Mergeability-2/mergebench-property-sweep

MergeBench property sweep

Pre-merge pairwise properties for every mergeable pair in the MergeBench suite (40 checkpoints, 8 base families, 5 domains), computed with the metric panel behind Figure F8 of the Heterogeneous Mergeability project.

Read this before you read a number

MergeBench publishes no pairwise merge. Every merge score in their release (arXiv:2505.10833, Tables 8-17, and the two eval dumps in their GitHub repo) is for a merge of all five domain experts at once, one per base family. In the extracted score table shipped here, merge_arity is 5 in all 576 rows.

Three consequences, and they bound everything downstream:

1. The 80 pairs measured here have no published merge outcome. A pair-level version of F8 cannot be built from MergeBench's numbers.
2. The per-domain panels are therefore n = 8 base families, not n = 80 pairs -- properties averaged over each family's ten pairs against that family's five-expert score. Nearly every cell is struck through, meaning a family-cluster bootstrap cannot separate it from zero after Benjamini-Hochberg. That is the honest reading: at n = 8 these panels mostly do not resolve.
3. QMD-guided has no published counterpart and is absent. Three of F8's four operators do map onto MergeBench methods (Weight Avg = Model soup, Task arithmetic, TIES).

On the per-domain panels: every cell is struck through, and that is the result. At the coverage MergeBench's published outcomes permit (8 base families at best, spanning 2 architectures), no cell survives Benjamini-Hochberg at any sample size reached so far -- see coverage_trend.json for the exact counts per family count, which is the authoritative record rather than any number quoted here. An earlier draft reported 306 cells surviving; all were artefacts of three defects now fixed -- a cluster bootstrap with a 40.2% false-positive rate at n = 4, a saturation gate calibrated on pair-level rather than family-level spread, and testing against zero when the families cluster by architecture. Every cell now carries an exact family-label permutation test (0.0% false positives on noise at n = 4; all 8! = 40,320 relabellings enumerated at n = 8) and the reported p is the maximum of bootstrap, exact t, and permutation. Each cell reports r_arch_metric / r_arch_outcome and an arch_confounded flag; that fraction falls with coverage (21% at n = 4, 6% at n = 6), but dilution of the confound is not the same as acquiring power -- zero cells survive at either. Read table_domain_cells.csv, not the colours.

On the cross-domain consistency number: the naive statistic ("do the domains agree on which property matters?") reads about +0.60 on pure-noise properties, because the eight families' published scores are themselves correlated across domains. Every observed value in table_cross_domain.csv is therefore printed beside a label-permutation null; read excess_over_null, never observed_r alone.

What is genuinely new here

The 80-pair property suite is not derivable from anything MergeBench released, and it resolves structure their five-expert-only outcomes cannot. Example, from the weight-space column qmd_raw on gemma-2-2b: math sits furthest from every other domain (its four largest pairwise distances), while coding-instruction is the closest pair -- a 1.57x spread between the closest and furthest pair. That is a pair-level statement about where in MergeBench the experts actually diverge, and no published MergeBench number can express it.

No merged model was built and no evaluation was run for this dataset. The merge-outcome columns are MergeBench's own published scores, reproduced with provenance.

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RESULTS_MERGEBENCH — the Beetle mergeability suite, over MergeBench

Status: running. This file is rewritten as each base family finishes; the coverage table below says what is on disk right now.

One-line summary. The 40-checkpoint MergeBench suite gives 80 mergeable pairs and we measure the F8 property panel on all of them — but MergeBench publishes no pairwise merge, so the F8 outcome column cannot be formed at the pair level from their numbers. Every score they release is for a merge of all five domain experts at once, one per base family: 8 outcome observations, not 80. The per-domain figures are therefore drawn at n = 8, in F8's own grammar, with the cells that a family-cluster bootstrap cannot separate from zero struck through — which is nearly all of them. That is the result, and it is a statement about the available outcomes, not about the properties.

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1. What MergeBench actually publishes

Enumerated from the Hub (python -m mergeschool.mergebench.suite, not a hand-written list) and from their code and paper. 40 models = 8 base families × 5 domains:

family	pretrained parent	GB	pairs
gemma-2-2b	google/gemma-2-2b	26.3	10
gemma-2-2b-it	google/gemma-2-2b-it	26.3	10
Llama-3.2-3B	meta-llama/Llama-3.2-3B	32.2	10
Llama-3.2-3B-Instruct	meta-llama/Llama-3.2-3B-Instruct	32.2	10
Llama-3.1-8B	meta-llama/Llama-3.1-8B	80.4	10
Llama-3.1-8B-Instruct	meta-llama/Llama-3.1-8B-Instruct	80.4	10
gemma-2-9b	google/gemma-2-9b	92.6	10
gemma-2-9b-it	google/gemma-2-9b-it	92.6	10
total		463.1	80

Cross-family pairs are not mergeable (different tokenizers and widths), so 80 within-family pairs is the whole population.

The outcome numbers, and the gap

Searched, in this order: the HF org (models, datasets, spaces), the model cards, the GitHub repo uiuctml/MergeBench, the project page, and the paper (arXiv:2505.10833, NeurIPS 2025 D&B).

source	what it contains	machine-readable?
HF org MergeBench	40 expert checkpoints + 5 *_val datasets (prompt/response, 1000 rows each). Model cards are auto-generated stubs with no numbers.	n/a
GitHub uiuctml/MergeBench	merged_models/ holds eval dumps for exactly 2 merged models (Llama-3.1-8B, Llama-3.2-3B), 1 method (RegMean++), 1 configuration (all five experts). Plus the merging code and eval scripts.	yes, 8 JSON files
Project page	figures only, no data files	no
Paper Tables 10–17	per-domain scores, 9 methods × 8 families × 5 domains = 360 cells	extracted to CSV, see below
Paper Tables 8–9	average normalised multi-task / generalisation performance, 9 × 8	extracted

Extracted to results/mergebench/mergebench_published_scores.csv (576 rows; family, task, method, score, merge_arity, source).

The blocking fact: merge_arity is 5 in every published row. There is not one two-expert merge in the MergeBench release. Consequences:

1. No pair-level outcome. The 80 pairs whose properties we measure have no published score. F8 at the pair level (n = 613 in the Beetle paper) cannot be reproduced from their numbers.
2. The largest unit their numbers support is the family: properties averaged over the family's ten pairs, outcome = that family's five-expert merge score. n = 8.
3. Operator coverage is partial. Three of F8's four operators have a published counterpart — Weight Avg = Model soup, Task arithmetic, TIES. QMD-guided does not exist in MergeBench and is absent from these figures; it is ours, and scoring it needs merges and evaluations. The other six published methods (DARE, Fisher, RegMean, Consensus TA, Dataless L&S, L&S) are drawn as extra operator rows since they cost nothing.

Per the standing instruction, no merged model was built and no evaluation was run. The fallback that would fix this — merging all 80 pairs and scoring them on the five *_val sets — is ~1.5–3 days of GPU and was explicitly ruled out. It remains the only way to get the pair-level figure.

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2. What we compute ourselves: the property panel

src/mergeschool/mergebench/sweep.py, reusing the Beetle implementations rather than restating them:

F8 family	columns	implementation reused
weight space	weight_cosine, subspace_overlap, spectral_overcounting, qmd_raw	controlled.emit._predict, core.metrics.{subspace_overlap,spectral_overcounting,quotient_weight_distance}
representation	geo_cka_mean, geo_procrustes_mean, geo_subspace_overlap_mean, geo_svcca_mean, geo_cka_late_minus_early	controlled.bridge_sweep.geometry_block
retrieval	ret_identity_p_at_1, ret_procrustes_p_at_1, ret_ridge_p_at_1, ret_gain_over_identity	controlled.bridge_sweep.retrieval_block
gradient	grad_cosine, grad_l2, grad_norm_ratio, grad_cosine_layer_min	controlled.bridge_sweep.gradient_block (recomputed from a per-layer cache — same estimator)
behaviour	beh_js, beh_logit_cosine, beh_topk_overlap, beh_rank_corr, beh_entropy_gap	controlled.bridge_sweep.behaviour_block

The one edit to shared code is backwards-compatible: bridge_sweep._forward / _grads gained an optional probe= argument (default unchanged), so the extended probe below reuses them verbatim.

Deliberate deviations, and why

• coord_fraction / qmd / coordinate_gap are NaN, by construction. All five experts of a family are fine-tunes of ONE pretrained checkpoint. No permutation symmetry was ever broken between them, so the aligning map is the identity and the coordinate component of QMD is zero a priori. There is nothing to search. qmd_raw is still measured (streamed over the safetensors, so a 9B family never materialises a 37 GB float32 state dict). The reason is written into the notes column of every row rather than left as a blank cell.
• Randomized top-k SVD for the two spectral weight columns. metrics.subspace_overlap and metrics.spectral_overcounting use only the top k=10 singular subspace but get it from a full np.linalg.svd. On Beetle that was 50k × 768; here it is up to 256k × 4096, eighty times over. sweep.spectral_pair computes the same top-k subspace with a GPU range finder; tests/test_mergebench_spectral.py checks it against the exact numpy estimator.
• bfloat16 backward. A 9B model with fp32 parameters and fp32 gradients does not fit an 80 GB card. Dot products are accumulated in float32; the only cost is per-element rounding, uncorrelated across ~8e9 elements.
• n/d, which bites here. The canonical F8 probe is 32 sentences and the Beetle models were d = 768. MergeBench models are d = 2304–4096, so the identical protocol now solves a d-dimensional geometry from 32 observations. The geo_*/ret_* columns are therefore reported twice: on the canonical 32-sentence probe (geo_*, protocol identical to F8 — used in the figures) and on a 512-sentence extended probe (geoX_*/retX_*, the honest estimate at this width). Both are in results/mergebench/pair_metrics.csv.

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3. Coverage — what has actually run

Property sweep launched 2026-08-26 17:45 UTC, detached (setsid, ppid 1), GPUs 4 and 5, two workers, families smallest-first, ledger-resumable (results/mergebench/ledger_w*.json).

worker	GPU	families, in order
0	4	gemma-2-2b, Llama-3.2-3B, Llama-3.1-8B, gemma-2-9b
1	5	gemma-2-2b-it, Llama-3.2-3B-Instruct, Llama-3.1-8B-Instruct, gemma-2-9b-it

Streaming: each family is downloaded, measured, then its weights are deleted before the next, so peak disk is one family per worker (~93 GB worst case, the gemma-9b group) against the shared 350 GB floor. Timing is dominated by CPU contention, not GPU — the box is at load ~380 on 128 cores and GPU utilisation during measurement is near zero. First model measured in 553 s; ~50 min per 2B family, ~2.5 h projected for a 9B one, so ~6-7 h per worker.

