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 20:50 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,31m,70m,160m,410m}-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; BLiMP accuracy on the same merges | 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); MultiBLiMP 1.0 accuracy on the same merges |
| What the metric is | Δfloor is a likelihood metric; BLiMP is an accuracy metric | Δfloor is a likelihood metric; MultiBLiMP is an accuracy metric |
Δfloor is a likelihood metric, not benchmark accuracy — and here they come apart. The audit's sharpest point is that a likelihood rescue has not been shown to transfer to accuracy. We tested that transfer directly, on the same merges, with BLiMP (SET 1) and MultiBLiMP 1.0 (SET 4), and it does not hold in either direction: in SET 1 a ~70% Δfloor rescue buys ~0.03 BLiMP accuracy over the naive merge, and in SET 4 a merge whose Δfloor says it is destroyed still scores 0.68 on MultiBLiMP-English. Neither metric may be reported as a proxy for the other. Every table below states which one it is.
Headline findings
- Naive averaging of two seed-only-different real LMs is catastrophic, at every size. Δfloor 14m: +32.4 · 31m: +20.4 · 70m: +20.2 · 160m: +8.8 · 410m: +6.3 nats/token against parent floors of 3–4.4 nats/token, i.e. above the uniform-over-vocabulary reference of 10.8 for all but the largest. n = 36 / 36 / 36 / 23 / 2 pairs.
- Unit alignment removes a large fraction of that gap and still does not produce a usable model. Best of permutation / Procrustes removes 14m: 72% · 31m: 57% · 70m: 55% · 160m: 31% · 410m: 8% — leaving 9.0 · 8.1 · 8.7 · 5.9 · 5.8 nats/token above the better parent.
- The rescue shrinks monotonically with scale (14m: 72% → 410m: 8%) while the naive gap shrinks too — so the coordinate-removable share of the obstruction is falling in exactly the direction the field is scaling. (Per-size n is listed in (1); the largest sizes carry the fewest pairs, so read the trend from the sizes with complete 36-pair grids and treat the largest as directional.)
- The likelihood rescue does not transfer to accuracy. On pythia-14m (n=36), parents average 0.652 on BLiMP; the naive merge 0.518 and the aligned merge 0.544, against chance 0.500. A ~70% Δfloor rescue buys ~0.026 accuracy. Pairwise, the two rescues are uncorrelated.
- On the real bilingual-composition models the merge fails and alignment does not rescue it. Goldfish eng×{nld,spa,ell,pol}: naive Δfloor on English text +0.91 nats/byte against a 0.81 floor; the best M1 rung +0.90. The binding constraint is the vocabulary, not the coordinate frame — the English tokenizer UNK-s 45% of Greek and 11% of Polish, and no permutation or rotation can address that.
- …and the accuracy dissociation runs the other way there. The same likelihood-destroyed Goldfish merges retain 0.68 on MultiBLiMP-English (parent 0.96, chance 0.50). Δfloor and benchmark accuracy dissociate in both directions; neither implies the other.
- P0-2: the pre-merge predictors do not predict the realised rescue. Held out by seed pair on a complete 36-pair grid with a seed-cluster permutation null, no predictor survives BH correction. Reported as the negative transfer result it is.
- This is not an under-trying artifact. REPAIR-style statistics correction on top of the alignment — the strongest training-free merge here — improves the likelihood further and still leaves BLiMP near chance.
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 — 36 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 | 36 | 23.79 | 20.16 | 18.93 | 13.88 | 0/36 | 0.0% |
| M1_perm_avg | 36 | 14.62 | 10.99 | 8.77 | 6.69 | 31/36 | 43.9% |
| M1_orth_avg | 36 | 13.32 | 9.70 | 9.90 | 6.30 | 36/36 | 50.4% |
| M2_task_arith | 36 | 95.14 | 91.52 | 90.58 | 45.14 | 0/36 | -357.8% |
| M3_ties | 36 | 151.39 | 147.77 | 147.75 | 112.97 | 0/36 | -650.7% |
Linear-mode-connectivity barrier (eval.merge_barrier): naive 20.17, permutation-aligned 10.98 nats/token.
pythia-160m — 23 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 | 23 | 12.03 | 8.77 | 8.32 | 6.88 | 0/23 | 0.0% |
| M1_perm_avg | 23 | 9.84 | 6.59 | 6.34 | 5.50 | 21/23 | 23.7% |
| M1_orth_avg | 23 | 9.41 | 6.16 | 6.11 | 5.15 | 23/23 | 29.2% |
| M2_task_arith | 23 | 30.47 | 27.22 | 27.31 | 17.88 | 0/23 | -209.7% |
| M3_ties | 23 | 60.06 | 56.81 | 57.09 | 49.69 | 0/23 | -555.4% |
Linear-mode-connectivity barrier (eval.merge_barrier): naive 8.76, permutation-aligned 6.58 nats/token.
