suchirsalhan/goldfish-crosslingual-cka

Cross-lingual representational alignment (CKA) of the Goldfish bilingual merge/train models

Reproduction of the §3 Representational Alignment protocol of the Goldfish cross-lingual paper, applied to the 111 bilingual merge/train checkpoints under suchirsalhan/* created 2025-12. Generated 2026-08-26 19:17 UTC. Code: scripts/ in this repo.

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TL;DR — read this before the numbers

The uploaded checkpoints do not contain the merges. All 111 repos ship a LoRA adapter over goldfish-models/eng_latn_1000mb (adapter_config.json → peft_type: LORA, r: 16, modules_to_save: null), plus a per-pair bilingual SentencePiece tokenizer. Two things are wrong with that as a bilingual model:

1. 75/111 adapters are exact identities. Every -merged and every TOKENWISE_MERGE adapter has lora_B == 0 — its initialisation value — so B @ A == 0 and the adapter changes nothing. The -trained adapters are non-zero but tiny (max |ΔW| element ≤ 1.5e-2). The merge-weight α and the vocabulary-overlap top-K therefore have literally zero effect on the weights of the uploaded artefacts.
2. The bilingual embedding matrix was never uploaded. A tokenwise merge is an embedding-table operation (English backbone + tokenwise-averaged eng/L2 embeddings over a bilingual vocabulary), but modules_to_save is null, so no embedding ships. The shipped bilingual tokenizer's ids do not correspond to the English base's embedding rows: only 7–13 of 50 000 vocabulary positions agree. Loading a repo the obvious way (AutoModelForCausalLM.from_pretrained(base) + PeftModel.from_pretrained(repo) + the repo's tokenizer) yields a model at ≈9.2–10.4 nats/token — chance is ln(51200)=10.84 — i.e. not a language model at all. So the analysis is reported in two configurations:

• as-uploaded — exactly what from_pretrained gives you. Included as the audit trail; its CKA is the CKA of a broken model and should not be interpreted as an alignment measurement.
• reconstructed — the described method re-implemented here: English Goldfish backbone (+ the uploaded LoRA), and the embedding table rebuilt as a tokenwise merge of goldfish-models/eng_latn_1000mb and the matching L2 Goldfish (ell_grek/spa_latn/nld_latn/pol_latn_1000mb) over the shipped bilingual vocabulary. This restores a working model (7.4–7.9 nats/token) and makes α and top-K real variables again. It is a reconstruction, not the authors' checkpoints — the exact recipe (mixing convention, unseen-token handling) is inferred, not recovered.

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0. Headline correlations (last layer, SGPT pooling)

design variable	reconstructed	as-uploaded	reading
merge weight α	ρ = +0.744 (mean of 4 within-pair ρ)	ρ = +0.206 (mean of 4 within-pair ρ)	alignment rises with the English share of the merged embedding, then plateaus — interior optimum α≈50–75
vocabulary overlap top-K	ρ = +0.994 (mean of 4 within-pair ρ)	ρ = -0.054 (mean of 4 within-pair ρ)	alignment increases monotonically with shared vocabulary; no interaction with merged-vs-trained
model quality (mean NLL)	ρ = -0.743 (p = 2.3e-17, n = 92)	ρ = -0.054 (p = 0.58, n = 111)	better language models align better — the Platonic-Representation prediction, and stronger than the paper's ρ=−0.43
URIEL syntactic distance	ρ = -0.800 (p = 0.2, n = 4)	ρ = -0.800 (p = 0.2, n = 4)	typologically closer to English ⇒ better aligned; same sign as the paper's ρ = −0.64. n = 4, so p can never fall below 0.0833
merged vs trained (paired)	Δ = +0.00019 (Wilcoxon p = 0.846, n = 32 paired cells)	Δ = +0.02275 (Wilcoxon p = 0.000, n = 36 paired cells)	null once tokenization is controlled. Merging preserves alignment exactly as well as joint training — but only because the two arms are nearly the same weights; the as-uploaded Δ is a tokenizer effect (the arms never share a tokenizer.json)

Read the reconstructed column. The as-uploaded column is what the published artefacts actually give you, and for the α and top-K sweeps it is a measurement of a constant.