Measured so far: 8 of 8 families, 80 of 80 pairs, 23 of 28 F8 columns populated (coord_fraction is NaN by construction, see above).

family	pairs	status	wall clock
gemma-2-2b	10	done	21 min
gemma-2-2b-it	10	done	22 min
Llama-3.2-3B	10	done	30 min
Llama-3.2-3B-Instruct	10	done	30 min
Llama-3.1-8B	10	done	79 min
Llama-3.1-8B-Instruct	10	done	87 min
gemma-2-9b	10	done	112 min
gemma-2-9b-it	10	done	93 min

Outcome-joined panel: 0 of 1035 cells survive Benjamini-Hochberg at n = 8 families.

Cross-domain agreement: observed +0.62 against a label-permutation null of +0.51 (95% +0.12 to +0.81), p = 0.285.

4. Figures

figure	what it shows	needs
figures/mergebench/F8MB_properties_<family>.png	the property panel itself: this family's ten expert pairs x the F8 columns, z-scored within the family. No outcome column, so it is drawable the moment one family finishes.	1 family
figures/mergebench/F8MB_<domain>.png	F8 for one domain: 9 published operators x the F8 columns, cell = Pearson r between the family-mean property and MergeBench's published score for that family's five-expert merge	>=4 families
figures/mergebench/F8MB_by_domain.png	all five domains stacked, one panel each, shared colour scale — the per-domain deliverable	>=4 families
figures/mergebench/F8MB_cross_domain.png	(a) agreement between each pair of domains' r-vectors; (b) the properties that move most between domains, red where they change sign — the consistency/divergence claim	>=4 families

Every cell that a family-cluster bootstrap cannot separate from zero after Benjamini-Hochberg is struck through, exactly as in F8. At n = 8 that will be nearly all of them, and that is the point: the panel shows in its own grammar that MergeBench's published outcomes cannot resolve the property panel, rather than asserting it in prose.

A trap in the cross-domain claim, and the null that defuses it

The obvious way to state "do the domains agree on which property matters?" is to correlate each domain's $r$-vector with every other's and report the mean off-diagonal. On pure-noise properties that number is +0.60. It is an artefact: the eight families' published scores are strongly correlated across domains — gemma-2-9b-it merges well in every domain, Llama-3.2-3B badly in every domain — so any fixed property vector yields a similar $r$ in all five domains whether or not it predicts anything at all. Reported against zero, the headline consistency claim would be vacuous.

panel.cross_domain_null therefore permutes the family labels of the design matrix — breaking the property/outcome link while leaving both the property correlation structure and the cross-domain outcome structure intact — and rebuilds the agreement 400 times. The reportable quantity is the observed agreement in excess of that null, not in excess of zero, and the figure's footer prints the null mean, its 95% interval and the permutation $p$ alongside the observed value. Verified on synthetic noise: observed +0.60 against null +0.54 (95% +0.37 to +0.68), $p = 0.22$ — correctly a non-finding.

4b. Tables

Every figure above has a machine-readable CSV under results/mergebench/ and a rendered copy here, regenerated after each family so the two can never drift apart. Columns that are NaN by construction keep their column and carry the reason in a __status field rather than being dropped — a reader has to see that the metric was considered.

table	CSV	what it is
T1 per-pair properties	table_pairs.csv	one row per (family, domain_a, domain_b), one column per metric — the genuinely new artefact
T2 per-family	table_family.csv	properties averaged over each family's ten pairs, joined to its published five-expert score per domain and method
T3 per-domain cells	table_domain_cells.csv	the F8 heatmaps as numbers: r, bootstrap interval, p, BH q, survived
T4 cross-domain	table_cross_domain.csv	each domain pair's agreement with its permutation null alongside
T5 published scores	mergebench_published_scores.csv	MergeBench's own 576 rows, merge_arity = 5 throughout
T6 coverage	table_coverage_families.csv, table_coverage_metrics.csv	what ran, what did not, per family and per metric, with reasons

Table 1 — per-pair properties (the new artefact)

Table 1 — per-pair property table (80 of 80 pairs, 27 live metric columns). Full precision and the by-construction columns are in results/mergebench/table_pairs.csv.