pythia-410m — 2 seed pairs · mean parent floor 2.970 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 | 2 | 9.32 | 6.35 | 6.35 | 6.19 | 0/2 | 0.0% |
| M1_perm_avg | 2 | 8.81 | 5.84 | 5.84 | 5.64 | 2/2 | 7.9% |
| M1_orth_avg | 2 | 8.95 | 5.98 | 5.98 | 5.81 | 2/2 | 5.8% |
| M2_task_arith | 2 | 14.69 | 11.72 | 11.72 | 10.37 | 0/2 | -85.4% |
| M3_ties | 2 | 12.77 | 9.80 | 9.80 | 9.43 | 0/2 | -54.6% |
Linear-mode-connectivity barrier (eval.merge_barrier): naive 6.31, permutation-aligned 5.83 nats/token.
What this says.
- 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.
- 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.
- 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. - 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 | 36 | 3.63 | 20.16 | 43.9% | 50.4% | 55.1% | 0.671 | 0.428 | 0.0793 |
| pythia-160m | 23 | 3.26 | 8.77 | 23.7% | 29.2% | 31.3% | 0.766 | 0.786 | 0.0925 |
| pythia-410m | 2 | 2.97 | 6.35 | 7.9% | 5.8% | 7.9% | 0.381 | 0.342 | 0.0484 |
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 | M1g_emb_procrustes | M1h_emb_proc_units | M1f_perm_novocab |
|---|---|---|---|---|---|---|---|---|---|
| eng–nld_Latn | 0.889 | 1.056 | 1.058 | 1.058 | 1.167 | 0.990 | 1.085 | 0.975 | 0.891 |
| eng–spa_Latn | 0.892 | 1.034 | 1.033 | 1.033 | 1.131 | 1.054 | 0.973 | 0.970 | 0.891 |
| eng–ell_Grek | 0.983 | 1.054 | 1.054 | 1.054 | 1.080 | 1.041 | 0.965 | 1.006 | 0.983 |
| eng–pol_Latn | 0.859 | 0.976 | 0.976 | 0.976 | 1.093 | 0.985 | 1.057 | 0.972 | 0.859 |
| mean of the 4 | 0.906 | 1.030 | 1.030 | 1.030 | 1.118 | 1.018 | 1.020 | 0.981 | 0.906 |
Averaged over the four pairs the best M1 rung removes 1.4% of the naive merge's Δfloor. For contrast, on SET 1 — where the two parents share data, architecture and tokenizer and differ only in seed — the same family of aligners removes 70% at 14M. The Goldfish obstruction is not the kind of obstruction alignment addresses.
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 | M1g_emb_procrustes | M1h_emb_proc_units | M1f_perm_novocab |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| eng–nld_Latn | 27.8% | 0.811 | 0.792 | 1.689 | 1.763 | 1.766 | 1.766 | 2.004 | 1.601 | 1.732 | 1.559 | 1.691 |
| eng–spa_Latn | 23.1% | 0.811 | 0.746 | 1.643 | 1.637 | 1.635 | 1.635 | 1.831 | 1.632 | 1.503 | 1.426 | 1.643 |
| eng–ell_Grek | 12.9% | 0.811 | 0.428 | 0.844 | 0.942 | 0.943 | 0.943 | 1.491 | 1.353 | 1.078 | 1.202 | 0.844 |
| eng–pol_Latn | 15.5% | 0.811 | 0.799 | 1.789 | 1.687 | 1.687 | 1.687 | 2.065 | 1.656 | 1.693 | 1.693 | 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 | M1g_emb_procrustes | 1.085 | 2.380 | 0.043 |
| eng–nld_Latn | M1h_emb_proc_units | 0.975 | 2.143 | -0.130 |
| 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 | M1g_emb_procrustes | 0.973 | 2.032 | -0.141 |
| eng–spa_Latn | M1h_emb_proc_units | 0.970 | 1.883 | -0.217 |
| 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 | M1g_emb_procrustes | 0.965 | 1.191 | 0.234 |
| eng–ell_Grek | M1h_emb_proc_units | 1.006 | 1.397 | 0.358 |
| 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 | M1g_emb_procrustes | 1.057 | 2.329 | -0.096 |
| eng–pol_Latn | M1h_emb_proc_units | 0.972 | 2.414 | -0.096 |
| 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 | 27 | 0.716 | 0.722 | 0.518 | 0.538 | 0.543 | 24.2% |
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 | 27 | 0.206 | 10.94 | 0.0322 |
Did we try hard enough? · REPAIR on top of the alignment
The obvious objection to a negative merging result is that averaging is a weak merge: it halves the variance of every pre-activation, and REPAIR (Jordan et al., ICLR 2023) shows that restoring those statistics recovers most of the remaining barrier on vision nets. This rung adds it, training-free: after the permutation-aligned average, walk the layers in order and affine-correct each Linear's per-unit pre-activation mean and std to the average of the two parents' own statistics on the same corpus. M5 applies the same correction to the naive merge, to separate what alignment contributes from what statistics-repair contributes.
