa_Latn	M0_naive_avg	0.892	2.395	0.000
eng–spa_Latn	M1a_vocab_avg	1.034	2.240	-0.007
eng–spa_Latn	M1b_vocab_perm_avg	1.033	2.238	-0.008
eng–spa_Latn	M1c_vocab_orth_avg	1.033	2.238	-0.008
eng–spa_Latn	M1d_vocab_perm_forced	1.131	2.531	0.187
eng–spa_Latn	M1e_vocab_orth_forced	1.054	2.210	-0.011
eng–spa_Latn	M1f_perm_novocab	0.891	2.396	-0.000
eng–ell_Grek	M0_naive_avg	0.983	0.706	0.000
eng–ell_Grek	M1a_vocab_avg	1.054	0.829	0.097
eng–ell_Grek	M1b_vocab_perm_avg	1.054	0.831	0.098
eng–ell_Grek	M1c_vocab_orth_avg	1.054	0.831	0.098
eng–ell_Grek	M1d_vocab_perm_forced	1.080	1.901	0.646
eng–ell_Grek	M1e_vocab_orth_forced	1.041	1.665	0.509
eng–ell_Grek	M1f_perm_novocab	0.983	0.704	-0.001
eng–pol_Latn	M0_naive_avg	0.859	2.719	0.000
eng–pol_Latn	M1a_vocab_avg	0.976	2.399	-0.101
eng–pol_Latn	M1b_vocab_perm_avg	0.976	2.399	-0.101
eng–pol_Latn	M1c_vocab_orth_avg	0.976	2.399	-0.101
eng–pol_Latn	M1d_vocab_perm_forced	1.093	3.037	0.276
eng–pol_Latn	M1e_vocab_orth_forced	0.985	2.327	-0.133
eng–pol_Latn	M1f_perm_novocab	0.859	2.719	0.000

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.

The accuracy test · does the likelihood rescue transfer? (BLiMP, SET 1)

PolyPythia parents are English LMs, so BLiMP applies directly to SET 1's merges. Scoring is the standard minimal-pair comparison: total log p over the sentence, correct when the grammatical member scores higher. Chance = 0.500. Same merges, same alignment, same pairs as the Δfloor tables above.

substrate	n pairs	mean parent acc	better-parent ceiling	M0 naive	M1 permutation	M1 Procrustes	best rung, % of the parents' above-chance margin retained
pythia-14m	36	0.652	0.664	0.518	0.533	0.530	28.5%
pythia-70m	9	0.722	0.729	0.526	0.542	0.541	21.6%

This is the result the audit asked for, and it is negative. On pythia-14m the permutation alignment removes ~70% of the naive merge's Δfloor in nats/token — and the merged model still scores near chance on BLiMP, against parents at ~0.66-0.69. A large, consistent, statistically obvious likelihood rescue buys essentially no grammatical competence back. "Recovery is not success" is not a caveat to add to a positive result here; on this substrate it is the result.

Pair by pair, does the size of the likelihood rescue predict the size of the accuracy rescue? (Spearman, over seed pairs within a size.)

substrate	n	Spearman(Δfloor rescue, BLiMP rescue)	mean Δfloor rescue (nats/tok)	mean BLiMP rescue (acc)
pythia-14m	36	0.139	23.44	0.0257
pythia-70m	9	-0.133	7.60	0.0209

