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RESULTS_COMPOSE_AUDIT.md

@@ -1,6 +1,6 @@
 # Compose-audit: putting the alignment map and the merging payoff on the SAME real models
 
-_Generated 2026-08-26 20:59 UTC · training-free · code: `/root/compose-audit` · operators/aligners/metrics imported unmodified from `mergeschool.core` (`/root/mergeability`, treated as read-only)._
+_Generated 2026-08-26 21:04 UTC · training-free · code: `/root/compose-audit` · operators/aligners/metrics imported unmodified from `mergeschool.core` (`/root/mergeability`, treated as read-only)._
 
 ## Read this first: what substrate, and what metric
 
@@ -23,9 +23,9 @@ _Generated 2026-08-26 20:59 UTC · training-free · code: `/root/compose-audit`
 
 ## Headline findings
 
-1. **Naive averaging of two seed-only-different real LMs is catastrophic, at every size.** Δfloor 14m: +32.4 · 31m: +20.4 · 70m: +20.2 · 160m: +8.8 · 410m: +6.5 nats/token against parent floors of 3–4.4 nats/token, i.e. above the uniform-over-vocabulary reference of 10.8 for all but the largest. n = 36 / 36 / 36 / 28 / 3 pairs.
-2. **Unit alignment removes a large fraction of that gap and still does not produce a usable model.** Best of permutation / Procrustes removes 14m: 72% · 31m: 57% · 70m: 55% · 160m: 32% · 410m: 11% — leaving 9.0 · 8.1 · 8.7 · 6.0 · 5.7 nats/token above the better parent.
-3. **The rescue shrinks monotonically with scale** (14m: 72% → 410m: 11%) while the naive gap shrinks too — so the coordinate-removable share of the obstruction is falling in exactly the direction the field is scaling. (Per-size n is listed in (1); the largest sizes carry the fewest pairs, so read the trend from the sizes with complete 36-pair grids and treat the largest as directional.)
+1. **Naive averaging of two seed-only-different real LMs is catastrophic, at every size.** Δfloor 14m: +32.4 · 31m: +20.4 · 70m: +20.2 · 160m: +8.8 · 410m: +6.5 nats/token against parent floors of 3–4.4 nats/token, i.e. above the uniform-over-vocabulary reference of 10.8 for all but the largest. n = 36 / 36 / 36 / 30 / 3 pairs.
+2. **Unit alignment removes a large fraction of that gap and still does not produce a usable model.** The exactly function-preserving permutation rung removes 14m: 70% · 31m: 48% · 70m: 44% · 160m: 23% · 410m: 11% — leaving 9.6 · 9.6 · 11.0 · 6.7 · 5.7 nats/token above the better parent, i.e. an absolute 14.0 · 13.5 · 14.6 · 10.0 · 8.7 nats/token against parent floors of 3.0–4.4 and a uniform-over-vocabulary reference of 10.8. At 14m, 31m, 70m the aligned merge is still *worse than predicting uniformly over the vocabulary*; at the larger sizes it is below that line but still 2–3x the parent's loss. (A Procrustes rung is also reported, but it is **not** function-preserving on LayerNorm transformers — see Validation — so the coordinate claim rests on the permutation rung.)
+3. **The rescue shrinks monotonically with scale** (14m: 70% → 410m: 11% on the exact rung) while the naive gap shrinks too — so the coordinate-removable share of the obstruction is falling in exactly the direction the field is scaling. (Per-size n is listed in (1); the largest sizes carry the fewest pairs, so read the trend from the sizes with complete 36-pair grids and treat the largest as directional.)
 4. **The likelihood rescue does not transfer to accuracy.** On pythia-14m (n=36), parents average 0.652 on BLiMP; the naive merge 0.518 and the aligned merge 0.544, against chance 0.500. A ~70% Δfloor rescue buys ~0.026 accuracy. Pairwise, the two rescues are uncorrelated.
 5. **On the real bilingual-composition models the merge fails and alignment does not rescue it.** Goldfish eng×{nld,spa,ell,pol}: naive Δfloor on English text +0.91 nats/byte against a 0.81 floor; the best M1 rung +0.90. The binding constraint is the **vocabulary**, not the coordinate frame — the English tokenizer UNK-s 45% of Greek and 11% of Polish, and no permutation or rotation can address that.
 6. **…and the accuracy dissociation runs the other way there.** The same likelihood-destroyed Goldfish merges retain 0.68 on MultiBLiMP-English (parent 0.96, chance 0.50). Δfloor and benchmark accuracy dissociate in **both** directions; neither implies the other.
@@ -77,17 +77,17 @@ Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **20.30**, permut
 Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **20.17**, permutation-aligned **10.98** nats/token.
 