| substrate | n pairs | rung | mean Δfloor (nats/tok) | median Δfloor | BLiMP accuracy | % of the parents' above-chance margin retained |
|---|---|---|---|---|---|---|
| pythia-14m | 27 | M0_naive_avg | 32.25 | 30.70 | 0.512 | 7.2% |
| pythia-14m | 27 | M1_perm_avg | 9.53 | 9.06 | 0.534 | 20.6% |
| pythia-14m | 27 | M4_perm_repair | 7.72 | 7.10 | 0.532 | 19.0% |
| pythia-14m | 27 | M5_naive_repair | 32.11 | 30.98 | 0.509 | 5.4% |
| pythia-14m | 27 | parents | 0.00 | 0.00 | 0.666 | 100.0% |
REPAIR does help the likelihood — it takes a further bite out of the aligned merge's Δfloor, and it is the best training-free merge in this report. It does not change the conclusion. The repaired aligned merge is still many nats/token above the better parent, still above the uniform-over-vocabulary reference at the small sizes, and still close to chance on BLiMP. Applied to the naive merge it barely moves anything, which is the expected pattern: variance repair is only useful once the units correspond.
So the negative result is not an artifact of using a deliberately weak merge operator. Naive averaging, unit-aligned averaging, orthogonal alignment, task arithmetic, TIES and REPAIR-corrected alignment were all tried on the same pairs; the best of them recovers most of the likelihood gap at 14M, a quarter of it at 160M, and grammatical competence in none of them.
SET 4 · the accuracy arm (MultiBLiMP 1.0)
jumelet/multiblimp covers exactly the four partner languages plus English. Minimal pairs are sen vs wrong_sen; correct when the grammatical member gets the higher total log-probability. Chance = 0.500. The merged models live in the English parent's token-id space, so partner-language items are scored through the English tokenizer — the UNK column says how badly that hurts, and where it is large the partner-language number is a tokenizer artifact, not a competence measurement.
Parents (each on its own tokenizer except the last column):
| pair | n items (partner) | UNK rate, English tok on partner items | English parent, MultiBLiMP-eng | partner parent, MultiBLiMP-partner | English parent, MultiBLiMP-partner |
|---|---|---|---|---|---|
| eng–nld_Latn | 1200 | 0.2% | 0.962 | 0.970 | 0.598 |
| eng–spa_Latn | 1200 | 5.1% | 0.962 | 0.926 | 0.502 |
| eng–ell_Grek | 1096 | 45.1% | 0.962 | 0.987 | 0.029 |
| eng–pol_Latn | 1200 | 11.2% | 0.962 | 0.963 | 0.494 |
Merged models, MultiBLiMP-English accuracy (the clean cell — 0.04% UNK; English parent ceiling in the first column):
| pair | English parent | M0_naive_avg | M1a_vocab_avg | M1b_vocab_perm_avg | M1c_vocab_orth_avg | M1e_vocab_orth_forced | M1g_emb_procrustes | M1h_emb_proc_units |
|---|---|---|---|---|---|---|---|---|
| eng–nld_Latn | 0.962 | 0.673 | 0.601 | 0.596 | 0.596 | 0.662 | 0.668 | 0.635 |
| eng–spa_Latn | 0.962 | 0.677 | 0.727 | 0.726 | 0.726 | 0.682 | 0.661 | 0.631 |
| eng–ell_Grek | 0.962 | 0.688 | 0.599 | 0.600 | 0.600 | 0.687 | 0.656 | 0.657 |
| eng–pol_Latn | 0.962 | 0.682 | 0.656 | 0.656 | 0.656 | 0.653 | 0.653 | 0.655 |
Merged models, MultiBLiMP-partner accuracy (partner parent ceiling in the first column; rows with a high UNK rate are struck through in interpretation, not in the numbers):
| pair | partner parent | UNK | M0_naive_avg | M1a_vocab_avg | M1b_vocab_perm_avg | M1c_vocab_orth_avg | M1e_vocab_orth_forced | M1g_emb_procrustes | M1h_emb_proc_units |
|---|---|---|---|---|---|---|---|---|---|
| eng–nld_Latn | 0.970 | 0% | 0.655 | 0.646 | 0.644 | 0.644 | 0.602 | 0.653 | 0.583 |
| eng–spa_Latn | 0.926 | 5% | 0.500 | 0.532 | 0.535 | 0.535 | 0.477 | 0.525 | 0.537 |
| eng–ell_Grek | 0.987 | 45% | 0.029 | 0.029 | 0.029 | 0.029 | 0.014 | 0.029 | 0.029 |
| eng–pol_Latn | 0.963 | 11% | 0.454 | 0.462 | 0.462 | 0.462 | 0.501 | 0.491 | 0.490 |
What the accuracy arm adds, and it cuts the other way from SET 1.