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1. Method (as reproduced)

• Linear CKA = HSIC(X,Y)/√(HSIC(X,X)·HSIC(Y,Y)), computed in the feature-space form (algebraically identical to the Gram form, O(n·d²)). Invariant to orthogonal transformation and isotropic rescaling.
• X, Y = the same bilingual model's sentence representations of the English side and the L2 side of parallel FLORES-200 devtest text.
• Matched = parallel order. Shuffled control = side A held in order, side B reordered by a single random permutation per language pair, drawn once (seed 42+1000) and applied identically at every layer and for every model, so every B sentence appears exactly once and the control preserves architecture and corpus statistics. The permutations used are stored in shuffle_perms.json. (A fresh permutation per layer would be a strictly weaker control; it was not used.)
• Every layer including the embedding layer: 13 layers (0 = embeddings, 1–12 = transformer blocks).
• Pooling: (i) attention-masked mean; (ii) SGPT position-weighted (Muennighoff et al. 2022) — the paper's strongest for causal LMs and the one quoted below; (iii) token-level word-aligned via SimAlign (bert/bpe, itermax), averaging subword states within each aligned word span.
• Data: FLORES-200 devtest (openlanguagedata/flores_plus), 1012 sentences per language; n = 500 sampled per pair (seed 42) for (i)/(ii), n = 250 for (iii). Tatoeba/OPUS/BouQUET not added — FLORES alone, as in the paper's headline numbers.
• Model quality = mean per-token NLL over the same sentences, both sides, teacher-forced.
• For pooling (iii) the CKA rows are aligned words, not sentences (≈5 400–6 100 word pairs per language pair), so the shuffled control there is a single permutation over those word rows — again drawn once per language pair and applied identically at every layer.

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2. Model inventory

111 models, created 2025-12 under suchirsalhan. Parsed grid:

family	n	grid
baseline	8	4 pairs × {merged, trained} — complete
alpha (-alpha{K}-TOKENWISE_MERGE)	32	4 pairs × α ∈ {10,25,33,50,66,75,90,100} — complete
top-K	64	4 pairs × K ∈ {10,20,25,33,50,66,75,100} × {merged, trained} — complete
alternate naming	7	en_es-top{10,20,66,75}_top…, en_nl-top{25,33,50}_top… — duplicate namings of top-K cells that already exist under <pair>_merge_top{K}-merged-top{K}; excluded from the design tables, still audited

No cells are missing. The 4 × (2 + 8 + 16) grid is full; the 7 extra repos are redundant re-uploads, not new cells.

Adapter audit (adapter_audit.csv)

family	arm	n	exact_identities	max_abs_delta_W	median_frobenius
alpha	merged	32	32	0.000000	0.000000
baseline	merged	4	4	0.000000	0.000000
baseline	trained	4	0	0.002994	0.923666
topk	merged	32	32	0.000000	0.000000
topk	trained	32	0	0.015440	3.618423

delta = B@A, the actual weight change the adapter applies. Every merged arm is an exact no-op.

Tokenizer provenance

pair	family	arm	tokenizer md5 (first 10)
en_el	alpha	merged	0b6e8ebd2f, 377d2055dc
en_el	baseline	merged	0b6e8ebd2f
en_el	baseline	trained	5d785f18bc
en_el	topk	merged	377d2055dc
en_el	topk	trained	bb4c05fbf8
en_es	alpha	merged	248c7914cb, cad7bb89e0
en_es	baseline	merged	cad7bb89e0
en_es	baseline	trained	baba93735d
en_es	topk	merged	248c7914cb
en_es	topk	trained	804273be16
en_nl	alpha	merged	8986b4dd2a, d2a8e7b606
en_nl	baseline	merged	d2a8e7b606
en_nl	baseline	trained	3eb4a951cb
en_nl	topk	merged	8986b4dd2a
en_nl	topk	trained	824f7f899a
en_pl	alpha	merged	ac737037a8, c4295ff30e
en_pl	baseline	merged	ac737037a8
en_pl	baseline	trained	7945a3a515
en_pl	topk	merged	c4295ff30e
en_pl	topk	trained	6e9eb8ff4d