 
-### pythia-160m — 28 seed pairs · mean parent floor **3.254** nats/token · uniform-over-vocabulary reference **10.826** nats/token
+### pythia-160m — 30 seed pairs · mean parent floor **3.254** nats/token · uniform-over-vocabulary reference **10.826** nats/token
 
 | rung | n | mean nats/tok | mean Δfloor | median Δfloor | best Δfloor | beats naive | % of naive Δfloor removed |
 |---|---|---|---|---|---|---|---|
-| M0_naive_avg | 28 | 12.10 | 8.84 | 8.38 | 6.88 | 0/28 | 0.0% |
-| M1_perm_avg | 28 | 9.97 | 6.72 | 6.38 | 5.50 | 25/28 | 22.6% |
-| M1_orth_avg | 28 | 9.38 | 6.12 | 6.04 | 5.13 | 28/28 | 29.8% |
-| M2_task_arith | 28 | 30.32 | 27.07 | 26.97 | 17.88 | 0/28 | -205.4% |
-| M3_ties | 28 | 60.19 | 56.93 | 57.41 | 49.30 | 0/28 | -554.6% |
+| M0_naive_avg | 30 | 12.10 | 8.84 | 8.38 | 6.88 | 0/30 | 0.0% |
+| M1_perm_avg | 30 | 9.96 | 6.70 | 6.38 | 5.50 | 27/30 | 22.8% |
+| M1_orth_avg | 30 | 9.42 | 6.16 | 6.14 | 5.13 | 30/30 | 29.4% |
+| M2_task_arith | 30 | 30.31 | 27.05 | 26.97 | 17.88 | 0/30 | -205.1% |
+| M3_ties | 30 | 60.28 | 57.03 | 57.47 | 49.30 | 0/30 | -555.5% |
 
-Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **8.84**, permutation-aligned **6.71** nats/token.
+Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **8.83**, permutation-aligned **6.70** nats/token.
 
 
 ### pythia-410m — 3 seed pairs · mean parent floor **2.971** nats/token · uniform-over-vocabulary reference **10.826** nats/token
@@ -111,10 +111,11 @@ Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **6.38**, permuta
    destroyed one. This is the pure-coordinate case: there is no data, architecture or tokenizer
    difference left to blame.
 2. **Unit alignment removes a large, highly consistent fraction of that gap** — the permutation rung
-   beats naive on essentially every pair — **and still does not produce a usable model.** The aligned
-   merge remains above the uniform reference at every size we ran. So on real LMs at this scale,
-   alignment *predicts and reduces* the obstruction without *enabling* the merge. Reporting the
-   reduction as "merging works once you align" would be wrong.
+   beats naive on essentially every pair — **and still does not produce a usable model.** At 14m/31m/70m
+   the aligned merge is still *worse than predicting uniformly over the vocabulary*; at 160m/410m it
+   drops below that line but still sits at 2–3× the better parent's loss. So on real LMs at this
+   scale, alignment *predicts and reduces* the obstruction without *enabling* the merge. Reporting
+   the reduction as "merging works once you align" would be wrong.
 3. **Task-arithmetic and TIES are not applicable here and the numbers show it.** PolyPythia seeds are
    independent re-initialisations: `EleutherAI/pythia-<size>` is *not* a shared ancestor, so the
    "task vectors" those operators subtract are not task vectors. Their rows are reported only to
@@ -123,6 +124,42 @@ Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **6.38**, permuta
    interior t that beats the better parent, aligned or not.
 