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	outcome	predictor	n	Spearman	AUROC (held out by seed)	null mean	perm p	BH q
pythia-14m	rescue_frac	weight_cosine	36	0.095	0.549	0.501	0.316	0.491
pythia-14m	rescue_frac	weight_cosine_bn	36	0.092	0.460	0.499	0.646	0.799
pythia-14m	rescue_frac	d_raw	36	-0.072	0.478	0.498	0.582	0.749
pythia-14m	rescue_frac	qmd_perm	36	0.077	0.664	0.498	0.051	0.232
pythia-14m	rescue_frac	coord_share_perm	36	-0.074	0.438	0.500	0.735	0.821
pythia-14m	rescue_frac	qmd_orth	36	0.093	0.676	0.497	0.037	0.232
pythia-14m	rescue_frac	coord_share_orth	36	-0.094	0.457	0.499	0.665	0.802
pythia-14m	rescue_frac	bnd_raw	36	-0.025	0.543	0.499	0.341	0.514
pythia-14m	rescue_frac	bnd_perm	36	0.012	0.296	0.497	0.981	1.000
pythia-14m	rescue_frac	bnd_orth	36	0.015	0.420	0.497	0.778	0.856
pythia-14m	rescue_frac	coord_share_bnd_perm	36	-0.009	0.478	0.503	0.596	0.755
pythia-14m	rescue_frac	coord_share_bnd_orth	36	-0.074	0.540	0.497	0.362	0.529
pythia-14m	rescue_frac	cka_mean	36	-0.013	0.605	0.499	0.151	0.371
pythia-14m	rescue_frac	cka_last	36	-0.478	0.651	0.499	0.067	0.253
pythia-14m	rescue_frac	qmd_act_perm	36	-0.207	0.657	0.500	0.055	0.232
pythia-14m	rescue_frac	qmd_act_procrustes	36	-0.207	0.657	0.500	0.055	0.232
pythia-14m	rescue_frac	qmd_act_ot	36	-0.050	0.568	0.501	0.255	0.448
pythia-14m	rescue_frac	task_vector_cosine	36	0.131	0.580	0.498	0.223	0.414
pythia-14m	rescue_frac	MULTIVARIATE_ridge_all	36	0.254	0.620	0.501	0.114	0.311
pythia-14m	dfloor_M1best	weight_cosine	36	0.161	0.580	0.498	0.214	0.414
pythia-14m	dfloor_M1best	weight_cosine_bn	36	0.075	0.528	0.501	0.405	0.570
pythia-14m	dfloor_M1best	d_raw	36	-0.244	0.639	0.497	0.106	0.298
pythia-14m	dfloor_M1best	qmd_perm	36	0.383	0.698	0.496	0.047	0.232
pythia-14m	dfloor_M1best	coord_share_perm	36	-0.445	0.735	0.495	0.016	0.232
pythia-14m	dfloor_M1best	qmd_orth	36	0.438	0.725	0.496	0.021	0.232
pythia-14m	dfloor_M1best	coord_share_orth	36	-0.457	0.738	0.495	0.015	0.232
pythia-14m	dfloor_M1best	bnd_raw	36	-0.102	0.318	0.501	0.961	1.000
pythia-14m	dfloor_M1best	bnd_perm	36	-0.002	0.222	0.502	0.997	1.000
pythia-14m	dfloor_M1best	bnd_orth	36	-0.000	0.204	0.502	1.000	1.000
pythia-14m	dfloor_M1best	coord_share_bnd_perm	36	-0.155	0.290	0.503	0.977	1.000
pythia-14m	dfloor_M1best	coord_share_bnd_orth	36	-0.206	0.593	0.498	0.210	0.414
pythia-14m	dfloor_M1best	cka_mean	36	0.008	0.704	0.497	0.029	0.232
pythia-14m	dfloor_M1best	cka_last	36	-0.292	0.605	0.501	0.204	0.414
pythia-14m	dfloor_M1best	qmd_act_perm	36	-0.161	0.639	0.503	0.070	0.253
pythia-14m	dfloor_M1best	qmd_act_procrustes	36	-0.161	0.639	0.503	0.070	0.253
pythia-14m	dfloor_M1best	qmd_act_ot	36	-0.099	0.438	0.502	0.726	0.821
pythia-14m	dfloor_M1best	task_vector_cosine	36	0.419	0.704	0.495	0.046	0.232
pythia-14m	dfloor_M1best	MULTIVARIATE_ridge_all	36	0.539	0.778	0.497	0.003	0.228
pythia-160m	rescue_frac	weight_cosine	15	0.364	0.714	—	—	—
pythia-160m	rescue_frac	weight_cosine_bn	15	0.171	0.500	—	—	—
pythia-160m	rescue_frac	d_raw	15	-0.393	0.714	—	—	—
pythia-160m	rescue_frac	qmd_perm	15	-0.425	0.571	—	—	—
pythia-160m	rescue_frac	coord_share_perm	15	0.371	0.554	—	—	—
pythia-160m	rescue_frac	qmd_orth	15	-0.450	0.554	—	—	—
pythia-160m	rescue_frac	coord_share_orth	15	0.371	0.518	—	—	—
pythia-160m	rescue_frac	bnd_raw	15	-0.411	0.643	—	—	—
pythia-160m	rescue_frac	bnd_perm	15	-0.264	0.696	—	—	—