- The English-side accuracy of the naive merge (mean 0.680, parent 0.962) is far below the parent but far above chance — while its Δfloor on the same text is roughly a nat per byte, i.e. by the likelihood metric the model is destroyed. A merge can look annihilated in nats and still retain a large fraction of an agreement benchmark.
- The unit-aligned rungs are a wash against the naive merge on accuracy. Averaged over the four pairs the naive merge scores 0.680 on MultiBLiMP-English against 0.645–0.671 for the aligned rungs, and 0.536 on the partner side (Greek excluded) against 0.527–0.556. Individual cells go both ways — the vocabulary-transported rungs help Spanish and hurt Dutch — with no consistent direction and a spread far smaller than the ~0.30 gap to the parents. Nothing in the M1 family recovers composition; they reshuffle a uniformly bad result.
- Greek is the clean illustration of the tokenizer wall: at a 45% UNK rate the English parent scores
0.03 on MultiBLiMP-Greek — far below chance, because
<unk>-collapsed sentences make the ungrammatical member the likelier string. Nothing about Greek grammar is being measured there. Any cross-tokenizer merge that keeps one parent's vocabulary inherits this, and it is a property of the vocabulary, not of the coordinate frame — no alignment over the permutation or orthogonal group can touch it. - Taken with SET 1: Δfloor and benchmark accuracy dissociate in both directions. In SET 1 a large likelihood rescue buys almost no accuracy. In SET 4 a catastrophic likelihood loss leaves a lot of accuracy standing. Whichever of the two you report, the other does not follow from it.
SET 4 · what would SUCCESS look like? The jointly-trained bilingual ceiling
A merge that fails is only interpretable against what a bilingual model of the same budget actually achieves. B-GPT (Arnett et al.) trains English+X jointly with one shared tokenizer — the target the composition literature is trying to reach without joint training. B-GPT's context window is 128 tokens, so every arm in this table, including the Goldfish parents and merges, is re-scored at a matched 128-token context; these numbers are therefore not directly comparable to the 512-token SET 4 tables above, only to each other.
nats/byte, English (lower is better)
| pair | bgpt_joint_bilingual | goldfish_eng_parent | goldfish_partner_parent | merge_M0_naive | merge_M1a_vocab |
|---|---|---|---|---|---|
| eng–nld_Latn | 0.871 | 0.848 | 1.473 | 1.697 | 1.835 |
| eng–spa_Latn | 0.872 | 0.848 | 1.609 | 1.685 | 1.834 |
nats/byte, partner (lower is better)
| pair | bgpt_joint_bilingual | goldfish_eng_parent | goldfish_partner_parent | merge_M0_naive | merge_M1a_vocab |
|---|---|---|---|---|---|
| eng–nld_Latn | 0.898 | 2.336 | 0.823 | 3.281 | 3.302 |
| eng–spa_Latn | 0.889 | 1.940 | 0.777 | 3.126 | 2.969 |
MultiBLiMP-English (higher is better, chance 0.500)
| pair | bgpt_joint_bilingual | goldfish_eng_parent | goldfish_partner_parent | merge_M0_naive | merge_M1a_vocab |
|---|---|---|---|---|---|
| eng–nld_Latn | 0.966 | 0.962 | 0.694 | 0.673 | 0.601 |
| eng–spa_Latn | 0.968 | 0.962 | 0.656 | 0.677 | 0.727 |
MultiBLiMP-partner (higher is better, chance 0.500)
| pair | bgpt_joint_bilingual | goldfish_eng_parent | goldfish_partner_parent | merge_M0_naive | merge_M1a_vocab |
|---|---|---|---|---|---|
| eng–nld_Latn | 0.952 | 0.598 | 0.970 | 0.655 | 0.646 |
| eng–spa_Latn | 0.879 | 0.502 | 0.926 | 0.500 | 0.532 |
This is the cleanest single statement the audit can make about SET 4. A jointly trained bilingual model of the same parameter budget is good at both languages at once — near the monolingual parents on likelihood and on MultiBLiMP. The merge of two monolingual models is not close, on either metric, under any rung, in either anchoring direction. The gap is not a coordinate gap that a better aligner might close; the joint model also has a shared vocabulary, which is exactly the axis the alignment group cannot act on.