 
+### Validation: is the alignment actually function-preserving? (One rung is not.)
+
+Every M1 rung is only an *alignment* if `g.θ_B` computes exactly what `θ_B` computes. This was checked
+empirically rather than assumed: take a parent, apply the map, and re-evaluate.
+
+
+| substrate | map | change in the parent's nats/token | verdict |
+|---|---|---|---|
+| set1_pythia14m | permutation_residual+mlp | +3.026e-06 | EXACT |
+| set1_pythia14m | permutation_full(+heads) | +5.893e-06 | EXACT |
+| set1_pythia14m | orthogonal_residual+mlp | +27.262 | **NOT function-preserving** |
+| set4_goldfish_nld | perm_residual_only | +0.000e+00 | EXACT |
+| set4_goldfish_nld | mlp_only | +0.000e+00 | EXACT |
+| set4_goldfish_nld | heads_only | +0.000e+00 | EXACT |
+| set4_goldfish_nld | perm_full | +0.000e+00 | EXACT |
+| set4_goldfish_nld | orth_full | +0.069 | negligible |
+
+**The permutation family is exact** — residual basis, free MLP hidden axis and attention heads, on
+both architectures, to float32 noise. Those rungs are genuine alignments.
+
+**The orthogonal/Procrustes residual map is not**, and on GPTNeoX it is badly not: applying it to a
+PolyPythia parent costs that parent **+27 nats/token on its own**. The reason is structural rather
+than a bug — LayerNorm subtracts the mean over the residual axis and applies a learned elementwise
+gain, and neither commutes with a general rotation (an RMSNorm model would be much closer to safe).
+On the GPT-2 Goldfish models the same map costs only +0.07 nats/token, so the defect is
+architecture-specific in magnitude.
+
+**Consequence for the tables.** The `M1_orth` / `M1c` / `M1e` rows are still *real measurements of a
+merged model's loss* — a merge is a merge, and the number is what it is — but they must **not** be
+read as "how much of the obstruction is coordinate". On SET 1 they merge parent A with a *damaged*
+copy of parent B, and any apparent rescue is partly the arithmetic of averaging toward one parent.
+The coordinate claim in this report rests on the **permutation** rung, which is exact. Where the two
+disagree, believe the permutation rung. This is flagged again at every table that contains an
+orthogonal row.
+
+
 ### The scale trend — alignment's coordinate rescue WEAKENS with model size
 
 | substrate | n pairs | parent floor | naive Δfloor | rescue, permutation | rescue, Procrustes | rescue, best of the two | unaligned CKA | aligned CKA | weight coordinate share |
@@ -130,11 +167,15 @@ Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **6.38**, permuta
 | pythia-14m | 36 | 4.38 | 32.43 | 69.9% | 50.5% | 72.0% | 0.588 | 0.374 | 0.0652 |
 | pythia-31m | 36 | 3.94 | 20.35 | 47.7% | 46.4% | 57.4% | 0.632 | 0.380 | 0.0645 |
 | pythia-70m | 36 | 3.63 | 20.16 | 43.9% | 50.4% | 55.1% | 0.671 | 0.428 | 0.0793 |
-| pythia-160m | 28 | 3.25 | 8.84 | 22.6% | 29.8% | 31.5% | 0.751 | 0.765 | 0.0874 |
+| pythia-160m | 30 | 3.25 | 8.84 | 22.8% | 29.4% | 31.2% | 0.739 | 0.746 | 0.0871 |
 | pythia-410m | 3 | 2.97 | 6.49 | 11.2% | 9.2% | 11.2% | 0.410 | 0.372 | 0.0333 |
 