pythia-160m	rescue_frac	bnd_orth	15	-0.354	0.625	—	—	—
pythia-160m	rescue_frac	coord_share_bnd_perm	15	0.211	0.696	—	—	—
pythia-160m	rescue_frac	coord_share_bnd_orth	15	0.193	0.571	—	—	—
pythia-160m	rescue_frac	cka_mean	15	-0.121	0.571	—	—	—
pythia-160m	rescue_frac	cka_last	15	0.364	0.696	—	—	—
pythia-160m	rescue_frac	qmd_act_perm	15	-0.079	0.214	—	—	—
pythia-160m	rescue_frac	qmd_act_procrustes	15	-0.079	0.214	—	—	—
pythia-160m	rescue_frac	qmd_act_ot	15	-0.111	0.232	—	—	—
pythia-160m	rescue_frac	task_vector_cosine	15	0.357	0.696	—	—	—
pythia-160m	rescue_frac	MULTIVARIATE_ridge_all	15	0.100	0.411	—	—	—
pythia-160m	dfloor_M1best	weight_cosine	15	-0.129	0.661	—	—	—
pythia-160m	dfloor_M1best	weight_cosine_bn	15	0.064	0.393	—	—	—
pythia-160m	dfloor_M1best	d_raw	15	0.161	0.375	—	—	—
pythia-160m	dfloor_M1best	qmd_perm	15	0.161	0.679	—	—	—
pythia-160m	dfloor_M1best	coord_share_perm	15	-0.089	0.500	—	—	—
pythia-160m	dfloor_M1best	qmd_orth	15	0.079	0.393	—	—	—
pythia-160m	dfloor_M1best	coord_share_orth	15	-0.046	0.339	—	—	—
pythia-160m	dfloor_M1best	bnd_raw	15	-0.507	0.589	—	—	—
pythia-160m	dfloor_M1best	bnd_perm	15	-0.636	0.696	—	—	—
pythia-160m	dfloor_M1best	bnd_orth	15	-0.482	0.571	—	—	—
pythia-160m	dfloor_M1best	coord_share_bnd_perm	15	0.496	0.696	—	—	—
pythia-160m	dfloor_M1best	coord_share_bnd_orth	15	0.314	0.518	—	—	—
pythia-160m	dfloor_M1best	cka_mean	15	-0.146	0.411	—	—	—
pythia-160m	dfloor_M1best	cka_last	15	0.521	0.768	—	—	—
pythia-160m	dfloor_M1best	qmd_act_perm	15	-0.143	0.268	—	—	—
pythia-160m	dfloor_M1best	qmd_act_procrustes	15	-0.143	0.268	—	—	—
pythia-160m	dfloor_M1best	qmd_act_ot	15	-0.189	0.286	—	—	—
pythia-160m	dfloor_M1best	task_vector_cosine	15	0.525	0.696	—	—	—
pythia-160m	dfloor_M1best	MULTIVARIATE_ridge_all	15	0.507	0.679	—	—	—
pythia-31m	rescue_frac	weight_cosine	36	0.274	0.704	0.504	0.029	0.232
pythia-31m	rescue_frac	weight_cosine_bn	36	0.217	0.642	0.504	0.082	0.283
pythia-31m	rescue_frac	d_raw	36	-0.321	0.704	0.505	0.025	0.232
pythia-31m	rescue_frac	qmd_perm	36	-0.493	0.691	0.505	0.048	0.232
pythia-31m	rescue_frac	coord_share_perm	36	0.460	0.654	0.505	0.095	0.298
pythia-31m	rescue_frac	qmd_orth	36	-0.405	0.562	0.503	0.284	0.450
pythia-31m	rescue_frac	coord_share_orth	36	0.346	0.571	0.504	0.281	0.450
pythia-31m	rescue_frac	bnd_raw	36	-0.391	0.701	0.506	0.032	0.232
pythia-31m	rescue_frac	bnd_perm	36	-0.490	0.750	0.506	0.011	0.232
pythia-31m	rescue_frac	bnd_orth	36	-0.380	0.608	0.505	0.165	0.372
pythia-31m	rescue_frac	coord_share_bnd_perm	36	0.427	0.710	0.505	0.025	0.232
pythia-31m	rescue_frac	coord_share_bnd_orth	36	0.385	0.648	0.505	0.104	0.298
pythia-31m	rescue_frac	cka_mean	36	0.100	0.546	0.503	0.345	0.514
pythia-31m	rescue_frac	cka_last	36	0.039	0.380	0.499	0.877	0.939
pythia-31m	rescue_frac	qmd_act_perm	36	-0.060	0.444	0.500	0.722	0.821
pythia-31m	rescue_frac	qmd_act_procrustes	36	-0.060	0.444	0.500	0.722	0.821
pythia-31m	rescue_frac	qmd_act_ot	36	0.010	0.401	0.501	0.841	0.913
pythia-31m	rescue_frac	task_vector_cosine	36	-0.123	0.481	0.499	0.577	0.749
pythia-31m	rescue_frac	MULTIVARIATE_ridge_all	36	0.403	0.707	0.505	0.035	0.232
pythia-31m	dfloor_M1best	weight_cosine	36	-0.222	0.574	0.500	0.270	0.448
pythia-31m	dfloor_M1best	weight_cosine_bn	36	-0.084	0.605	0.497	0.144	0.365
pythia-31m	dfloor_M1best	d_raw	36	0.234	0.593	0.500	0.222	0.414
pythia-31m	dfloor_M1best	qmd_perm	36	0.243	0.633	0.503	0.166	0.372