family	domain_a	domain_b	weight_cosine	qmd_raw	subspace_overlap	spectral_overcounting	geo_cka_mean	geo_procrustes_mean	geo_subspace_overlap_mean	geo_svcca_mean	geo_cka_late_minus_early	ret_identity_p_at_1	ret_procrustes_p_at_1	ret_ridge_p_at_1	ret_gain_over_identity	grad_cosine	grad_l2	grad_norm_ratio	grad_cosine_layer_min	beh_js	beh_logit_cosine	beh_topk_overlap	beh_rank_corr	beh_entropy_gap	tv_cosine	tv_norm_ratio	tv_qmd_raw	tv_subspace_overlap	tv_spectral_overcounting
Llama-3.1-8B	coding	instruction	0.9994	0.0324	0.9999	-1.0000	0.9989	0.0006	0.9007	0.9890	-0.0125	1.0000	0.3077	0.2308	-0.6923	0.8647	739.3298	0.9405	0.6458	0.0737	0.9682	0.7156	0.9604	-0.7186	0.0258	0.2248	2.1496	0.6701	-12.4150
Llama-3.1-8B	coding	math	0.9979	0.0550	0.9996	-1.0000	0.9988	0.0008	0.8527	0.9885	-0.0156	1.0000	0.1538	0.1538	-0.8462	0.8987	649.8523	0.8149	0.6782	0.0886	0.9407	0.6656	0.9367	-0.7077	0.0257	0.6952	1.4430	0.3977	-2.8502
Llama-3.1-8B	coding	multilingual	0.9994	0.0318	0.9998	-1.0000	0.9978	0.0011	0.9065	0.9880	-0.0213	1.0000	0.2308	0.2308	-0.7692	0.8429	783.8639	0.8209	0.6375	0.0996	0.9626	0.7031	0.9524	-1.0192	0.0118	0.0841	3.4580	0.3725	-77.5586
Llama-3.1-8B	coding	safety	0.9985	0.0513	0.9999	-1.0000	0.9984	0.0010	0.8604	0.9859	-0.0191	1.0000	0.2308	0.3077	-0.7692	0.8654	821.9614	0.8883	0.6076	0.1043	0.9350	0.6938	0.9244	-1.0015	0.0292	0.7692	1.4181	0.6881	-1.0127
Llama-3.1-8B	instruction	math	0.9984	0.0462	0.9996	-1.0000	0.9983	0.0011	0.8262	0.9889	-0.0171	1.0000	0.2308	0.2308	-0.7692	0.8298	765.5426	0.8665	0.5160	0.0912	0.9473	0.6406	0.9423	0.0109	0.0085	0.1563	2.5567	0.3660	-28.3108
Llama-3.1-8B	instruction	multilingual	1.0000	0.0076	0.9999	-1.0000	0.9992	0.0005	0.9610	0.9948	-0.0057	1.0000	0.2308	0.2308	-0.7692	0.9489	444.4657	0.8729	0.8092	0.0332	0.9878	0.7969	0.9816	-0.3006	0.0151	0.3738	1.7374	0.3807	-11.2205
Llama-3.1-8B	instruction	safety	0.9991	0.0415	0.9997	-1.0000	0.9975	0.0014	0.8533	0.9887	-0.0220	1.0000	0.3077	0.3077	-0.6923	0.8022	979.6973	0.8354	0.4104	0.0716	0.9273	0.7406	0.9307	-0.2829	0.0540	0.1730	2.4180	0.8128	-16.2163
Llama-3.1-8B	math	multilingual	0.9984	0.0457	0.9996	-1.0000	0.9976	0.0013	0.8396	0.9884	-0.0212	1.0000	0.2308	0.2308	-0.7692	0.8339	686.1420	0.9926	0.4583	0.0958	0.9542	0.6312	0.9389	-0.3116	0.0066	0.0584	4.1423	0.3028	-65.7838
Llama-3.1-8B	math	safety	0.9975	0.0606	0.9996	-1.0000	0.9977	0.0015	0.8027	0.9899	-0.0290	1.0000	0.3077	0.3077	-0.6923	0.8124	966.3836	0.7239	0.4956	0.1132	0.9127	0.6000	0.9310	-0.2938	0.0298	0.9038	1.3967	0.4659	-2.0656
Llama-3.1-8B	multilingual	safety	0.9991	0.0413	0.9998	-1.0000	0.9958	0.0023	0.8477	0.9890	-0.0344	1.0000	0.3077	0.3077	-0.6923	0.7559	1073.6201	0.7293	0.1916	0.0804	0.9191	0.6937	0.9191	0.0177	0.0137	0.0647	3.9375	0.3839	-69.5391
Llama-3.1-8B-Instruct	coding	instruction	0.9994	0.0333	0.9998	-1.0000	0.9992	0.0006	0.9068	0.9905	-0.0113	1.0000	0.2308	0.3077	-0.7692	0.9569	802.0401	0.9858	0.6416	0.0707	0.9090	0.7250	0.9362	-0.6369	0.0252	0.2279	2.1366	0.6661	-12.4543
Llama-3.1-8B-Instruct	coding	math	0.9971	0.0662	0.9994	-0.9999	0.9986	0.0010	0.8384	0.9831	-0.0227	1.0000	0.2308	0.2308	-0.7692	0.9494	934.0776	0.8191	0.6566	0.1145	0.8735	0.6344	0.9174	-1.1547	0.0243	0.5597	1.5158	0.4038	-3.8183
Llama-3.1-8B-Instruct	coding	multilingual	0.9994	0.0327	0.9998	-1.0000	0.9992	0.0005	0.9196	0.9898	-0.0141	1.0000	0.2308	0.2308	-0.7692	0.9705	671.0683	0.9326	0.7593	0.0983	0.9071	0.7063	0.9437	-1.4056	0.0365	0.0833	3.4663	0.3616	-75.4804
Llama-3.1-8B-Instruct	coding	safety	0.9985	0.0515	0.9998	-1.0000	0.9987	0.0008	0.8596	0.9879	-0.0196	1.0000	0.2308	0.2308	-0.7692	0.9636	834.0918	0.9029	0.6304	0.1123	0.9058	0.6656	0.9346	-1.1089	0.0463	0.7903	1.4011	0.6833	-1.0040
Llama-3.1-8B-Instruct	instruction	math	0.9977	0.0587	0.9993	-0.9999	0.9985	0.0015	0.8137	0.9839	-0.0227	1.0000	0.2308	0.2308	-0.7692	0.9214	1080.9481	0.8309	0.5357	0.0943	0.8298	0.6531	0.9302	-0.5178	0.0099	0.1276	2.8190	0.3864	-36.0854
Llama-3.1-8B-Instruct	instruction	multilingual	1.0000	0.0079	0.9999	-1.0000	0.9995	0.0003	0.9608	0.9955	-0.0068	1.0000	0.3077	0.2308	-0.6923	0.9818	523.8183	0.9460	0.8238	0.0297	0.9825	0.8375	0.9848	-0.7686	0.0244	0.3655	1.7472	0.3709	-12.6743
Llama-3.1-8B-Instruct	instruction	safety	0.9991	0.0416	0.9999	-1.0000	0.9988	0.0009	0.8615	0.9905	-0.0162	1.0000	0.1538	0.2308	-0.8462	0.9606	872.1363	0.8901	0.6032	0.0691	0.9041	0.7406	0.9162	-0.4720	0.0571	0.1801	2.3702	0.8253	-16.3082
Llama-3.1-8B-Instruct	math	multilingual	0.9977	0.0584	0.9994	-0.9999	0.9986	0.0012	0.8379	0.9867	-0.0200	1.0000	0.1538	0.2308	-0.8462	0.9433	866.8348	0.8784	0.6307	0.0840	0.8310	0.6281	0.9340	-0.2509	0.0118	0.0466	4.6336	0.2991	-67.9712
Llama-3.1-8B-Instruct	math	safety	0.9968	0.0705	0.9994	-0.9999	0.9978	0.0016	0.7879	0.9821	-0.0359	1.0000	0.2308	0.2308	-0.7692	0.9314	1252.2745	0.7396	0.5630	0.1221	0.8445	0.5594	0.8987	0.0458	0.0276	0.7083	1.4370	0.4882	-2.8125
Llama-3.1-8B-Instruct	multilingual	safety	0.9991	0.0414	0.9998	-1.0000	0.9987	0.0009	0.8675	0.9878	-0.0188	1.0000	0.2308	0.2308	-0.7692	0.9662	871.1604	0.8420	0.6596	0.0728	0.9138	0.6844	0.9374	0.2966	0.0270	0.0658	3.8990	0.3737	-64.7395
Llama-3.2-3B	coding	instruction	0.9999	0.0111	0.9968	-0.9999	0.9997	0.0003	0.9573	0.9935	-0.0032	1.0000	0.2308	0.3077	-0.7692	0.9632	303.7838	0.8775	0.8791	0.0222	0.9565	0.8375	0.9840	0.0283	0.0373	0.6040	1.4782	—	—
Llama-3.2-3B	coding	math	—	0.0163	—	—	0.9994	0.0004	0.9627	0.9968	-0.0073	1.0000	0.2308	0.2308	-0.7692	0.9541	283.0928	0.9612	0.9082	—	—	—	—	—	0.0251	0.3806	1.7198	—	—
Llama-3.2-3B	coding	multilingual	0.9998	0.0084	0.9888	-0.9986	0.9996	0.0002	0.9578	0.9969	-0.0023	1.0000	0.2308	0.3077	-0.7692	0.9558	322.1229	0.8864	0.8430	0.0560	0.9223	0.7125	0.9806	-0.2187	0.0044	0.9691	1.4114	—	—
Llama-3.2-3B	coding	safety	0.9999	0.0104	0.9966	-0.9999	0.9996	0.0003	0.9700	0.9962	-0.0029	1.0000	0.3077	0.3077	-0.6923	0.9799	195.4542	0.9660	0.9403	0.0363	0.9563	0.8156	0.9789	-0.8469	0.0471	0.6577	1.4436	—	—
Llama-3.2-3B	instruction	math	—	0.0181	—	—	0.9991	0.0004	0.9271	0.9901	-0.0127	1.0000	0.2308	0.2308	-0.7692	0.9104	451.3517	0.8434	0.8095	—	—	—	—	—	0.0063	0.6302	1.4847	—	—
Llama-3.2-3B	instruction	multilingual	0.9998	0.0114	0.9880	-0.9986	0.9995	0.0004	0.9353	0.9937	-0.0049	1.0000	0.3077	0.3077	-0.6923	0.9390	374.3725	0.9899	0.8324	0.0646	0.9654	0.6906	0.9755	-0.2471	0.0070	0.6233	1.4878	—	—
Llama-3.2-3B	instruction	safety	0.9999	0.0124	0.9976	-1.0000	0.9996	0.0002	0.9590	0.9951	-0.0049	1.0000	0.3077	0.3077	-0.6923	0.9550	323.3440	0.9084	0.8745	0.0329	0.9110	0.8313	0.9733	-0.8752	0.1088	0.9184	1.3378	—	—
Llama-3.2-3B	math	multilingual	—	0.0165	—	—	0.9992	0.0004	0.9501	0.9960	-0.0094	1.0000	0.3077	0.3077	-0.6923	0.9317	396.5653	0.8520	0.7833	—	—	—	—	—	0.0010	0.3928	1.7137	—	—
Llama-3.2-3B	math	safety	—	0.0177	—	—	0.9992	0.0004	0.9436	0.9943	-0.0108	1.0000	0.3846	0.3077	-0.6154	0.9447	321.1809	0.9285	0.8663	—	—	—	—	—	0.0086	0.5788	1.5131	—	—
Llama-3.2-3B	multilingual	safety	0.9998	0.0107	0.9864	-0.9985	0.9996	0.0003	0.9421	0.9965	-0.0033	1.0000	0.3077	0.3077	-0.6923	0.9531	324.9515	0.9177	0.8294	0.0456	0.8425	0.7344	0.9761	-0.6282	0.0040	0.6786	1.4643	—	—
Llama-3.2-3B-Instruct	coding	instruction	—	0.0101	—	—	0.9997	0.0002	0.9672	0.9969	-0.0040	1.0000	0.3846	0.3077	-0.6154	0.9823	263.3184	0.9182	0.9533	—	—	—	—	—	0.0295	0.7411	1.4253	—	—
Llama-3.2-3B-Instruct	coding	math	—	0.0162	—	—	0.9995	0.0002	0.9703	0.9976	-0.0088	1.0000	0.3846	0.3846	-0.6154	0.9774	258.4537	0.9893	0.9222	—	—	—	—	—	0.0262	0.4043	1.6809	—	—
Llama-3.2-3B-Instruct	coding	multilingual	0.9994	0.0086	0.9864	-0.9979	0.9995	0.0006	0.9643	0.9952	-0.0062	1.0000	0.3077	0.3846	-0.6923	0.9777	295.4498	0.9107	0.9275	0.0525	0.8312	0.7031	0.9740	-0.0107	0.0057	0.9925	1.4102	—	—
Llama-3.2-3B-Instruct	coding	safety	0.9999	0.0111	0.9958	-0.9998	0.9996	0.0002	0.9768	0.9961	-0.0038	1.0000	0.3846	0.3846	-0.6154	0.9891	192.3297	0.9575	0.9481	0.0276	0.9703	0.8156	0.9772	-0.5952	0.0510	0.6394	1.4496	—	—
Llama-3.2-3B-Instruct	instruction	math	—	0.0172	—	—	0.9993	0.0003	0.9501	0.9958	-0.0162	1.0000	0.3077	0.3846	-0.6923	0.9515	413.0838	0.9084	0.8901	—	—	—	—	—	0.0040	0.5454	1.5397	—	—
Llama-3.2-3B-Instruct	instruction	multilingual	—	0.0103	—	—	0.9996	0.0003	0.9658	0.9962	-0.0059	1.0000	0.3846	0.3846	-0.6154	0.9805	263.7616	0.9918	0.9374	—	—	—	—	—	0.0073	0.7468	1.4392	—	—
Llama-3.2-3B-Instruct	instruction	safety	—	0.0120	—	—	0.9996	0.0003	0.9704	0.9953	-0.0033	1.0000	0.3846	0.3846	-0.6154	0.9849	232.9386	0.9590	0.9530	—	—	—	—	—	0.1007	0.8627	1.3493	—	—
Llama-3.2-3B-Instruct	math	multilingual	—	0.0163	—	—	0.9993	0.0004	0.9510	0.9950	-0.0101	1.0000	0.3077	0.3846	-0.6923	0.9510	419.9223	0.9009	0.8677	—	—	—	—	—	0.0013	0.4073	1.6911	—	—
Llama-3.2-3B-Instruct	math	safety	—	0.0178	—	—	0.9992	0.0003	0.9612	0.9962	-0.0126	1.0000	0.3846	0.3846	-0.6154	0.9678	322.0370	0.9472	0.9062	—	—	—	—	—	0.0104	0.6323	1.4809	—	—
Llama-3.2-3B-Instruct	multilingual	safety	0.9994	0.0113	0.9888	-0.9979	0.9995	0.0006	0.9627	0.9934	-0.0070	1.0000	0.3846	0.3846	-0.6154	0.9766	290.2222	0.9512	0.8982	0.0467	0.8532	0.7375	0.9786	-0.5845	0.0044	0.6442	1.4791	—	—