The merged and trained arms never share a tokenizer file. In all four pairs and both families the two arms ship different tokenizer.jsons. Any merged-vs-trained difference measured on the uploaded artefacts is therefore confounded with tokenization: since the merged weights are the untouched base model and the trained weights differ from it by ≤1.5e-2, the tokenizer is the only substantial difference between the arms. The reconstructed configuration removes this confound by giving both arms the same bilingual tokenizer, which is why its merged-vs-trained Δ collapses to ≈0 while the as-uploaded Δ does not.

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3. Results

3.1 reconstructed — last-layer summary by language pair (sgpt pooling)

pair	n_models	matched	shuffled	delta	nll	URIEL_syntax_knn
en–el (Greek, Greek script)	23	0.1660	0.0936	0.0724	8.1286	0.2169
en–es (Spanish)	23	0.2563	0.1023	0.1540	7.4894	0.1784
en–nl (Dutch)	23	0.2470	0.0965	0.1505	7.4796	0.0757
en–pl (Polish)	23	0.2185	0.1075	0.1111	7.8529	0.2136

3.2 as-uploaded — last-layer summary by language pair (sgpt pooling)

pair	n_models	matched	shuffled	delta	nll	URIEL_syntax_knn
en–el (Greek, Greek script)	26	0.1083	0.0878	0.0205	9.8134	0.2169
en–es (Spanish)	30	0.1368	0.0885	0.0483	9.6887	0.1784
en–nl (Dutch)	29	0.1523	0.0930	0.0593	9.5197	0.0757
en–pl (Polish)	26	0.1063	0.0777	0.0286	9.7188	0.2136

3.3 Stage 1 — merged vs trained (the paired baseline contrast)

config	pair	arm	cka_matched	cka_shuffled	delta	nll_mean
as-uploaded	en_el	merged	0.1237	0.0880	0.0358	9.8013
as-uploaded	en_el	trained	0.1239	0.0887	0.0352	9.7972
as-uploaded	en_es	merged	0.1444	0.0879	0.0565	9.2884
as-uploaded	en_es	trained	0.1464	0.0891	0.0573	9.3032
as-uploaded	en_nl	merged	0.1161	0.0871	0.0290	9.1630
as-uploaded	en_nl	trained	0.1169	0.0876	0.0293	9.1845
as-uploaded	en_pl	merged	0.1149	0.0816	0.0333	9.6213
as-uploaded	en_pl	trained	0.1147	0.0815	0.0332	9.6226
reconstructed	en_el	merged	0.1890	0.1040	0.0850	7.9466
reconstructed	en_el	trained	0.1894	0.1045	0.0849	7.9430
reconstructed	en_es	merged	0.2893	0.1059	0.1834	7.4213
reconstructed	en_es	trained	0.2883	0.1069	0.1814	7.4276
reconstructed	en_nl	merged	0.2836	0.1024	0.1812	7.3902
reconstructed	en_nl	trained	0.2821	0.1009	0.1812	7.3868
reconstructed	en_pl	merged	0.2489	0.1152	0.1337	7.7426
reconstructed	en_pl	trained	0.2490	0.1157	0.1333	7.7483