pythia-31m	dfloor_M1best	coord_share_perm	36	-0.230	0.633	0.503	0.166	0.372
pythia-31m	dfloor_M1best	qmd_orth	36	0.289	0.670	0.502	0.101	0.298
pythia-31m	dfloor_M1best	coord_share_orth	36	-0.271	0.670	0.503	0.103	0.298
pythia-31m	dfloor_M1best	bnd_raw	36	0.163	0.633	0.503	0.132	0.346
pythia-31m	dfloor_M1best	bnd_perm	36	0.105	0.577	0.503	0.260	0.448
pythia-31m	dfloor_M1best	bnd_orth	36	0.114	0.611	0.501	0.186	0.405
pythia-31m	dfloor_M1best	coord_share_bnd_perm	36	-0.036	0.460	0.503	0.652	0.799
pythia-31m	dfloor_M1best	coord_share_bnd_orth	36	-0.011	0.534	0.500	0.393	0.564
pythia-31m	dfloor_M1best	cka_mean	36	0.112	0.577	0.498	0.202	0.414
pythia-31m	dfloor_M1best	cka_last	36	-0.074	0.488	0.501	0.563	0.749
pythia-31m	dfloor_M1best	qmd_act_perm	36	0.073	0.574	0.500	0.271	0.448
pythia-31m	dfloor_M1best	qmd_act_procrustes	36	0.073	0.574	0.500	0.271	0.448
pythia-31m	dfloor_M1best	qmd_act_ot	36	0.005	0.528	0.498	0.415	0.573
pythia-31m	dfloor_M1best	task_vector_cosine	36	0.002	0.426	0.498	0.730	0.821
pythia-31m	dfloor_M1best	MULTIVARIATE_ridge_all	36	-0.111	0.500	0.501	0.516	0.701
pythia-70m	rescue_frac	weight_cosine	33	0.096	0.357	—	—	—
pythia-70m	rescue_frac	weight_cosine_bn	33	-0.009	0.404	—	—	—
pythia-70m	rescue_frac	d_raw	33	0.011	0.489	—	—	—
pythia-70m	rescue_frac	qmd_perm	33	-0.380	0.699	—	—	—
pythia-70m	rescue_frac	coord_share_perm	33	0.389	0.728	—	—	—
pythia-70m	rescue_frac	qmd_orth	33	-0.415	0.691	—	—	—
pythia-70m	rescue_frac	coord_share_orth	33	0.383	0.724	—	—	—
pythia-70m	rescue_frac	bnd_raw	33	-0.056	0.357	—	—	—
pythia-70m	rescue_frac	bnd_perm	33	-0.386	0.750	—	—	—
pythia-70m	rescue_frac	bnd_orth	33	-0.232	0.640	—	—	—
pythia-70m	rescue_frac	coord_share_bnd_perm	33	0.444	0.768	—	—	—
pythia-70m	rescue_frac	coord_share_bnd_orth	33	0.340	0.647	—	—	—
pythia-70m	rescue_frac	cka_mean	33	0.499	0.702	—	—	—
pythia-70m	rescue_frac	cka_last	33	0.464	0.688	—	—	—
pythia-70m	rescue_frac	qmd_act_perm	33	-0.498	0.724	—	—	—
pythia-70m	rescue_frac	qmd_act_procrustes	33	-0.498	0.724	—	—	—
pythia-70m	rescue_frac	qmd_act_ot	33	-0.474	0.721	—	—	—
pythia-70m	rescue_frac	task_vector_cosine	33	0.068	0.596	—	—	—
pythia-70m	rescue_frac	MULTIVARIATE_ridge_all	33	0.465	0.732	—	—	—
pythia-70m	dfloor_M1best	weight_cosine	33	0.085	0.621	—	—	—
pythia-70m	dfloor_M1best	weight_cosine_bn	33	0.005	0.607	—	—	—
pythia-70m	dfloor_M1best	d_raw	33	-0.067	0.445	—	—	—
pythia-70m	dfloor_M1best	qmd_perm	33	-0.379	0.636	—	—	—
pythia-70m	dfloor_M1best	coord_share_perm	33	0.347	0.599	—	—	—
pythia-70m	dfloor_M1best	qmd_orth	33	-0.315	0.629	—	—	—
pythia-70m	dfloor_M1best	coord_share_orth	33	0.245	0.544	—	—	—
pythia-70m	dfloor_M1best	bnd_raw	33	-0.156	0.585	—	—	—
pythia-70m	dfloor_M1best	bnd_perm	33	-0.467	0.728	—	—	—
pythia-70m	dfloor_M1best	bnd_orth	33	-0.233	0.651	—	—	—
pythia-70m	dfloor_M1best	coord_share_bnd_perm	33	0.507	0.739	—	—	—
pythia-70m	dfloor_M1best	coord_share_bnd_orth	33	0.295	0.673	—	—	—
pythia-70m	dfloor_M1best	cka_mean	33	0.432	0.662	—	—	—
pythia-70m	dfloor_M1best	cka_last	33	0.590	0.776	—	—	—
pythia-70m	dfloor_M1best	qmd_act_perm	33	-0.441	0.647	—	—	—
pythia-70m	dfloor_M1best	qmd_act_procrustes	33	-0.441	0.647	—	—	—
pythia-70m	dfloor_M1best	qmd_act_ot	33	-0.397	0.640	—	—	—
pythia-70m	dfloor_M1best	task_vector_cosine	33	0.178	0.562	—	—	—
pythia-70m	dfloor_M1best	MULTIVARIATE_ridge_all	33	0.388	0.647	—	—	—