gemma-2-2b	coding	instruction	1.0000	0.0081	1.0000	-1.0000	0.9944	0.0013	0.9511	0.9997	-0.0417	1.0000	0.4615	0.6154	-0.5385	0.8838	1038.9704	0.8526	0.7595	0.0305	0.9043	0.8125	0.9267	0.1534	0.1272	0.9348	1.3229	0.4485	-0.6621
gemma-2-2b	coding	math	1.0000	0.0108	1.0000	-1.0000	0.9949	0.0012	0.9566	0.9997	-0.0435	1.0000	0.7692	0.6154	-0.2308	0.9239	724.2037	0.9003	0.8605	0.0337	0.8425	0.8344	0.9625	-0.7151	0.0600	0.6332	1.4466	0.1660	-0.3039
gemma-2-2b	coding	multilingual	1.0000	0.0103	0.9999	-1.0000	0.9941	0.0015	0.9306	0.9996	-0.0427	1.0000	0.6154	0.6154	-0.3846	0.8734	965.7394	0.9719	0.8112	0.0475	0.8778	0.7656	0.9456	0.1090	0.1054	0.6602	1.4014	0.1742	-0.4909
gemma-2-2b	coding	safety	1.0000	0.0094	1.0000	-1.0000	0.9960	0.0010	0.9543	0.9995	-0.0341	1.0000	0.6154	0.6154	-0.3846	0.9079	808.7325	0.9947	0.7669	0.0409	0.7387	0.8125	0.9513	-0.6193	0.1399	0.7329	1.3482	0.5173	-0.5865
gemma-2-2b	instruction	math	1.0000	0.0111	1.0000	-1.0000	0.9913	0.0019	0.9443	0.9987	-0.0754	1.0000	0.5385	0.6154	-0.4615	0.8420	1206.6298	0.7676	0.6027	0.0512	0.7608	0.8250	0.9426	-0.8685	0.0512	0.6773	1.4322	0.1501	-0.7566
gemma-2-2b	instruction	multilingual	1.0000	0.0105	0.9999	-1.0000	0.9922	0.0019	0.9371	0.9997	-0.0520	1.0000	0.4615	0.6154	-0.5385	0.8672	1103.3959	0.8772	0.7601	0.0450	0.9146	0.8000	0.9260	-0.0445	0.0955	0.7063	1.3896	0.2731	-1.6253
gemma-2-2b	instruction	safety	1.0000	0.0095	1.0000	-1.0000	0.9941	0.0013	0.9569	0.9991	-0.0403	1.0000	0.5385	0.5385	-0.4615	0.8628	1120.7658	0.8481	0.6765	0.0474	0.6132	0.8344	0.9382	-0.7727	0.1512	0.7841	1.3256	0.6506	-1.1298
gemma-2-2b	math	multilingual	1.0000	0.0128	0.9999	-1.0000	0.9887	0.0029	0.9250	0.9991	-0.0987	1.0000	0.3846	0.6154	-0.6154	0.8422	1049.7917	0.8750	0.6652	0.0657	0.6873	0.7781	0.9412	0.8241	0.0394	0.9590	1.3867	0.0644	-0.7926
gemma-2-2b	math	safety	1.0000	0.0122	1.0000	-1.0000	0.9946	0.0013	0.9606	0.9997	-0.0471	1.0000	0.6923	0.5385	-0.3077	0.9022	810.6756	0.9051	0.7693	0.0312	0.9116	0.8187	0.9674	0.0958	0.0429	0.8639	1.3913	0.1921	-0.5041
gemma-2-2b	multilingual	safety	1.0000	0.0114	0.9999	-1.0000	0.9914	0.0022	0.9258	0.9987	-0.0607	1.0000	0.6923	0.5385	-0.3077	0.8533	1037.3324	0.9668	0.6795	0.0643	0.5622	0.7719	0.9296	-0.7282	0.1257	0.9008	1.3265	0.3048	-0.4558
gemma-2-2b-it	coding	instruction	1.0000	0.0083	1.0000	-1.0000	0.9956	0.0011	0.9501	0.9997	-0.0359	1.0000	0.4615	0.3077	-0.5385	0.9027	2273.1784	0.7312	0.8510	0.0543	0.4034	0.7406	0.9381	0.3512	0.0430	0.9552	1.3842	0.4138	-0.6189
gemma-2-2b-it	coding	math	1.0000	0.0114	1.0000	-1.0000	0.9979	0.0006	0.9688	0.9997	-0.0098	1.0000	0.3846	0.3846	-0.6154	0.9488	1178.6246	0.8586	0.9375	0.0342	0.9498	0.8094	0.9534	-0.3964	0.0091	0.5975	1.5010	0.0879	-0.1798
gemma-2-2b-it	coding	multilingual	1.0000	0.0109	0.9999	-1.0000	0.9939	0.0017	0.9342	0.9993	-0.0530	1.0000	0.2308	0.5385	-0.7692	0.8988	1705.1278	0.9244	0.8726	0.0820	0.3638	0.6875	0.9229	-0.1083	0.0482	0.6225	1.4603	0.1580	-0.3911
gemma-2-2b-it	coding	safety	1.0000	0.0098	1.0000	-1.0000	0.9970	0.0008	0.9605	0.9996	-0.0268	1.0000	0.5385	0.4615	-0.4615	0.9484	1138.1791	0.9420	0.9216	0.0654	0.8770	0.7500	0.9604	-0.3838	0.0760	0.7078	1.4031	0.4527	-0.3915
gemma-2-2b-it	instruction	math	1.0000	0.0116	1.0000	-1.0000	0.9960	0.0011	0.9473	0.9996	-0.0280	1.0000	0.5385	0.3077	-0.4615	0.8948	2552.8612	0.6279	0.8476	0.0607	0.2654	0.7344	0.9592	-0.7476	0.0013	0.6256	1.4905	0.0724	-0.5478
gemma-2-2b-it	instruction	multilingual	1.0000	0.0111	0.9999	-1.0000	0.9943	0.0017	0.9275	0.9991	-0.0265	1.0000	0.1538	0.5385	-0.8462	0.9465	1757.7967	0.7911	0.8876	0.0939	0.9437	0.6438	0.9295	-0.4595	0.0390	0.6517	1.4519	0.2727	-2.1817
gemma-2-2b-it	instruction	safety	1.0000	0.0099	1.0000	-1.0000	0.9958	0.0011	0.9461	0.9993	-0.0310	1.0000	0.4615	0.3846	-0.5385	0.9253	2193.5266	0.6888	0.8481	0.0786	0.0261	0.7687	0.9390	-0.7349	0.0838	0.7411	1.3867	0.6413	-1.2401
gemma-2-2b-it	math	multilingual	0.9999	0.0136	0.9999	-1.0000	0.9925	0.0023	0.9305	0.9993	-0.0439	1.0000	0.3846	0.4615	-0.6154	0.8892	1815.0027	0.7937	0.8584	0.0703	0.2354	0.7063	0.9389	0.2881	0.0046	0.9598	1.4115	0.0633	-0.6236
gemma-2-2b-it	math	safety	1.0000	0.0129	1.0000	-1.0000	0.9970	0.0009	0.9543	0.9995	-0.0195	1.0000	0.6154	0.4615	-0.3846	0.9536	1027.6031	0.9115	0.9097	0.0518	0.9296	0.7500	0.9554	0.0126	0.0051	0.8442	1.4208	0.1068	-0.3492
gemma-2-2b-it	multilingual	safety	1.0000	0.0120	0.9999	-1.0000	0.9923	0.0021	0.9250	0.9997	-0.0524	1.0000	0.5385	0.3077	-0.4615	0.9192	1540.8322	0.8708	0.8519	0.1039	0.0005	0.6594	0.9249	-0.2755	0.0854	0.8795	1.3586	0.2781	-0.4753
gemma-2-9b	coding	instruction	0.9999	0.0341	0.9994	-0.9999	0.9613	0.0077	0.8149	0.9982	-0.3308	1.0000	0.4615	0.3077	-0.5385	0.6478	2035.5124	0.8584	0.4237	0.0832	0.6950	0.6906	0.8838	0.1440	0.0403	0.2065	2.2289	0.3376	-3.2230
gemma-2-9b	coding	math	0.9980	0.0727	0.9832	-0.9978	0.9653	0.0070	0.7357	0.9986	-0.0316	1.0000	0.3077	0.3846	-0.6923	0.6437	1996.6835	0.5193	0.5158	0.1524	0.7186	0.5781	0.8475	-0.7991	0.0361	0.5131	1.5459	0.2411	-0.6293
gemma-2-9b	coding	multilingual	0.9999	0.0337	0.9993	-0.9999	0.9547	0.0087	0.8091	0.9979	-0.3078	1.0000	0.5385	0.5385	-0.4615	0.6180	2063.5954	0.7729	0.4246	0.0806	0.8395	0.7031	0.8925	-0.2629	0.0408	0.0910	3.3167	0.0708	-6.5547
gemma-2-9b	coding	safety	0.9997	0.0524	0.9996	-0.9999	0.9770	0.0050	0.7677	0.9983	-0.0396	1.0000	0.2308	0.1538	-0.7692	0.7173	1893.1749	0.9519	0.5352	0.1702	0.5453	0.6062	0.8277	-0.2616	0.0503	0.8042	1.3954	0.4266	-0.5252
gemma-2-9b	instruction	math	0.9980	0.0659	0.9845	-0.9977	0.9081	0.0169	0.7135	0.9976	-0.4032	1.0000	0.3846	0.4615	-0.6154	0.6023	1764.7328	0.6049	0.4385	0.1870	0.2540	0.5437	0.8300	-0.9431	0.0112	0.1060	3.0854	0.1823	-2.6581
gemma-2-9b	instruction	multilingual	1.0000	0.0072	1.0000	-1.0000	0.9945	0.0011	0.9592	0.9992	-0.0244	1.0000	0.4615	0.5385	-0.5385	0.9127	903.5310	0.9004	0.8827	0.0302	0.8841	0.8250	0.9717	-0.4069	0.1501	0.4406	1.5525	0.1984	-0.7717
gemma-2-9b	instruction	safety	0.9998	0.0421	0.9993	-0.9998	0.9360	0.0118	0.7685	0.9978	-0.2868	1.0000	0.1538	0.1538	-0.8462	0.5981	2100.9230	0.9018	0.4106	0.1496	0.0300	0.6531	0.8191	-0.4056	0.0561	0.1661	2.4648	0.4937	-4.5674
gemma-2-9b	math	multilingual	0.9980	0.0656	0.9846	-0.9977	0.9006	0.0180	0.7123	0.9975	-0.3748	1.0000	0.3846	0.5385	-0.6154	0.5738	1641.7941	0.6718	0.4370	0.1573	0.5650	0.5625	0.8395	0.5362	0.0189	0.0467	4.6291	0.0706	-10.7098
gemma-2-9b	math	safety	0.9980	0.0758	0.9842	-0.9980	0.9776	0.0053	0.7103	0.9997	-0.0611	1.0000	0.0769	0.0769	-0.9231	0.6289	1916.7571	0.5455	0.4574	0.2092	0.8183	0.4906	0.7996	0.5375	0.0559	0.6381	1.4469	0.3384	-0.6204
gemma-2-9b	multilingual	safety	0.9998	0.0419	0.9991	-0.9998	0.9264	0.0135	0.7533	0.9973	-0.2702	1.0000	0.1538	0.1538	-0.8462	0.5593	2124.4436	0.8120	0.3751	0.1446	0.3583	0.6438	0.8185	0.0013	0.0398	0.0732	3.6960	0.1233	-9.0608
gemma-2-9b-it	coding	instruction	0.9999	0.0344	0.9995	-0.9999	0.9930	0.0023	0.8748	0.9966	-0.0291	1.0000	0.0769	0.0769	-0.9231	0.3738	11498.3304	0.3603	0.2801	0.1056	0.6779	0.7063	0.8966	0.4979	0.0275	0.2120	2.2075	0.3381	-3.0719
gemma-2-9b-it	coding	math	0.9980	0.0730	0.9864	-0.9978	0.9867	0.0042	0.7734	0.9933	-0.0076	1.0000	0.2308	0.3846	-0.7692	0.3542	4237.2995	0.5144	0.1251	0.1541	0.7611	0.5875	0.8629	-0.8748	0.0327	0.5141	1.5472	0.2071	-0.5692
gemma-2-9b-it	coding	multilingual	0.9999	0.0339	0.9994	-0.9999	0.9922	0.0022	0.8733	0.9971	-0.0390	1.0000	0.0769	0.0769	-0.9231	0.3643	4591.0943	0.7997	0.1161	0.1065	0.7735	0.6844	0.8697	-0.4826	0.0226	0.0792	3.5590	0.0859	-4.3373
gemma-2-9b-it	coding	safety	0.9997	0.0526	0.9996	-0.9999	0.9926	0.0024	0.7982	0.9964	-0.0059	1.0000	0.0769	0.0769	-0.9231	0.7387	3821.8928	0.7899	0.5203	0.1516	0.4902	0.6656	0.8620	-0.5298	0.0424	0.8100	1.3999	0.4105	-0.4571
gemma-2-9b-it	instruction	math	0.9980	0.0662	0.9868	-0.9977	0.9798	0.0066	0.7707	0.9912	-0.0372	1.0000	0.1538	0.3846	-0.8462	0.2603	12004.2922	0.1853	0.0407	0.2417	0.2472	0.5063	0.8566	-1.3727	0.0072	0.1090	3.0443	0.1530	-4.3229
gemma-2-9b-it	instruction	multilingual	1.0000	0.0076	1.0000	-1.0000	0.9979	0.0007	0.9535	0.9991	-0.0169	1.0000	0.1538	0.0769	-0.8462	0.5905	10682.7678	0.2881	0.3934	0.0813	0.3800	0.7875	0.9639	-0.9805	0.0244	0.3733	1.7330	0.1639	-0.5398
gemma-2-9b-it	instruction	safety	0.9998	0.0421	0.9994	-0.9999	0.9916	0.0027	0.8320	0.9947	-0.0349	1.0000	0.0769	0.0769	-0.9231	0.5237	10593.1000	0.4561	0.4372	0.1525	-0.1413	0.6656	0.8540	-1.0277	0.0455	0.1717	2.4296	0.5146	-4.6078
gemma-2-9b-it	math	multilingual	0.9980	0.0658	0.9867	-0.9977	0.9801	0.0060	0.7722	0.9901	-0.0469	1.0000	0.1538	0.0769	-0.8462	0.5068	3117.0031	0.6433	0.3675	0.1898	0.8485	0.5094	0.8398	0.3923	0.0142	0.0407	4.9582	0.0803	-10.6862
gemma-2-9b-it	math	safety	0.9981	0.0761	0.9859	-0.9979	0.9863	0.0046	0.7442	0.9977	-0.0099	1.0000	0.0769	0.0769	-0.9231	0.2886	5454.2045	0.4063	0.0297	0.1813	0.7907	0.5406	0.8218	0.3451	0.0532	0.6347	1.4505	0.3055	-0.6019
gemma-2-9b-it	multilingual	safety	0.9998	0.0418	0.9993	-0.9998	0.9901	0.0030	0.8167	0.9947	-0.0475	1.0000	0.0769	0.0769	-0.9231	0.2927	5736.0553	0.6317	0.0483	0.1336	0.7523	0.6344	0.8318	-0.0472	0.0262	0.0641	3.9506	0.1799	-7.7602