Paired over (pair × top-K × α) cells:

config	pooling	n_pairs	mean_merged	mean_trained	mean_diff_trained_minus_merged	sd_diff	wilcoxon_W	wilcoxon_p	paired_t	t_p
reconstructed	mean	32	0.22267	0.22293	0.00026	0.00087	211.00000	0.33092	1.69668	0.09978
reconstructed	sgpt	32	0.21489	0.21508	0.00019	0.00111	253.00000	0.84646	0.97457	0.33732
reconstructed	word_aligned	4	0.17703	0.17720	0.00017	0.00101	4.00000	0.87500	0.33701	0.75831
as-uploaded	mean	36	0.12202	0.14191	0.01989	0.02230	50.00000	0.00000	5.35093	0.00001
as-uploaded	sgpt	36	0.11995	0.14270	0.02275	0.02792	48.00000	0.00000	4.88960	0.00002
as-uploaded	word_aligned	4	0.13825	0.13825	-0.00000	0.00066	5.00000	1.00000	-0.00171	0.99875

With tokenization controlled, merging preserves cross-lingual alignment exactly as well as joint training. In reconstructed — where both arms use the same bilingual tokenizer and differ only by the uploaded LoRA — the mean trained−merged difference in last-layer matched CKA is +0.00019 (Wilcoxon p = 0.846, paired t p = 0.337, n = 32 paired cells): indistinguishable from zero.

In as-uploaded the same contrast is +0.02275 (Wilcoxon p = 7.1e-07, n = 36) — apparently significant, but this is a tokenizer effect, not a training effect: the two arms never ship the same tokenizer.json (see Tokenizer provenance above), and the merged arm's weights are the untouched base model. Note also that the word-aligned pooling, which reduces both arms to the same aligned word spans, gives −0.00000 for the same comparison — consistent with the difference being tokenization.

Either way this is a null by construction, not a scientific finding about merging: the audit above shows the merged arm is the base model and the trained arm differs from it by ≤1.5e-2 in any weight. A real merged-vs-trained comparison needs the merged embedding tables, which were never uploaded.

3.4 Stage 2 — merge weight α

config	subset	spearman_rho	p_value	n	note
reconstructed	all pairs pooled	0.4195	0.0168	32	sweep points share a base model -> repeated measures; p assumes indepe
reconstructed	within en_el	0.9286	0.0009	8	within-pair sweep; n = sweep points
reconstructed	within en_es	0.5238	0.1827	8	within-pair sweep; n = sweep points
reconstructed	within en_nl	0.7619	0.0280	8	within-pair sweep; n = sweep points
reconstructed	within en_pl	0.7619	0.0280	8	within-pair sweep; n = sweep points
reconstructed	mean of within-pair rho	0.7440		4	average of the per-pair rhos (the repeated-measures-safe summary)
as-uploaded	all pairs pooled	0.0603	0.7429	32	sweep points share a base model -> repeated measures; p assumes indepe
as-uploaded	within en_el	0.4124	0.3100	8	within-pair sweep; n = sweep points
as-uploaded	within en_es	0.4124	0.3100	8	within-pair sweep; n = sweep points
as-uploaded	within en_nl	-0.4124	0.3100	8	within-pair sweep; n = sweep points
as-uploaded	within en_pl	0.4124	0.3100	8	within-pair sweep; n = sweep points
as-uploaded	mean of within-pair rho	0.2062		4	average of the per-pair rhos (the repeated-measures-safe summary)

as-uploaded is degenerate. Distinct last-layer matched-CKA values actually observed along the sweep:

pair	arm	n_points	n_distinct
en_el	merged	8	2
en_es	merged	8	2
en_nl	merged	8	2
en_pl	merged	8	2

Bit-identical CKA means bit-identical models. Seven of the eight en_el-alpha* repos ship tokenizer 377d2055dc and return matched CKA 0.10644523 to eight decimal places; only alpha90, which ships a different tokenizer file (0b6e8ebd2f), differs. The variation in this sweep is tokenizer variation, not merge-weight variation.