-The coordinator flagged this from the first two pairs and asked whether it survives the full grid.
-**It does, monotonically, across every size we ran.** The naive merge's Δfloor shrinks with scale
+Read the **permutation** column: it is the one that is exactly function-preserving (see Validation
+above). The Procrustes column is shown for completeness but on GPTNeoX that map damages the model it
+is applied to, so its "rescue" is not a clean coordinate measurement.
+
+The coordinator flagged this trend from the first two pairs and asked whether it survives the full
+grid. **It does, monotonically, across every size we ran, on the exact rung alone.** The naive merge's Δfloor shrinks with scale
 *and* the share of it that alignment can remove shrinks faster. Two things are worth separating:
 
 - The **naive** merge gets less catastrophic with scale, which on its own would be an encouraging
@@ -248,8 +289,9 @@ PolyPythia parents are English LMs, so BLiMP applies directly to SET 1's merges.
 | substrate | n pairs | mean parent acc | better-parent ceiling | M0 naive | M1 permutation | M1 Procrustes | best rung, % of the parents' above-chance margin retained |
 |---|---|---|---|---|---|---|---|
 | pythia-14m | 36 | 0.652 | 0.664 | 0.518 | 0.533 | 0.530 | 28.5% |
-| pythia-31m | 11 | 0.688 | 0.695 | 0.514 | 0.530 | 0.535 | 22.8% |
-| pythia-70m | 35 | 0.717 | 0.722 | 0.515 | 0.540 | 0.542 | 24.4% |
+| pythia-31m | 30 | 0.690 | 0.697 | 0.523 | 0.532 | 0.534 | 24.3% |
+| pythia-70m | 36 | 0.717 | 0.722 | 0.516 | 0.541 | 0.542 | 24.4% |
+| pythia-160m | 1 | 0.774 | 0.780 | 0.562 | 0.545 | 0.556 | 22.1% |
 
 **This is the result the audit asked for, and it is negative.** On pythia-14m the permutation
 alignment removes ~70% of the naive merge's Δfloor in nats/token — and the merged model still scores
@@ -263,8 +305,8 @@ Pair by pair, does the size of the likelihood rescue predict the size of the acc
 | substrate | n | Spearman(Δfloor rescue, BLiMP rescue) | mean Δfloor rescue (nats/tok) | mean BLiMP rescue (acc) |
 |---|---|---|---|---|
 | pythia-14m | 36 | 0.139 | 23.44 | 0.0257 |
-| pythia-31m | 11 | -0.327 | 14.16 | 0.0303 |
-| pythia-70m | 35 | 0.239 | 11.31 | 0.0370 |
+| pythia-31m | 30 | -0.141 | 12.58 | 0.0213 |
+| pythia-70m | 36 | 0.169 | 11.43 | 0.0361 |
 
 ## Did we try hard enough? · REPAIR on top of the alignment
 
@@ -277,11 +319,11 @@ The obvious objection to a negative merging result is that averaging is a weak m
 | pythia-14m | 36 | M4_perm_repair | 7.88 | 7.41 | 0.527 | 16.7% |
 | pythia-14m | 36 | M5_naive_repair | 32.50 | 31.10 | 0.512 | 7.2% |
 | pythia-14m | 36 | **parents** | 0.00 | 0.00 | 0.664 | 100.0% |
-| pythia-70m | 4 | M0_naive_avg | 20.95 | 19.69 | 0.544 | 19.0% |
-| pythia-70m | 4 | M1_perm_avg | 21.63 | 20.06 | 0.541 | 17.6% |
-| pythia-70m | 4 | M4_perm_repair | 21.67 | 20.37 | 0.532 | 13.7% |
-| pythia-70m | 4 | M5_naive_repair | 20.02 | 20.22 | 0.518 | 8.0% |
-| pythia-70m | 4 | **parents** | 0.00 | 0.00 | 0.731 | 100.0% |
+| pythia-70m | 10 | M0_naive_avg | 18.33 | 17.75 | 0.523 | 10.3% |
+| pythia-70m | 10 | M1_perm_avg | 16.91 | 16.26 | 0.541 | 17.9% |
+| pythia-70m | 10 | M4_perm_repair | 16.88 | 17.01 | 0.535 | 15.6% |
+| pythia-70m | 10 | M5_naive_repair | 18.29 | 18.49 | 0.516 | 7.1% |
+| pythia-70m | 10 | **parents** | 0.00 | 0.00 | 0.727 | 100.0% |
 