SET 4 · reverse direction (the partner language is the anchor)
Identical rungs, but the merged model lives in the partner language's tokenizer and residual basis and English is transported into it. If the failure were an artifact of anchoring on English it would not survive the swap.
| anchor | floor (anchor lang) | floor (English) | M0_naive_avg | M1a_vocab_avg | M1b_vocab_perm_avg | M1c_vocab_orth_avg | M1e_vocab_orth_forced | M1g_emb_procrustes |
|---|---|---|---|---|---|---|---|---|
| nld_Latn | 0.792 | 0.811 | 1.342 | 1.335 | 1.337 | 1.337 | 1.384 | 1.425 |
Δfloor, mean over the two languages, nats/UTF-8 byte. The failure is symmetric: anchoring on the partner language does not make the merge work either.
P0-2 · Do the pre-merge predictors predict the realised rescue?
Showing, per substrate and per outcome, the six predictors with the largest |AUROC − 0.5| plus the multivariate ridge. The full table (every predictor, both outcomes, every substrate) is results/predictor_auroc.csv; selecting the extremes here is deliberately generous to the positive claim.
| substrate | outcome | predictor | n | Spearman | AUROC (held out by seed) | null mean | perm p | BH q |
|---|---|---|---|---|---|---|---|---|
| pythia-14m | rescue_frac | bnd_perm | 36 | 0.012 | 0.296 | 0.497 | 0.981 | 0.998 |
| pythia-14m | rescue_frac | qmd_orth | 36 | 0.093 | 0.676 | 0.497 | 0.037 | 0.251 |
| pythia-14m | rescue_frac | qmd_perm | 36 | 0.077 | 0.664 | 0.498 | 0.051 | 0.261 |
| pythia-14m | rescue_frac | qmd_act_perm | 36 | -0.207 | 0.657 | 0.500 | 0.055 | 0.261 |
| pythia-14m | rescue_frac | qmd_act_procrustes | 36 | -0.207 | 0.657 | 0.500 | 0.055 | 0.261 |
| pythia-14m | rescue_frac | cka_last | 36 | -0.478 | 0.651 | 0.499 | 0.067 | 0.268 |
| pythia-14m | rescue_frac | MULTIVARIATE_ridge_all | 36 | 0.254 | 0.620 | 0.501 | 0.114 | 0.278 |
| pythia-31m | rescue_frac | bnd_perm | 36 | -0.490 | 0.750 | 0.506 | 0.011 | 0.251 |
| pythia-31m | rescue_frac | coord_share_bnd_perm | 36 | 0.427 | 0.710 | 0.505 | 0.025 | 0.251 |
| pythia-31m | rescue_frac | weight_cosine | 36 | 0.274 | 0.704 | 0.504 | 0.029 | 0.251 |
| pythia-31m | rescue_frac | d_raw | 36 | -0.321 | 0.704 | 0.505 | 0.025 | 0.251 |
| pythia-31m | rescue_frac | bnd_raw | 36 | -0.391 | 0.701 | 0.506 | 0.032 | 0.251 |
| pythia-31m | rescue_frac | qmd_perm | 36 | -0.493 | 0.691 | 0.505 | 0.048 | 0.261 |
| pythia-31m | rescue_frac | MULTIVARIATE_ridge_all | 36 | 0.403 | 0.707 | 0.505 | 0.035 | 0.251 |
| pythia-70m | rescue_frac | coord_share_bnd_perm | 36 | 0.462 | 0.806 | 0.500 | 0.002 | 0.133 |
| pythia-70m | rescue_frac | bnd_perm | 36 | -0.404 | 0.787 | 0.501 | 0.003 | 0.133 |
| pythia-70m | rescue_frac | coord_share_orth | 36 | 0.341 | 0.722 | 0.497 | 0.033 | 0.251 |
| pythia-70m | rescue_frac | qmd_orth | 36 | -0.373 | 0.713 | 0.497 | 0.067 | 0.268 |