Table 2 — per-family properties, joined to the published score

Table 2a — family-mean properties (8 families).

family	n_pairs	weight_cosine	qmd_raw	subspace_overlap	spectral_overcounting	geo_cka_mean	geo_procrustes_mean	geo_subspace_overlap_mean	geo_svcca_mean	geo_cka_late_minus_early	ret_identity_p_at_1	ret_procrustes_p_at_1	ret_ridge_p_at_1	ret_gain_over_identity	grad_cosine	grad_l2	grad_norm_ratio	grad_cosine_layer_min	beh_js	beh_logit_cosine	beh_topk_overlap	beh_rank_corr	beh_entropy_gap	tv_cosine	tv_norm_ratio	tv_qmd_raw	tv_subspace_overlap	tv_spectral_overcounting
Llama-3.1-8B	10	0.9988	0.0414	0.9998	-1.0000	0.9980	0.0012	0.8651	0.9891	-0.0198	1.0000	0.2538	0.2538	-0.7462	0.8455	791.0859	0.8485	0.5450	0.0852	0.9455	0.6881	0.9418	-0.4607	0.0220	0.3503	2.4657	0.4840	-28.6973
Llama-3.1-8B-Instruct	10	0.9985	0.0462	0.9997	-1.0000	0.9988	0.0009	0.8654	0.9878	-0.0188	1.0000	0.2231	0.2385	-0.7769	0.9545	870.8450	0.8767	0.6504	0.0868	0.8901	0.6834	0.9333	-0.5973	0.0290	0.3155	2.5426	0.4858	-29.3348
Llama-3.2-3B	10	0.9999	0.0133	0.9924	-0.9992	0.9994	0.0003	0.9505	0.9949	-0.0062	1.0000	0.2846	0.2923	-0.7154	0.9487	329.6220	0.9131	0.8566	0.0429	0.9257	0.7703	0.9781	-0.4646	0.0250	0.6433	1.5054	—	—
Llama-3.2-3B-Instruct	10	0.9996	0.0131	0.9904	-0.9985	0.9995	0.0003	0.9640	0.9958	-0.0078	1.0000	0.3615	0.3769	-0.6385	0.9739	295.1517	0.9434	0.9204	0.0423	0.8849	0.7521	0.9766	-0.3968	0.0241	0.6616	1.4945	—	—
gemma-2-2b	10	1.0000	0.0106	1.0000	-1.0000	0.9932	0.0016	0.9442	0.9994	-0.0536	1.0000	0.5769	0.5923	-0.4231	0.8759	986.6237	0.8959	0.7352	0.0457	0.7813	0.8053	0.9431	-0.2566	0.0938	0.7853	1.3771	0.2941	-0.7308
gemma-2-2b-it	10	1.0000	0.0112	1.0000	-1.0000	0.9952	0.0013	0.9444	0.9995	-0.0327	1.0000	0.4308	0.4154	-0.5692	0.9227	1718.2732	0.8140	0.8786	0.0695	0.4995	0.7250	0.9422	-0.2454	0.0395	0.7585	1.4269	0.2547	-0.6999
gemma-2-9b	10	0.9991	0.0491	0.9933	-0.9990	0.9502	0.0095	0.7744	0.9982	-0.2130	1.0000	0.3154	0.3308	-0.6846	0.6502	1844.1148	0.7539	0.4901	0.1364	0.5708	0.6297	0.8530	-0.1860	0.0500	0.3085	2.5361	0.2483	-3.9320
gemma-2-9b-it	10	0.9991	0.0493	0.9943	-0.9991	0.9890	0.0035	0.8209	0.9951	-0.0275	1.0000	0.1154	0.1385	-0.8846	0.4294	7173.6040	0.5075	0.2358	0.1498	0.5580	0.6287	0.8659	-0.4080	0.0296	0.3009	2.6280	0.2439	-3.6954

Table 2b — the published five-expert merge score joined to each family, for the three operators F8 shares with MergeBench. All nine methods are in table_family.csv.

family	score__instruction__Model_soup	score__instruction__Task_arithmetic	score__instruction__TIES	score__math__Model_soup	score__math__Task_arithmetic	score__math__TIES	score__multilingual__Model_soup	score__multilingual__Task_arithmetic	score__multilingual__TIES	score__coding__Model_soup	score__coding__Task_arithmetic	score__coding__TIES	score__safety__Model_soup	score__safety__Task_arithmetic	score__safety__TIES
Llama-3.1-8B	8.3	31.2	12.2	50.1	55.5	56.3	54.0	49.1	54.5	49.6	48.8	49.0	71.0	59.0	61.9
Llama-3.1-8B-Instruct	37.5	47.0	43.4	64.4	60.3	65.7	53.6	54.8	53.9	62.1	61.8	62.6	81.4	79.8	90.4
Llama-3.2-3B	7.2	25.3	9.6	16.2	27.7	26.6	46.8	47.0	47.6	37.0	41.1	37.6	39.2	46.1	40.4
Llama-3.2-3B-Instruct	56.0	59.7	56.6	53.9	55.1	56.7	45.0	45.2	44.6	52.4	49.8	52.5	84.6	80.6	94.5
gemma-2-2b	19.6	29.4	19.8	25.2	28.2	26.3	47.9	47.9	48.2	30.3	35.2	30.4	52.4	45.1	38.4
gemma-2-2b-it	51.9	51.9	49.2	38.7	38.7	38.5	49.2	49.2	49.3	40.2	40.2	39.6	81.3	81.3	76.3
gemma-2-9b	30.3	31.2	28.8	60.3	64.5	65.3	60.0	57.1	59.5	51.5	50.8	52.3	70.6	74.4	75.3
gemma-2-9b-it	50.5	59.3	52.9	64.4	64.3	66.3	60.9	63.0	60.6	58.5	59.8	59.5	68.2	75.3	71.6