Sweep range in last-layer matched CKA:

config	pair	arm	n_points	cka_min	cka_max	cka_range
reconstructed	en_el	merged	8	0.147327	0.190715	0.043388
reconstructed	en_es	merged	8	0.243647	0.289314	0.045667
reconstructed	en_nl	merged	8	0.225677	0.291076	0.065399
reconstructed	en_pl	merged	8	0.185076	0.262211	0.077135
as-uploaded	en_el	merged	8	0.106445	0.123727	0.017282
as-uploaded	en_es	merged	8	0.121622	0.144393	0.022771
as-uploaded	en_nl	merged	8	0.116102	0.146294	0.030191
as-uploaded	en_pl	merged	8	0.103031	0.114875	0.011844

Reconstructed sweep (last-layer matched CKA, sgpt):

alpha	en_el	en_es	en_nl	en_pl
10.0000	0.1473	0.2436	0.2257	0.1851
25.0000	0.1698	0.2590	0.2517	0.1997
33.0000	0.1856	0.2661	0.2583	0.2128
50.0000	0.1892	0.2888	0.2829	0.2489
66.0000	0.1907	0.2852	0.2911	0.2622
75.0000	0.1907	0.2791	0.2889	0.2600
90.0000	0.1907	0.2764	0.2862	0.2553
100.0000	0.1907	0.2732	0.2841	0.2526

Best setting per pair:

pair	arm	argmax	cka_at_argmax	cka_at_min_setting	cka_at_max_setting
en_el	merged	75.0000	0.1907	0.1473	0.1907
en_es	merged	50.0000	0.2893	0.2436	0.2732
en_nl	merged	66.0000	0.2911	0.2257	0.2841
en_pl	merged	66.0000	0.2622	0.1851	0.2526

α is not monotone — there is an interior optimum. Alignment climbs steeply from α=10 to α≈50–75, then flattens or falls slightly toward α=100 (per-pair argmax: en_el=75, en_es=50, en_nl=66, en_pl=66). Spearman is a monotone statistic and understates this; read the curve in figures/alignment_vs_alpha_reconstructed.png. Quote the mean of the four within-pair ρ from the table above, not the pooled p.

3.5 Stage 3 — vocabulary overlap top-K

config	subset	spearman_rho	p_value	n	note
reconstructed	all pairs pooled	0.5486	0.0000	64	sweep points share a base model -> repeated measures; p assumes indepe
reconstructed	within en_el	0.9941	0.0000	16	within-pair sweep; n = sweep points
reconstructed	within en_es	0.9941	0.0000	16	within-pair sweep; n = sweep points
reconstructed	within en_nl	0.9941	0.0000	16	within-pair sweep; n = sweep points
reconstructed	within en_pl	0.9941	0.0000	16	within-pair sweep; n = sweep points
reconstructed	mean of within-pair rho	0.9941		4	average of the per-pair rhos (the repeated-measures-safe summary)
as-uploaded	all pairs pooled	-0.0604	0.6354	64	sweep points share a base model -> repeated measures; p assumes indepe
as-uploaded	within en_el	0.6257	0.0095	16	within-pair sweep; n = sweep points
as-uploaded	within en_es	-0.2528	0.3448	16	within-pair sweep; n = sweep points
as-uploaded	within en_nl	-0.1959	0.4671	16	within-pair sweep; n = sweep points
as-uploaded	within en_pl	-0.3919	0.1333	16	within-pair sweep; n = sweep points
as-uploaded	mean of within-pair rho	-0.0537		4	average of the per-pair rhos (the repeated-measures-safe summary)

as-uploaded is degenerate. Distinct last-layer matched-CKA values actually observed along the sweep:

pair	arm	n_points	n_distinct
en_el	merged	8	1
en_el	trained	8	8
en_es	merged	8	1
en_es	trained	8	8
en_nl	merged	8	1
en_nl	trained	8	8
en_pl	merged	8	1
en_pl	trained	8	8

Bit-identical CKA means bit-identical models. The merged arm returns a single value at every K — all eight repos are the same identity-adapter model with the same tokenizer. The trained arm varies only because its LoRA deltas are non-zero (by ≤1.5e-2 in any weight) and because some cells ship a different tokenizer file.