| pythia-70m | rescue_frac | coord_share_perm | 36 | 0.356 | 0.698 | 0.500 | 0.065 | 0.268 |
| pythia-70m | rescue_frac | qmd_perm | 36 | -0.357 | 0.688 | 0.500 | 0.084 | 0.268 |
| pythia-70m | rescue_frac | MULTIVARIATE_ridge_all | 36 | 0.387 | 0.688 | 0.499 | 0.080 | 0.268 |
| pythia-160m | rescue_frac | qmd_orth | 23 | -0.592 | 0.803 | — | — | — |
| pythia-160m | rescue_frac | coord_share_orth | 23 | 0.445 | 0.795 | — | — | — |
| pythia-160m | rescue_frac | qmd_perm | 23 | -0.610 | 0.773 | — | — | — |
| pythia-160m | rescue_frac | coord_share_perm | 23 | 0.485 | 0.773 | — | — | — |
| pythia-160m | rescue_frac | bnd_orth | 23 | -0.302 | 0.750 | — | — | — |
| pythia-160m | rescue_frac | coord_share_bnd_orth | 23 | 0.265 | 0.750 | — | — | — |
| pythia-160m | rescue_frac | MULTIVARIATE_ridge_all | 23 | 0.342 | 0.598 | — | — | — |
| pythia-14m | dfloor_M1best | bnd_orth | 36 | -0.000 | 0.204 | 0.502 | 1.000 | 1.000 |
| pythia-14m | dfloor_M1best | bnd_perm | 36 | -0.002 | 0.222 | 0.502 | 0.997 | 1.000 |
| pythia-14m | dfloor_M1best | coord_share_orth | 36 | -0.457 | 0.738 | 0.495 | 0.015 | 0.251 |
| pythia-14m | dfloor_M1best | coord_share_perm | 36 | -0.445 | 0.735 | 0.495 | 0.016 | 0.251 |
| pythia-14m | dfloor_M1best | qmd_orth | 36 | 0.438 | 0.725 | 0.496 | 0.021 | 0.251 |
| pythia-14m | dfloor_M1best | coord_share_bnd_perm | 36 | -0.155 | 0.290 | 0.503 | 0.977 | 0.998 |
| pythia-14m | dfloor_M1best | MULTIVARIATE_ridge_all | 36 | 0.539 | 0.778 | 0.497 | 0.003 | 0.133 |
| pythia-31m | dfloor_M1best | qmd_orth | 36 | 0.289 | 0.670 | 0.502 | 0.101 | 0.268 |
| pythia-31m | dfloor_M1best | coord_share_orth | 36 | -0.271 | 0.670 | 0.503 | 0.103 | 0.268 |
| pythia-31m | dfloor_M1best | qmd_perm | 36 | 0.243 | 0.633 | 0.503 | 0.166 | 0.322 |
| pythia-31m | dfloor_M1best | coord_share_perm | 36 | -0.230 | 0.633 | 0.503 | 0.166 | 0.322 |
| pythia-31m | dfloor_M1best | bnd_raw | 36 | 0.163 | 0.633 | 0.503 | 0.132 | 0.299 |
| pythia-31m | dfloor_M1best | bnd_orth | 36 | 0.114 | 0.611 | 0.501 | 0.186 | 0.343 |
| pythia-31m | dfloor_M1best | MULTIVARIATE_ridge_all | 36 | -0.111 | 0.500 | 0.501 | 0.516 | 0.647 |
| pythia-70m | dfloor_M1best | coord_share_bnd_perm | 36 | 0.529 | 0.713 | 0.501 | 0.037 | 0.251 |
| pythia-70m | dfloor_M1best | bnd_perm | 36 | -0.485 | 0.704 | 0.502 | 0.033 | 0.251 |
| pythia-70m | dfloor_M1best | cka_last | 36 | 0.476 | 0.691 | 0.499 | 0.090 | 0.268 |
| pythia-70m | dfloor_M1best | cka_mean | 36 | 0.427 | 0.667 | 0.501 | 0.105 | 0.268 |
| pythia-70m | dfloor_M1best | qmd_act_perm | 36 | -0.433 | 0.667 | 0.501 | 0.103 | 0.268 |
| pythia-70m | dfloor_M1best | qmd_act_procrustes | 36 | -0.433 | 0.667 | 0.501 | 0.103 | 0.268 |
| pythia-70m | dfloor_M1best | MULTIVARIATE_ridge_all | 36 | 0.386 | 0.599 | 0.500 | 0.207 | 0.347 |