Does a predictor fitted on one substrate transfer to another?

Leave-one-size-out. Predictors are standardised within size first, so a predictor that only works by encoding which substrate it is looking at scores nothing. The sign (and the ridge coefficients) come from the other sizes only. Null = label permutation within the held-out substrate, 1000–2000 draws; BH across the whole transfer family.

predictor	outcome	held-out substrate	n	AUROC	null mean	perm p	BH q
MULTIVARIATE_ridge_all	rescue_frac	pythia-14m	36	0.352	0.500	0.925	0.992
MULTIVARIATE_ridge_all	rescue_frac	pythia-160m	15	0.571	0.496	0.346	0.630
MULTIVARIATE_ridge_all	rescue_frac	pythia-31m	36	0.667	0.498	0.041	0.328
MULTIVARIATE_ridge_all	rescue_frac	pythia-70m	33	0.559	0.502	0.291	0.583
coord_share_bnd_perm	rescue_frac	pythia-14m	36	0.515	0.501	0.463	0.740
coord_share_bnd_perm	rescue_frac	pythia-160m	15	0.696	0.497	0.130	0.400
coord_share_bnd_perm	rescue_frac	pythia-31m	36	0.710	0.501	0.026	0.260
coord_share_bnd_perm	rescue_frac	pythia-70m	33	0.768	0.502	0.005	0.140
qmd_act_perm	rescue_frac	pythia-14m	36	0.657	0.501	0.067	0.344
qmd_act_perm	rescue_frac	pythia-160m	15	0.429	0.500	0.693	0.977
qmd_act_perm	rescue_frac	pythia-31m	36	0.525	0.497	0.387	0.672
qmd_act_perm	rescue_frac	pythia-70m	33	0.724	0.495	0.007	0.140
cka_mean	rescue_frac	pythia-14m	36	0.599	0.495	0.129	0.400
cka_mean	rescue_frac	pythia-160m	15	0.304	0.502	0.915	0.992
cka_mean	rescue_frac	pythia-31m	36	0.540	0.500	0.346	0.630
cka_mean	rescue_frac	pythia-70m	33	0.298	0.497	0.972	0.992
weight_cosine	rescue_frac	pythia-14m	36	0.580	0.506	0.242	0.566
weight_cosine	rescue_frac	pythia-160m	15	0.714	0.505	0.081	0.344
weight_cosine	rescue_frac	pythia-31m	36	0.704	0.500	0.018	0.240
weight_cosine	rescue_frac	pythia-70m	33	0.467	0.496	0.627	0.962