Table 3 — the per-domain panels as numbers

Table 3 — the per-domain F8 panels as numbers (1035 cells; 0 survive Benjamini-Hochberg; 0 are flagged architecture-confounded). The reported p is the MOST CONSERVATIVE of a model-clustered bootstrap, an exact t-test on r, and an exact family-label permutation test -- all three are printed so a reader can see which binds. r_arch_metric/r_arch_outcome give each cell's correlation with the gemma-vs-Llama indicator: when both exceed 0.7 the cell cannot separate a property effect from an architecture effect and is flagged. The fifteen largest |r| are shown; every cell is in results/mergebench/table_domain_cells.csv.

domain	operator	metric_label	n_families	r	p_bootstrap	p_parametric	p_perm	p	q_bh	survives_bh	r_arch_metric	r_arch_outcome	arch_confounded
multilingual	Model soup	JS Divergence	8	0.9842	0.0003	0.0000	0.0001	0.0003	0.0518	False	0.4626	0.4157	False
multilingual	Fisher Merging	Top-$k$ Overlap	8	-0.9764	0.0005	0.0000	0.0003	0.0005	0.0565	False	0.2186	0.1781	False
multilingual	TIES	JS Divergence	8	0.9722	0.0003	0.0001	0.0001	0.0003	0.0518	False	0.4626	0.3918	False
multilingual	Model soup	Subspace Ov. Mean	8	-0.9674	0.0003	0.0001	0.0005	0.0005	0.0565	False	0.3068	0.4157	False
multilingual	TIES	Subspace Ov. Mean	8	-0.9630	0.0003	0.0001	0.0005	0.0005	0.0565	False	0.3068	0.3918	False
multilingual	Consensus TA	JS Divergence	8	0.9602	0.0003	0.0002	0.0001	0.0003	0.0518	False	0.4626	0.5061	False
multilingual	Dataless L&S	JS Divergence	8	0.9589	0.0003	0.0002	0.0000	0.0003	0.0518	False	0.4626	0.4089	False
multilingual	DARE	JS Divergence	8	0.9574	0.0003	0.0002	0.0001	0.0003	0.0518	False	0.4626	0.4580	False
multilingual	Dataless L&S	Grad. Cos. Min Layer	8	-0.9509	0.0010	0.0003	0.0010	0.0010	0.0590	False	0.3620	0.4089	False
multilingual	Task arithmetic	JS Divergence	8	0.9465	0.0003	0.0004	0.0001	0.0004	0.0565	False	0.4626	0.4642	False
multilingual	L&S	Grad. Cos. Min Layer	8	-0.9444	0.0010	0.0004	0.0004	0.0010	0.0590	False	0.3620	0.3157	False
multilingual	Model soup	Rank Corr.	8	-0.9403	0.0003	0.0005	0.0009	0.0009	0.0590	False	0.6515	0.4157	False
multilingual	Consensus TA	Rank Corr.	8	-0.9399	0.0003	0.0005	0.0010	0.0010	0.0590	False	0.6515	0.5061	False
multilingual	TIES	Grad. Cos. Min Layer	8	-0.9394	0.0010	0.0005	0.0002	0.0010	0.0590	False	0.3620	0.3918	False
multilingual	DARE	Subspace Ov. Mean	8	-0.9380	0.0003	0.0006	0.0005	0.0006	0.0565	False	0.3068	0.4580	False

Table 4 — cross-domain consistency, with its null

Table 4 — cross-domain consistency,every observed value beside its null. The null permutes family labels, breaking the property/outcome link while preserving both the property correlations and the cross-domain outcome structure. Read excess_over_null, not observed_r: on pure-noise properties this statistic reads about +0.60, because the eight families' published scores are themselves correlated across domains.

domain_a	domain_b	observed_r	null_mean	null_lo	null_hi	excess_over_null	p_vs_null	n_perm
instruction	math	0.3435	0.4672	-0.3034	0.9046	-0.1238	0.7050	400
instruction	multilingual	0.4433	0.1138	-0.6791	0.7511	0.3295	0.1925	400
instruction	coding	0.2830	0.4234	-0.3127	0.8899	-0.1404	0.6775	400
instruction	safety	0.2479	0.6622	0.1717	0.9115	-0.4142	0.9425	400
math	multilingual	0.9112	0.6002	-0.1340	0.9323	0.3109	0.0500	400
math	coding	0.9454	0.8930	0.6915	0.9828	0.0524	0.3200	400
math	safety	0.7985	0.6616	0.0793	0.9244	0.1370	0.3225	400
multilingual	coding	0.7701	0.5186	-0.1982	0.9141	0.2515	0.2325	400
multilingual	safety	0.6991	0.2178	-0.5795	0.7578	0.4813	0.0425	400
coding	safety	0.7850	0.5628	-0.1224	0.9060	0.2223	0.2300	400
ALL	(mean off-diagonal)	0.6227	0.5121	0.1156	0.8148	0.1106	0.2850	400

Table 5 — MergeBench's published scores, as extracted

All 576 rows in results/mergebench/mergebench_published_scores.csv (family, task, method, score, merge_arity, source). merge_arity is 5 in every row — that is the finding of §1.

Table 6 — coverage and provenance

Table 6 — coverage and provenance. Per family: what ran. Per metric: whether it is live, constant, missing, or not computable on this substrate, and why.

family	pairs_measured	pairs_expected	status	seconds	error
gemma-2-2b	10	10	done	1239
gemma-2-2b-it	10	10	done	1341
Llama-3.2-3B	10	10	done	1812
Llama-3.2-3B-Instruct	10	10	done	1789
Llama-3.1-8B	10	10	done	4756
Llama-3.1-8B-Instruct	10	10	done	5240
gemma-2-9b	10	10	done	6698
gemma-2-9b-it	10	10	done	5565

metric	label	family	n_pairs_with_value	status	reason
weight_cosine	Weight Cos. Sim.	weight space	69	pair-level only	computed and varying across pairs, but across the 8 families its mean spans only 1.5e-03 of its own scale (gate: 1e-2), so it cannot carry a family-level correlation. This is the shared-base saturation of section 4f; see the tv_* task-vector twins for the informative version.
qmd_raw	Quotient Dist.	weight space	80	live	computed and used in the per-domain panels
coord_fraction	Coord. Share	weight space	0	not computable	NaN by construction: both experts are fine-tunes of one pretrained checkpoint, so no permutation symmetry separates them and the aligning map is the identity -- there is no coordinate component to measure.
subspace_overlap	Subspace Overlap	weight space	69	pair-level only	computed and varying across pairs, but across the 8 families its mean spans only 9.6e-03 of its own scale (gate: 1e-2), so it cannot carry a family-level correlation. This is the shared-base saturation of section 4f; see the tv_* task-vector twins for the informative version.
spectral_overcounting	Spectral Over-count	weight space	69	pair-level only	computed and varying across pairs, but across the 8 families its mean spans only 1.5e-03 of its own scale (gate: 1e-2), so it cannot carry a family-level correlation. This is the shared-base saturation of section 4f; see the tv_* task-vector twins for the informative version.
geo_cka_mean	CKA Mean	representation	80	live	computed and used in the per-domain panels
geo_procrustes_mean	Procrustes Mean	representation	80	live	computed and used in the per-domain panels
geo_subspace_overlap_mean	Subspace Ov. Mean	representation	80	live	computed and used in the per-domain panels
geo_svcca_mean	SVCCA Mean	representation	80	live	computed and used in the per-domain panels
geo_cka_late_minus_early	CKA Late$-$Early	representation	80	live	computed and used in the per-domain panels
ret_identity_p_at_1	Identity P@1	retrieval	80	constant	computed, but identical on every pair (sd = 0) -- it carries no information and cannot enter a correlation
ret_procrustes_p_at_1	Procrustes P@1	retrieval	80	live	computed and used in the per-domain panels
ret_ridge_p_at_1	Ridge P@1	retrieval	80	live	computed and used in the per-domain panels
ret_gain_over_identity	Gain over Identity	retrieval	80	live	computed and used in the per-domain panels
grad_cosine	Grad. Cos. Sim.	gradient	80	live	computed and used in the per-domain panels
grad_l2	Grad. L2 Dist.	gradient	80	live	computed and used in the per-domain panels
grad_norm_ratio	Grad. Magn. Ratio	gradient	80	live	computed and used in the per-domain panels
grad_cosine_layer_min	Grad. Cos. Min Layer	gradient	80	live	computed and used in the per-domain panels
beh_js	JS Divergence	behaviour	69	live	computed and used in the per-domain panels
beh_logit_cosine	Logit Cos. Sim.	behaviour	69	live	computed and used in the per-domain panels
beh_topk_overlap	Top-$k$ Overlap	behaviour	69	live	computed and used in the per-domain panels
beh_rank_corr	Rank Corr.	behaviour	69	live	computed and used in the per-domain panels
beh_entropy_gap	Entropy Gap	behaviour	69	live	computed and used in the per-domain panels
tv_cosine	TV Cosine	weight space
(task vectors)	80	live	computed and used in the per-domain panels
tv_norm_ratio	TV Norm Ratio	weight space
(task vectors)	80	live	computed and used in the per-domain panels
tv_qmd_raw	TV Quotient Dist.	weight space
(task vectors)	80	live	computed and used in the per-domain panels
tv_subspace_overlap	TV Subspace Ov.	weight space
(task vectors)	60	live	computed and used in the per-domain panels
tv_spectral_overcounting	TV Spectral Over-count	weight space
(task vectors)	60	live	computed and used in the per-domain panels

Table 7 — partial NaNs, attributed to a checkpoint

Table 7 — every metric that is present on most pairs of a family and NaN on a few (16 such (family, metric) cases). A metric that fails on a SUBSET of pairs is almost never the metric's fault: one bad checkpoint poisons exactly the four pairs it appears in, which identifies it. Full detail in results/mergebench/table_nan_provenance.csv.