| pythia-160m | dfloor_M1best | bnd_perm | 23 | -0.591 | 0.818 | — | — | — |
| pythia-160m | dfloor_M1best | coord_share_bnd_perm | 23 | 0.445 | 0.773 | — | — | — |
| pythia-160m | dfloor_M1best | bnd_orth | 23 | -0.587 | 0.765 | — | — | — |
| pythia-160m | dfloor_M1best | coord_share_bnd_orth | 23 | 0.489 | 0.742 | — | — | — |
| pythia-160m | dfloor_M1best | cka_last | 23 | 0.386 | 0.712 | — | — | — |
| pythia-160m | dfloor_M1best | cka_mean | 23 | -0.324 | 0.697 | — | — | — |
| pythia-160m | dfloor_M1best | MULTIVARIATE_ridge_all | 23 | 0.585 | 0.735 | — | — | — |
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 | 0.349 | 0.500 | 0.932 | 0.977 |
| MULTIVARIATE_ridge_all | rescue_frac | pythia-160m | 23 | 0.720 | 0.500 | 0.037 | 0.209 |
| MULTIVARIATE_ridge_all | rescue_frac | pythia-31m | 36 | 0.701 | 0.496 | 0.019 | 0.152 |
| MULTIVARIATE_ridge_all | rescue_frac | pythia-70m | 36 | 0.556 | 0.500 | 0.291 | 0.612 |
| coord_share_bnd_perm | rescue_frac | pythia-14m | 36 | 0.515 | 0.507 | 0.480 | 0.799 |
| coord_share_bnd_perm | rescue_frac | pythia-160m | 23 | 0.606 | 0.499 | 0.198 | 0.497 |
| coord_share_bnd_perm | rescue_frac | pythia-31m | 36 | 0.710 | 0.500 | 0.011 | 0.152 |
| coord_share_bnd_perm | rescue_frac | pythia-70m | 36 | 0.806 | 0.495 | 0.001 | 0.040 |
| qmd_act_perm | rescue_frac | pythia-14m | 36 | 0.657 | 0.494 | 0.045 | 0.209 |
| qmd_act_perm | rescue_frac | pythia-160m | 23 | 0.500 | 0.497 | 0.507 | 0.812 |
| qmd_act_perm | rescue_frac | pythia-31m | 36 | 0.525 | 0.498 | 0.399 | 0.725 |
| qmd_act_perm | rescue_frac | pythia-70m | 36 | 0.676 | 0.504 | 0.031 | 0.206 |
| cka_mean | rescue_frac | pythia-14m | 36 | 0.599 | 0.498 | 0.155 | 0.442 |
| cka_mean | rescue_frac | pythia-160m | 23 | 0.455 | 0.498 | 0.649 | 0.928 |
| cka_mean | rescue_frac | pythia-31m | 36 | 0.540 | 0.500 | 0.338 | 0.675 |
| cka_mean | rescue_frac | pythia-70m | 36 | 0.346 | 0.502 | 0.937 | 0.977 |
| weight_cosine | rescue_frac | pythia-14m | 36 | 0.580 | 0.505 | 0.232 | 0.545 |
| weight_cosine | rescue_frac | pythia-160m | 23 | 0.636 | 0.498 | 0.141 | 0.433 |
| weight_cosine | rescue_frac | pythia-31m | 36 | 0.704 | 0.497 | 0.014 | 0.152 |
| weight_cosine | rescue_frac | pythia-70m | 36 | 0.494 | 0.504 | 0.528 | 0.813 |
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 | 0.800 |
| qmd_orth | 0.400 |
| coord_share_orth | 0.800 |
| bnd_raw | 0.800 |
| bnd_perm | 0.800 |
| bnd_orth | 0.800 |
| coord_share_bnd_perm | 0.800 |
| coord_share_bnd_orth | 0.800 |
| 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 | -0.800 |
| weight_cosine_body | -0.800 |
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.
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) | 23 | 3.26 | 8.77 | 6.59 | 6.16 | 31.3% | 0.0925 |
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.