 REPAIR does help the likelihood — it is the best training-free merge in this report, taking a further
 bite out of the aligned merge's Δfloor (on pythia-14m, 9.61 → 7.88 nats/token, a further 18%). **And
@@ -635,7 +677,7 @@ SET 1's main grid uses `pythia-<size>-seed{n}`, which reseeds **both** the initi
 |---|---|---|---|---|---|---|---|
 | 160m-data | 3 | 3.27 | 3.13 | 3.00 | 3.00 | 3.9% | 0.0139 |
 | 160m-weight | 3 | 3.25 | 3.10 | 2.79 | 2.79 | 10.0% | 0.0123 |
-| 160m (init+data, main grid) | 28 | 3.25 | 8.84 | 6.72 | 6.12 | 31.5% | 0.0874 |
+| 160m (init+data, main grid) | 30 | 3.25 | 8.84 | 6.70 | 6.16 | 31.2% | 0.0871 |
 
 Reading: models that differ **only in data order** start far closer together — the naive merge's
 Δfloor is a small fraction of the reseeded-init case — and alignment does **nothing** for them,
@@ -653,12 +695,12 @@ init-plus-data-order number, not an init-only one.
 | SET 1 Δfloor · pythia-14m | 36/36 seed pairs | complete | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; LMC barrier for M0 and M1-perm |
 | SET 1 Δfloor · pythia-31m | 36/36 seed pairs | complete | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; LMC barrier for M0 and M1-perm |
 | SET 1 Δfloor · pythia-70m | 36/36 seed pairs | complete | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; LMC barrier for M0 and M1-perm |
-| SET 1 Δfloor · pythia-160m | 28/36 seed pairs | partial | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; LMC barrier for M0 and M1-perm |
+| SET 1 Δfloor · pythia-160m | 30/36 seed pairs | partial | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; LMC barrier for M0 and M1-perm |
 | SET 1 Δfloor · pythia-410m | 3/15 seed pairs | partial | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; LMC barrier for M0 and M1-perm |
 | SET 1 control · pythia-160m-data | 3/3 pairs | complete | init-seed-only vs data-order-only, same rungs |
 | SET 1 control · pythia-160m-weight | 3/3 pairs | complete | init-seed-only vs data-order-only, same rungs |
-| SET 1 accuracy · BLiMP | pythia-14m: 36/36, pythia-31m: 11/36, pythia-70m: 35/36 | RAN | 67 paradigms from `nyu-mll/blimp`, minimal-pair sentence-logprob scoring, on the SAME merges |
-| SET 1 · REPAIR rung | pythia-14m: 36/36, pythia-70m: 4/36 | RAN | M4 = permutation-aligned average + pre-activation statistics repair; M5 = naive + repair; Δfloor and BLiMP on the same merges |
+| SET 1 accuracy · BLiMP | pythia-14m: 36/36, pythia-31m: 30/36, pythia-70m: 36/36, pythia-160m: 1/36 | RAN | 67 paradigms from `nyu-mll/blimp`, minimal-pair sentence-logprob scoring, on the SAME merges |
+| SET 1 · REPAIR rung | pythia-14m: 36/36, pythia-70m: 10/36 | RAN | M4 = permutation-aligned average + pre-activation statistics repair; M5 = naive + repair; Δfloor and BLiMP on the same merges |
 | SET 4 Δfloor · English-anchored | 4/4 language pairs (nld_Latn, spa_Latn, ell_Grek, pol_Latn) | complete | M0 naive · M1a vocab-transport · M1b/c vocab+unit-aligned · M1d/e forced-residual · M1f units-only · M1g/h embedding-row Procrustes |
 | SET 4 Δfloor · partner-anchored (reverse) | 4/4 language pairs | complete | same rungs, roles swapped |
 | SET 4 accuracy · MultiBLiMP 1.0 | 4/4 language pairs | RAN | `jumelet/multiblimp`, English + partner, on the SAME merges; UNK rate reported per cell |