Sweep range in last-layer matched CKA:

config	pair	arm	n_points	cka_min	cka_max	cka_range
reconstructed	en_el	merged	8	0.135786	0.189002	0.053216
reconstructed	en_el	trained	8	0.136502	0.189351	0.052849
reconstructed	en_es	merged	8	0.205470	0.289314	0.083844
reconstructed	en_es	trained	8	0.208140	0.288274	0.080134
reconstructed	en_nl	merged	8	0.198468	0.283598	0.085131
reconstructed	en_nl	trained	8	0.200621	0.282118	0.081497
reconstructed	en_pl	merged	8	0.187646	0.248883	0.061236
reconstructed	en_pl	trained	8	0.187090	0.248983	0.061893
as-uploaded	en_el	merged	8	0.106445	0.106445	0.000000
as-uploaded	en_el	trained	8	0.102610	0.108030	0.005419
as-uploaded	en_es	merged	8	0.121622	0.121622	0.000000
as-uploaded	en_es	trained	8	0.145946	0.216120	0.070174
as-uploaded	en_nl	merged	8	0.146294	0.146294	0.000000
as-uploaded	en_nl	trained	8	0.170312	0.210925	0.040612
as-uploaded	en_pl	merged	8	0.103031	0.103031	0.000000
as-uploaded	en_pl	trained	8	0.101651	0.116791	0.015140

Reconstructed sweep (last-layer matched CKA, sgpt):

topk	en_el	en_es	en_nl	en_pl
10.0000	0.1361	0.2068	0.1995	0.1874
20.0000	0.1372	0.2230	0.2106	0.1908
25.0000	0.1424	0.2310	0.2126	0.1956
33.0000	0.1499	0.2411	0.2195	0.2068
50.0000	0.1614	0.2576	0.2430	0.2119
66.0000	0.1780	0.2774	0.2607	0.2258
75.0000	0.1819	0.2806	0.2689	0.2323
100.0000	0.1892	0.2888	0.2829	0.2489

Best setting per pair:

pair	arm	argmax	cka_at_argmax	cka_at_min_setting	cka_at_max_setting
en_el	merged	100.0000	0.1890	0.1358	0.1890
en_el	trained	100.0000	0.1894	0.1365	0.1894
en_es	merged	100.0000	0.2893	0.2055	0.2893
en_es	trained	100.0000	0.2883	0.2081	0.2883
en_nl	merged	100.0000	0.2836	0.1985	0.2836
en_nl	trained	100.0000	0.2821	0.2006	0.2821
en_pl	merged	100.0000	0.2489	0.1876	0.2489
en_pl	trained	100.0000	0.2490	0.1871	0.2490

top-K is monotone increasing in every pair and in both arms (within-pair ρ ≈ +0.99; argmax = 100 in 8/8 cells): the more of the L2 vocabulary is merged in, the better the English and L2 representations correspond. No interaction with merged-vs-trained — the two arms' curves sit within ~0.003 CKA of one another at every K.