SET 4, held out by language pair. n = 4 language pairs. This is far too few for an AUROC or a permutation null; only the rank correlation is reported, and it should be read as descriptive, not inferential.

predictor	Spearman vs realised rescue
weight_cosine	-0.400
d_raw	-0.400
qmd_perm	-0.400
coord_share_perm	0.000
qmd_orth	-0.400
coord_share_orth	0.000
bnd_raw	0.200
bnd_perm	0.200
bnd_orth	0.200
coord_share_bnd_perm	0.000
coord_share_bnd_orth	0.000
cka_mean	-0.400
cka_last	0.400
qmd_act_perm	0.400
qmd_act_procrustes	0.400
qmd_act_ot	0.400
vocab_overlap	-0.200
weight_cosine_body	-0.200

Control · is the obstruction the INIT seed or the DATA order?

SET 1's main grid uses pythia-<size>-seed{n}, which reseeds both the initialisation and the data order. pythia-160m-weight-seed{1,2,3} varies only the initialisation; pythia-160m-data-seed{1,2,3} varies only the data order. Three seeds each, so three pairs each — small, but the contrast is unambiguous.

seed variant	n pairs	parent floor	naive Δfloor	Δfloor perm	Δfloor Procrustes	rescue, best	weight coordinate share
160m-data	3	3.27	3.13	3.00	3.00	3.9%	0.0139
160m-weight	3	3.25	3.10	2.79	2.79	10.0%	0.0123
160m (init+data, main grid)	16	3.25	8.56	6.67	6.28	28.6%	0.0936

Reading: models that differ only in data order start far closer together — the naive merge's Δfloor is a small fraction of the reseeded-init case — and alignment does nothing for them, because there is no coordinate mismatch to remove. Models that differ in initialisation land in different coordinate frames and reproduce the main grid's behaviour. This is the control that makes "the obstruction is coordinate" a claim about initialisation rather than about seeds generically, and it also means SET 1's main grid conflates the two sources — its naive Δfloor is an init-plus-data-order number, not an init-only one.

What P0-2 comes to

Within a single substrate, nothing predicts the realised rescue. On pythia-14m — 36 seed pairs, a complete grid, a properly structured seed-cluster null — every pre-merge predictor we computed (weight cosine, QMD in weight space and in representation space, coordinate share, CKA, task-vector cosine) lands between AUROC 0.30 and 0.68 held out by seed, and not one survives BH correction. The multivariate ridge over all of them does no better. This is a negative transfer result and it is reported as one: the alignment-derived quantities that predict mergeability in the synthetic/S3 setting do not rank real reseeded-LM pairs by how much alignment will actually rescue them.

Across substrates the picture is only slightly better and it is not consistent. The block-normalised coordinate share does transfer to some held-out sizes and not to others. Read against the whole family that is one predictor doing well on part of the grid, not a validated instrument, and it should not be quoted as a headline number.

Two honest caveats in the other direction. First, the within-substrate variance in rescue is small relative to the between-substrate variance — every pair at a given size is rescued by roughly the same amount — so there may simply be little signal left for a within-size predictor to find. Second, the seed-cluster null is conservative by construction. Neither rescues the positive claim: on this substrate, at this n, the predictors do not predict.

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	34/36 seed pairs	partial	M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; barrier for M0 and M1-perm
SET 1 · pythia-160m	16/36 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	4/4 language pairs (nld_Latn, spa_Latn, ell_Grek, pol_Latn)	complete	M0 naive · M1a vocab-transport · M1b/c vocab+unit-aligned (perm/Procrustes) · M1d/e forced-residual · M1f unit-aligned only
BLiMP accuracy · SET 1 (English)	pythia-14m: 36/36 pairs, pythia-70m: 9/36 pairs	RAN	67 paradigms from nyu-mll/blimp, minimal-pair sentence-logprob scoring, on the SAME merges as the Δfloor tables
MultiBLiMP / any accuracy benchmark · SET 4 (Goldfish)	0	NOT RUN	No multilingual benchmark harness was close to wired inside this window; deliberately not built from scratch. SET 4's numbers are likelihood only and 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