family	metric	n_nan	n_pairs	implicated_domain	reason
Llama-3.2-3B	weight_cosine	4	10	math	every NaN pair contains 'math' and every pair containing it is NaN -> the math checkpoint is responsible (almost certainly non-finite logits or activations under bfloat16), not the metric
Llama-3.2-3B	subspace_overlap	4	10	math	every NaN pair contains 'math' and every pair containing it is NaN -> the math checkpoint is responsible (almost certainly non-finite logits or activations under bfloat16), not the metric
Llama-3.2-3B	spectral_overcounting	4	10	math	every NaN pair contains 'math' and every pair containing it is NaN -> the math checkpoint is responsible (almost certainly non-finite logits or activations under bfloat16), not the metric
Llama-3.2-3B	beh_js	4	10	math	every NaN pair contains 'math' and every pair containing it is NaN -> the math checkpoint is responsible (almost certainly non-finite logits or activations under bfloat16), not the metric
Llama-3.2-3B	beh_logit_cosine	4	10	math	every NaN pair contains 'math' and every pair containing it is NaN -> the math checkpoint is responsible (almost certainly non-finite logits or activations under bfloat16), not the metric
Llama-3.2-3B	beh_topk_overlap	4	10	math	every NaN pair contains 'math' and every pair containing it is NaN -> the math checkpoint is responsible (almost certainly non-finite logits or activations under bfloat16), not the metric
Llama-3.2-3B	beh_rank_corr	4	10	math	every NaN pair contains 'math' and every pair containing it is NaN -> the math checkpoint is responsible (almost certainly non-finite logits or activations under bfloat16), not the metric
Llama-3.2-3B	beh_entropy_gap	4	10	math	every NaN pair contains 'math' and every pair containing it is NaN -> the math checkpoint is responsible (almost certainly non-finite logits or activations under bfloat16), not the metric
Llama-3.2-3B-Instruct	weight_cosine	7	10		NaN on 7 of 10 pairs, spanning domains coding, instruction, math, multilingual, safety; no single checkpoint explains the pattern
Llama-3.2-3B-Instruct	subspace_overlap	7	10		NaN on 7 of 10 pairs, spanning domains coding, instruction, math, multilingual, safety; no single checkpoint explains the pattern
Llama-3.2-3B-Instruct	spectral_overcounting	7	10		NaN on 7 of 10 pairs, spanning domains coding, instruction, math, multilingual, safety; no single checkpoint explains the pattern
Llama-3.2-3B-Instruct	beh_js	7	10		NaN on 7 of 10 pairs, spanning domains coding, instruction, math, multilingual, safety; no single checkpoint explains the pattern
Llama-3.2-3B-Instruct	beh_logit_cosine	7	10		NaN on 7 of 10 pairs, spanning domains coding, instruction, math, multilingual, safety; no single checkpoint explains the pattern
Llama-3.2-3B-Instruct	beh_topk_overlap	7	10		NaN on 7 of 10 pairs, spanning domains coding, instruction, math, multilingual, safety; no single checkpoint explains the pattern
Llama-3.2-3B-Instruct	beh_rank_corr	7	10		NaN on 7 of 10 pairs, spanning domains coding, instruction, math, multilingual, safety; no single checkpoint explains the pattern
Llama-3.2-3B-Instruct	beh_entropy_gap	7	10		NaN on 7 of 10 pairs, spanning domains coding, instruction, math, multilingual, safety; no single checkpoint explains the pattern

4c. Published to the Hub

Everything here is pushed additively to Mergeability-2/mergebench-property-sweep (dataset repo) after each family completes — all CSVs, all figures (PNG + PDF), and this document as the dataset card with a lead block that states the coverage limitation before any number appears. Nothing on the remote is ever deleted, and the pre-existing Mergeability-2/mergeability-results repo is not touched. Manual equivalent: bash scripts/publish_mergebench.sh.

4d. Timing

Measured on gemma-2-2b (d=2304, 26 layers): 152–637 s per model (the spread is CPU contention, not the models — the box runs at load 150–380 on 128 cores and GPU utilisation during measurement is near zero). Five models + the weight-distance pass ≈ 30 min per 2B family.

Two throughput defects were found and fixed, both of which made the sweep look far more expensive than it is.

Thread oversubscription. /proc/loadavg showed 317 runnable tasks and 311,753 threads on a 128-core box while the GPUs sat near 0%. Four concurrent agents were each letting numpy/torch open a BLAS pool per core, several processes deep, so the processes preempted one another and identical work took 152 s or 637 s per model depending only on who else was running. Every pool is now bounded to MB_THREADS (default 8), exported by scripts/run_mergebench.sh before python imports numpy, plus torch.set_num_threads for torch's separate intra-op pool. Load fell to ~196 immediately.

Redundant factorisation. geometry_block re-derives both models' per-layer factorisation on every call, and each model appears in four of its family's ten pairs, so the same float64 SVD ran 8× more often than necessary — the pair loop had produced 0 of 10 pairs after 10 minutes. Factorisations are now computed once per model in measure_model; per-pair geometry cost fell from ~7.1 s to ~0.004 s, and the result is numerically identical (verified, 0 mismatches over 15 keys).

Projected, scaling by parameter count from the measured 2B figure:

family	params	projected
gemma-2-2b / -it	2.6B	~30 min
Llama-3.2-3B / -Instruct	3.2B	~37 min
Llama-3.1-8B / -Instruct	8.0B	~95 min
gemma-2-9b / -it	9.2B	~90–105 min

Two workers run in parallel on the base and instruct halves, so per worker that is ~4.5 h, and with contention margin ~5–6.5 h for all eight families.

Plan (deadline extended to ~02:00 UTC): run all eight families. The projection below leaves more than four hours of headroom, so the 9B tier is no longer a gamble and the earlier stop-at-four/six contingency is withdrawn. With the extra time the permutation test was also made exact at n = 8 -- all 8! = 40,320 relabellings are enumerated rather than sampled (8 s for a 1440-cell panel; false-positive rate on noise 5.7% against a 5% target). More families is more data, not a reason to lower the bar: the saturation exclusion, the architecture-confound flags and the three-test maximum all stay exactly as they are.

(superseded, kept for the record) Natural stopping point if time was short: the four small families (gemma-2-2b, gemma-2-2b-it, Llama-3.2-3B, Llama-3.2-3B-Instruct) — 40 of 80 pairs in ~1 h 10 m, which is also exactly the point at which the outcome-joined panels first become drawable (n ≥ 4). The trade is real, though: the outcome analysis is n-limited already, so stopping at four families halves an n that is only 8 at best. The 8B/9B families are worth the wait if ~5–6 h is acceptable; if not, the four small families still deliver the complete small-model half of the property suite, which is the novel part.

4e. Measured: the canonical probe breaks the retrieval family at these widths

The n/d concern flagged in §2 is not hypothetical, and the first family quantifies it. On gemma-2-2b (d = 2304), the two probes disagree completely about the retrieval block:

column	canonical 32-row probe	512-row extended probe
ret_identity_p_at_1	1.0000 (sd 0)	1.0000 (sd 0)
ret_procrustes_p_at_1	0.5769 (sd 0.122)	0.9863 (sd 0.013)
ret_ridge_p_at_1	0.5923 (sd 0.037)	0.9859 (sd 0.006)
ret_gain_over_identity	-0.4231	-0.0137

The canonical protocol fits a 2304x2304 map from 19 training rows and then scores it on 13. It reports that aligning destroys retrieval (gain -0.42). The 512-row twin reports the identity (gain -0.014) -- which is the correct answer for five fine-tunes of one pretrained checkpoint, where no coordinate mismatch exists to remove and the best map genuinely is the identity.

So the canonical-probe retrieval columns measure estimator overfit at MergeBench widths, not model geometry. They are kept because they are what F8's protocol specifies and dropping them would hide the problem, but every ret_* column now ships beside its retX_* twin in Table 1, and the retrieval family of the per-domain panels must be read with this in mind. ret_identity_p_at_1 is additionally constant at 1.0 across all pairs and therefore carries no information at all; it is marked constant in the coverage table.

This is the concrete payoff of computing both probes rather than assuming the Beetle protocol transfers to models three to five times wider.

4f. F8's weight-space family is dead here; task vectors replace it

Every MergeBench family shares one pretrained base, so the three raw weight-space columns sit at their analytic ceiling and cannot carry a correlation at all:

column	spread across the 10 gemma-2-2b pairs	status
weight_cosine	sd 1.1e-05 (1.00000-1.00001)	saturated
subspace_overlap	sd 2.0e-05 (0.9999-1.0000)	saturated
spectral_overcounting	sd 8.8e-06 (-1.000000 throughout)	saturated

spectral_overcounting = -1.0 is not a sentinel. The metric forms Wm = Wi + Wj and measures how much the merged basis over-counts; for Wi ~= Wj that is Wm ~= 2Wi, so s = 2, s - 1 = 1, and the negated score is exactly -1. The exact numpy estimator returns -1.000000 at zero drift and -0.931 at large drift. It is a correct measurement that has saturated, and it is reported as saturated with its sd -- never NaN'd as a failure.

A column this flat is dangerous, not merely useless: a Pearson $r$ against sd = 1e-5 is driven by float noise and would print as a finding. panel.SATURATED_SD = 1e-4 therefore excludes any such column from every correlation, at both the pair and family level.

The fix is to measure what a merge operator actually manipulates: the task vector tau = theta_expert - theta_base. mergebench/taskvec.py recomputes the family on tau, streamed key-by-key on the GPU from the safetensors (so a 9B family never holds a float32 state dict), using the pretrained bases -- all eight verified downloadable, not merely visible. Measured on gemma-2-2b:

raw column	sd	task-vector twin	sd	more spread
weight_cosine	1.1e-05	tv_cosine	4.2e-02	3,799x
subspace_overlap	2.0e-05	tv_subspace_overlap	1.9e-01	9,378x
spectral_overcounting	8.8e-06	tv_spectral_overcounting	3.9e-01	43,962x
qmd_raw	1.4e-03	tv_qmd_raw	4.5e-02	33x

tv_cosine spans 0.039 to 0.151 -- the task vectors are near-orthogonal, the regime task arithmetic assumes -- with math-multilingual least aligned (0.039) and instruction-safety most (0.151). That independently reproduces the divergence ordering the representation, gradient and behaviour families give, from a completely different measurement.

The task-vector columns are drawn as a sixth metric family in every panel (28 columns, not 23). The saturated raw columns are kept and drawn beside them rather than dropped, so a reader sees the saturation instead of having to take it on trust. taskvec.py is deliberately separate from the sweep and idempotent: it needs the pretrained base (which the sweep never fetches) and must retro-fit onto families whose expert weights were already deleted. It carries its own disk gate, because the sweep on two 8B families plus this pass on gemma-2-9b would otherwise leave ~337 GB against the 350 GB floor.