Coverage — what ran and what did not
| cell | n | status | what was measured |
|---|---|---|---|
| SET 1 Δfloor · pythia-14m | 36/36 seed pairs | complete | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; LMC barrier for M0 and M1-perm |
| SET 1 Δfloor · pythia-31m | 36/36 seed pairs | complete | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; LMC barrier for M0 and M1-perm |
| SET 1 Δfloor · pythia-70m | 36/36 seed pairs | complete | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; LMC barrier for M0 and M1-perm |
| SET 1 Δfloor · pythia-160m | 23/36 seed pairs | partial | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; LMC barrier for M0 and M1-perm |
| SET 1 Δfloor · pythia-410m | 2/15 seed pairs | partial | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; LMC barrier for M0 and M1-perm |
| SET 1 control · pythia-160m-data | 3/3 pairs | complete | init-seed-only vs data-order-only, same rungs |
| SET 1 control · pythia-160m-weight | 3/3 pairs | complete | init-seed-only vs data-order-only, same rungs |
| SET 1 accuracy · BLiMP | pythia-14m: 36/36, pythia-70m: 27/36 | RAN | 67 paradigms from nyu-mll/blimp, minimal-pair sentence-logprob scoring, on the SAME merges |
| SET 1 · REPAIR rung | pythia-14m: 27/36 | RAN | M4 = permutation-aligned average + pre-activation statistics repair; M5 = naive + repair; Δfloor and BLiMP on the same merges |
| SET 4 Δfloor · English-anchored | 4/4 language pairs (nld_Latn, spa_Latn, ell_Grek, pol_Latn) | complete | M0 naive · M1a vocab-transport · M1b/c vocab+unit-aligned · M1d/e forced-residual · M1f units-only · M1g/h embedding-row Procrustes |
| SET 4 Δfloor · partner-anchored (reverse) | 1/4 language pairs | partial | same rungs, roles swapped |
| SET 4 accuracy · MultiBLiMP 1.0 | 4/4 language pairs | RAN | jumelet/multiblimp, English + partner, on the SAME merges; UNK rate reported per cell |
| SET 4 · jointly-trained bilingual ceiling | 2/4 language pairs | RAN | catherinearnett/B-GPT_en_X_simultaneous vs the Goldfish parents and merges, all scored at a matched 128-token context |
| SET 4 · task-arithmetic / TIES | 0 | NOT APPLICABLE | Both operators need a shared ancestor. Two independently trained monolingual Goldfish models have none, and with one parent as a pseudo-base the operators reduce to returning the other parent. Excluded on definition, not on time. |
| SET 1 · pythia-410m full grid | 2/36 possible pairs | partial | 6 seeds only (15 possible pairs) and a reduced eval budget; the per-pair alignment cost is ~9 min at this width. Treat 410m as directional. |
| Goldfish other tiers / other languages | 0 | NOT RUN | Only the 1000mb tier and the four audit languages. |
| Any downstream task beyond BLiMP/MultiBLiMP | 0 | NOT RUN | Both benchmarks are minimal-pair grammaticality tests. They do not speak to reasoning, generation quality or instruction following. |
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,31m,70m,160m,410m}.jsonl SET 1 per-pair raw records (predictors, rungs, barriers)
results/set1_pairs.csv SET 1 per-pair flat table
results/abl_160m-{weight,data}.jsonl init-seed-only vs data-order-only control
results/blimp_{size}.jsonl, blimp_pairs.csv SET 1 BLiMP accuracy, per pair and per rung
results/repair_{size}.jsonl REPAIR rung (Δfloor + BLiMP on the same merges)
results/set4_goldfish.jsonl, set4_pairs.csv SET 4 Δfloor, English-anchored
results/set4_reverse.jsonl SET 4 Δfloor, partner-language-anchored
results/set4_multiblimp.jsonl SET 4 MultiBLiMP accuracy
results/set4_tokenizer_diag.json UNK rates / bytes-per-token per (tokenizer, language)
results/rung_summary.csv rung x substrate x metric summary
results/predictor_auroc.csv P0-2: held-out-by-seed AUROC, seed-cluster null, BH q
results/predictor_transfer_across_size.csv P0-2: leave-one-substrate-out transfer
results/set4_predictors.csv P0-2 on SET 4 (n=4, descriptive only)
figs/set1_dfloor_by_rung.png Δfloor by rung, per size
figs/set1_scale_trend.png obstruction and rescue vs model size
figs/set1_rescue_vs_predictor.png realised rescue vs coordinate share / CKA
figs/set1_roc.png held-out-by-seed ROC
figs/set1_blimp_dissociation.png likelihood rescue vs accuracy rescue
figs/set4_dfloor.png Δfloor by rung, Goldfish
code/*.py every script that produced the above
Reproducing. common.py holds the corpora and evaluation; gpt2_align.py holds the GPT-2
(Conv1D) symmetry factors that mergeschool.core.alignment's row-major aligners do not cover; the
set1_*/set4_* scripts are the drivers, each with a resumable JSONL ledger; analyze.py builds
the tables and figures and make_report.py writes this document. Merge operators, aligners, quotient
metrics and the barrier are imported unmodified from mergeschool.core.