3.6 Language pair vs URIEL typological distance

design_variable	config	pooling	spearman_rho	p_value	n	note
URIEL syntax_knn vs cka	reconstructed	mean	-0.8000	0.2000	4	n = 4 language pairs; minimum attainable Spearman p at n=4 i
URIEL syntax_knn vs delta	reconstructed	mean	-1.0000	0.0000	4	n = 4 language pairs; minimum attainable Spearman p at n=4 i
URIEL syntax_knn vs cka	reconstructed	sgpt	-0.8000	0.2000	4	n = 4 language pairs; minimum attainable Spearman p at n=4 i
URIEL syntax_knn vs delta	reconstructed	sgpt	-0.8000	0.2000	4	n = 4 language pairs; minimum attainable Spearman p at n=4 i
URIEL syntax_knn vs cka	reconstructed	word_aligned	0.2000	0.8000	4	n = 4 language pairs; minimum attainable Spearman p at n=4 i
URIEL syntax_knn vs delta	reconstructed	word_aligned	0.2000	0.8000	4	n = 4 language pairs; minimum attainable Spearman p at n=4 i
URIEL syntax_knn vs cka	as-uploaded	mean	-1.0000	0.0000	4	n = 4 language pairs; minimum attainable Spearman p at n=4 i
URIEL syntax_knn vs delta	as-uploaded	mean	-1.0000	0.0000	4	n = 4 language pairs; minimum attainable Spearman p at n=4 i
URIEL syntax_knn vs cka	as-uploaded	sgpt	-0.8000	0.2000	4	n = 4 language pairs; minimum attainable Spearman p at n=4 i
URIEL syntax_knn vs delta	as-uploaded	sgpt	-1.0000	0.0000	4	n = 4 language pairs; minimum attainable Spearman p at n=4 i
URIEL syntax_knn vs cka	as-uploaded	word_aligned	0.4000	0.6000	4	n = 4 language pairs; minimum attainable Spearman p at n=4 i
URIEL syntax_knn vs delta	as-uploaded	word_aligned	0.4000	0.6000	4	n = 4 language pairs; minimum attainable Spearman p at n=4 i

URIEL syntax_knn cosine distance from English: nld 0.0757, spa 0.1784, pol 0.2136, ell 0.2169.

n = 4. The smallest p a Spearman ρ can attain at n = 4 is 0.0833, so nothing here can be significant; the rank ordering is the whole content.

3.7 Model quality (mean sentence NLL) vs alignment — the Platonic-Representation test

config	pooling	subset	spearman_rho	p_value	n
reconstructed	mean	all models pooled	-0.7715	0.0000	92
reconstructed	mean	within en_el	-0.8182	0.0000	23
reconstructed	mean	within en_es	-0.6897	0.0003	23
reconstructed	mean	within en_nl	-0.8765	0.0000	23
reconstructed	mean	within en_pl	-0.9585	0.0000	23
reconstructed	sgpt	all models pooled	-0.7429	0.0000	92
reconstructed	sgpt	within en_el	-0.8152	0.0000	23
reconstructed	sgpt	within en_es	-0.7184	0.0001	23
reconstructed	sgpt	within en_nl	-0.8083	0.0000	23
reconstructed	sgpt	within en_pl	-0.9061	0.0000	23
reconstructed	word_aligned	all models pooled	0.0238	0.9554	8
reconstructed	word_aligned	within en_el			2
reconstructed	word_aligned	within en_es			2
reconstructed	word_aligned	within en_nl			2
reconstructed	word_aligned	within en_pl			2
as-uploaded	mean	all models pooled	-0.1301	0.1736	111
as-uploaded	mean	within en_el	-0.0059	0.9771	26
as-uploaded	mean	within en_es	0.5622	0.0012	30
as-uploaded	mean	within en_nl	0.6624	0.0001	29
as-uploaded	mean	within en_pl	0.5051	0.0085	26
as-uploaded	sgpt	all models pooled	-0.0538	0.5752	111
as-uploaded	sgpt	within en_el	-0.2538	0.2109	26
as-uploaded	sgpt	within en_es	0.5912	0.0006	30
as-uploaded	sgpt	within en_nl	0.6658	0.0001	29
as-uploaded	sgpt	within en_pl	0.1895	0.3538	26
as-uploaded	word_aligned	all models pooled	0.4048	0.3199	8
as-uploaded	word_aligned	within en_el			2
as-uploaded	word_aligned	within en_es			2
as-uploaded	word_aligned	within en_nl			2
as-uploaded	word_aligned	within en_pl			2

---

4. Non-independence — how to read the p-values

Every p above is computed as if the rows were independent draws. They are not.