4g. Finding: 11 of 80 MergeBench pairs are not elementwise-mergeable

The sweep logged js=nan on some Llama pairs. It is not a numerical failure -- the logits are 100% finite (min -7.84, max 20.0) -- and it is not a bug in the behaviour block. behaviour_block correctly returns nothing, because the two experts do not share a vocabulary.

Vocabulary sizes declared by the five experts of each family:

family	vocab sizes	pairs affected	min param_coverage
gemma-2-2b / -it	256000 (all five)	0/10	1.0000
Llama-3.2-3B	coding/instruction/multilingual/safety 128256, math 128320	4/10	0.8773
Llama-3.2-3B-Instruct	coding/multilingual/safety 128256, instruction 128257, math 128320	7/10	0.8773
Llama-3.1-8B / -Instruct	128256 (all five)	0/10	1.0000
gemma-2-9b / -it	256000 (all five)	0/10	1.0000

11 of 80 pairs (14%). The Llama-3.2-3B-Instruct family contains three different vocabulary sizes among five checkpoints that a user would reasonably assume are interchangeable.

Why it matters, beyond bookkeeping:

• embed_tokens and lm_head have different shapes, so no elementwise merge operator is defined on them. param_coverage for those pairs is 0.877, not 1.0 -- 12.3% of the parameter mass, and the most semantically loaded 12.3%, cannot be merged without vocabulary handling. The sweep hardcoded 1.0; mergebench/coverage.py now measures it and overwrites the column.
• The behaviour family is undefined for those pairs: a KL or top-k overlap between logits over different vocabularies compares incomparable objects. Those five columns are legitimately absent, and Table 7 attributes each NaN to the responsible checkpoint from the pattern of which pairs it hits.
• MergeBench's headline results merge all five experts at once per family, so every reported Llama-3.2-3B number is a merge across this mismatch. Their harness must be resolving it somehow (truncation or padding of the embedding); the resolution is not described in the paper.

This is measured from config.json alone -- the only differing dimension is the vocabulary and the tensors it governs are exactly embed_tokens and lm_head -- so it costs a few kB per model, needs no weights, and applies retroactively to families whose checkpoints were long deleted. It is refreshed on every panel run, so the column can never go stale.

It is also, for this project specifically, a cross-vocabulary merging case sitting inside a benchmark that presents as a clean shared-base suite -- the regime rqA_cross_tokenizer exists for.

4h. The outcome-joined panels resolve NOTHING at n = 4, and here is why that is the finding

An earlier draft of these panels reported 306 of 945 cells surviving Benjamini-Hochberg. Every one of them was an artefact. Three independent defects combined, and all three are now fixed.

(i) The cluster bootstrap cannot see how few observations there are. It resamples the same handful of families, so its p-value is not calibrated at this sample size. Measured on pure noise, 400 trials each:

n families	bootstrap p < 0.05 on NOISE	should be
4	40.2%	5%
6	12.2%	5%
8	9.0%	5%

(ii) The saturation gate was calibrated on the wrong quantity. It used pair-level spread (~1e-5), but the panels correlate FAMILY MEANS, whose spread is 10-50x larger, so saturated columns squeaked through. weight_cosine has a family-level range of 3.8e-4 on a quantity bounded at 1 and was producing r = 0.988, q = 0.001. The gate is now on the family-level range relative to the column's own scale (FAMILY_REL_RANGE_MIN = 1e-2), which excludes weight_cosine (3.8e-4), spectral_overcounting (1.5e-3), geo_svcca_mean (4.6e-3), geo_cka_mean (6.3e-3), subspace_overlap (9.6e-3) and ret_identity_p_at_1 (0), while keeping qmd_raw (0.22) and grad_l2 (1.71).

(iii) Testing against zero is the wrong null when the families cluster by architecture. With four families splitting 2-2 gemma/Llama, any metric that separates the architectures correlates ~0.98 with any outcome that also separates them. That is the architecture dichotomy measured twice, not a property-to-outcome relationship. Measured |r| with the gemma-vs-Llama indicator:

metric	|r| with architecture		metric	|r| with architecture
beh_rank_corr	0.9994		qmd_raw	0.9837
geo_svcca_mean	0.9894		geo_cka_mean	0.9634
subspace_overlap	0.9865		grad_cosine	0.8549
beh_topk_overlap	0.068

Only beh_topk_overlap is architecture-independent. So every cell now carries an exact family-label permutation test -- the same instrument that already protected the cross-domain statistic. It enumerates all 4! = 24 relabellings exactly at n = 4 (all 8! at n = 8 are sampled), and asks the right question: is this stronger than relabelling the families at random? Its false-positive rate on noise at n = 4 is 0.0%. Each cell also reports r_arch_metric and r_arch_outcome, and is flagged arch_confounded when both exceed 0.7.

The reported p is the maximum of all three tests (bootstrap, exact t on r, exact permutation), so no single test's blind spot can manufacture a finding. All three are printed in Table 3.

The result

0 of 720 cells survive BH at n = 4. For the strongest remaining cells the permutation test is what binds -- the bootstrap says p = 0.0004 and the permutation test says p = 0.08-0.12:

domain	operator	metric	r	p_boot	p_param	p_perm	q_bh	arch-conf
multilingual	DARE	Subspace Ov. Mean	-0.988	0.0004	0.012	0.120	1.00	yes
coding	DARE	Subspace Ov. Mean	+0.971	0.0004	0.029	0.080	1.00	yes
safety	RegMean	Grad. Cos. Min Layer	+0.969	0.0004	0.031	0.080	1.00	no

20% of all cells are flagged architecture-confounded.

How to read the per-domain panels: as a negative result. Every cell is struck through. At the coverage MergeBench's published outcomes permit -- 8 families at best, spanning 2 architectures -- the panel cannot distinguish a property effect from an architecture effect for any property, in any domain. This does not improve much at n = 8: the split becomes 4-4 and the confound is diluted, not removed. Anyone wanting the pair-level F8 needs pairwise merge outcomes, which do not exist.

None of this touches the property suite. The 80-pair measurements, qmd_raw, the task vectors and the vocabulary-mismatch finding are all independent of the outcome join and all stand.

4i. Does more coverage fix the confound? The n = 4 -> 8 trend, and what to read

results/mergebench/coverage_trend.json records the headline numbers on every panel run, keyed by family count, so this table is data rather than recollection.

n families	pairs	cells	survive BH	arch-confounded	cross-domain excess	p
4	40	855	0	176 (21%)	-0.059	0.52
6	60	990	0	55 (6%)	-0.056	0.62
7	70	1035	0	11 (1%)	-0.110	0.66
8	80	1035	0	0 (0%)	+0.111	0.28

The n = 4 row is recomputed on the four-family subset of the rows now on disk, using the current metric set and the current tests, so it is comparable with the later rows. It is therefore not identical to the 720-cell figure quoted in section 4h, which was produced before the task-vector family was added and before the family-level range gate; that number is left as written because it is what the run at the time actually reported.

Two things a reader should not misread.

(1) The cross-domain excess wanders around zero and never approaches significance. The four values are -0.059, -0.056, -0.110, +0.111 at n = 4, 6, 7, 8, with p never below 0.28. At three of four sample sizes the observed agreement sits below its own label-permutation null. The sign flips positive at n = 8, and that must not be read as a trend towards agreement -- it is a statistic fluctuating on both sides of zero at a sample size that cannot resolve it. The correct statement remains no evidence of shared predictive structure across domains.

This is also why the raw agreement number must never be quoted alone. At n = 8 the observed value is substantial-looking, but its null is nearly as large: the eight families' published scores are themselves correlated across domains, so a fixed property vector produces similar $r$ in every domain whether or not it predicts anything. Read excess_over_null in table_cross_domain.csv, never observed_r.

(2) The architecture confound dilutes to nothing, and the panels still resolve nothing. The flagged fraction falls monotonically 21% -> 6% -> 1% -> 0% as n goes 4 -> 6 -> 7 -> 8. With a balanced 4-4 gemma/Llama split, no cell any longer has both r_arch_metric and r_arch_outcome above 0.7: at full coverage the confound is genuinely gone. But 0 cells survive BH at every n, including n = 8. Dilution of a confound is not the same as acquiring power, and the two facts are independent.

The n = 8 result is informative, not merely underpowered. The exact permutation test at n = 8 enumerates all 8! = 40,320 relabellings and can resolve p down to 1/40,321, so a genuine effect could have surfaced. None did. With the architecture confound at 0% and the test at full resolution, the honest conclusion is that MergeBench's published five-expert outcomes cannot resolve which pre-merge property predicts merge success, in any domain -- not that our instrument was too blunt to see it.

5. What did NOT run, and why

not run	why	cost to fix
Pair-level Δfloor for the 80 pairs — the actual F8 outcome column	MergeBench publishes no two-expert merge; per instruction, we do not run our own evaluations	80 pairs × 4 operators × 5 domain val sets ≈ 1.5–3 days of GPU
QMD-guided operator row	no published counterpart; it is our operator	same as above
The aligned / transport arms (F8 uses the naive arm only, but the Beetle bench carries all four)	shared-init fine-tunes: the aligning map is the identity, so the aligned arm is the naive arm	n/a — it is degenerate here, not skipped
A pair-level null (the family-label permutation above is the only null run)	there is no pair-level outcome to permute against	falls out free once pair-level outcomes exist
Set-level (k=5) properties matched to the k=5 outcome	heuristics.kway_analysis measures genuine set-level over-counting; here the family design matrix is the mean of pairwise values, which is a summary of pairwise structure, not a set measurement	~1 GPU-day; would raise the quality of the n=8 fit but not its n
Cross-family pairs	different tokenizers and widths — not mergeable, so not a gap	n/a

6. Reproduce

PYTHONPATH=src python -m mergeschool.mergebench.suite       # enumerate the org
bash scripts/run_mergebench.sh 4 5                          # the property sweep, 2 GPUs
PYTHONPATH=src python -m mergeschool.mergebench.panel       # figures + panel.json
PYTHONPATH=src python tests/test_mergebench_spectral.py     # the SVD substitution check

Artefacts: results/mergebench/{pair_metrics.csv,mergebench_published_scores.csv,panel.json, suite.json,ledger_w*.json} and figures/mergebench/F8MB_*.{png,pdf}.