• All 111 uploaded models share one base model (goldfish-models/eng_latn_1000mb); 75 of them are that base model.
• Within a language pair, the α sweep and the top-K sweep are repeated measures on one base model + one tokenizer; they are 8 perturbations of a single object, not 8 samples.
• Within a design cell, merged and trained share the tokenizer and the backbone; the merged/trained comparison is therefore reported paired (Wilcoxon signed-rank and paired t over cells), which is the right test, but the cells themselves are still nested in 4 language pairs.
• The honest effective n for anything that varies across language pairs is 4, not 8/32/104. The mean of within-pair rho rows in correlations.csv are the repeated-measures-safe summary: compute ρ inside each pair, then average the four ρ's. Quote those, not the pooled p.

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5. What ran and what did not

item	status
Model enumeration (111 repos, HF API)	ran
Adapter integrity audit (all 111)	ran → adapter_audit.csv
FLORES-200 devtest, 4 pairs × 1012 sents	ran
Linear CKA, matched + single-permutation shuffled control, all 13 layers	ran
Pooling (i) mean	ran
Pooling (ii) SGPT position-weighted	ran
Pooling (iii) word-aligned (SimAlign)	ran on the 16 stage-1 models (8 as-uploaded + 8 reconstructed), n=250 — cka_layerwise_wordaligned.csv
Stage 1 merged vs trained, 4 pairs	ran
Stage 2 α sweep	ran (as-uploaded: null by construction; reconstructed: real)
Stage 3 top-K sweep	ran (same caveat)
URIEL typological distance (lang2vec syntax_knn, cosine)	ran
Mean sentence NLL per model	ran
Tatoeba / OPUS / BouQUET parallel data	not run — FLORES alone, which is what the paper's headline numbers use
B-GPT jointly-trained upper bound	not run — out of scope for this brief

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6. Files

file	contents
cka_layerwise.csv	model × layer × pooling × {matched, shuffled, Δ}, both configs
cka_lastlayer.csv	last-layer slice of the above
lastlayer_summary.csv	last-layer summary matrix per config × pair × pooling
correlations.csv	one row per design variable × config × pooling × subset
corr_merged_vs_trained.csv	the paired merged/trained contrast
adapter_audit.csv	per-repo LoRA weight-delta audit (the integrity finding)
model_inventory.json	the parsed design grid
uriel_distances.json	URIEL/lang2vec distances from English
shuffle_perms.json	the exact shuffled-control permutations
tables.md	all tables in markdown
figures/	Figure-2 equivalent, per-pair heatmaps, alignment-vs-α, alignment-vs-top-K, CKA-vs-NLL
sweep_flatness.csv	min/max/range of matched CKA along each sweep (the flatness evidence)
sweep_optimum.csv	argmax setting per sweep × pair × arm
lastlayer_matrix_<pair>.csv	the per-language-pair last-layer summary matrix
cka_layerwise_wordaligned.csv	the SimAlign word-aligned pooling run
scripts/	run_cka.py (pipeline), analyse.py, adapter_audit.py, prep_data.py, recon_probe.py, write_report.py, publish.py

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7. What would make this a real result

The design here is good and the reconstruction shows the questions are answerable. What is missing is one file per repo:

1. Upload the merged embedding table. Re-save with modules_to_save=["wte"] (or push the full merged model rather than a PEFT adapter). The tokenwise merge lives entirely in the embeddings; without them the repo carries none of the method.
2. Check lora_B before pushing. lora_B is zero-initialised; 75 of these repos were pushed before any gradient reached it. An assert that max|B| > 0 at save time would have caught all 75.
3. Keep the tokenizer fixed within a design cell. The merged and trained arms currently differ in tokenizer, which confounds the headline comparison the design was built to make. With those, re-running scripts/run_cka.py against the real checkpoints reproduces every table here in about 20 minutes on one GPU.