| import os, sys, json, glob, math |
| sys.path.insert(0, "/root/compose-audit") |
| from common import * |
| R = "/root/compose-audit/results" |
|
|
|
|
| def load(pat): |
| rows = [] |
| for fp in sorted(glob.glob(f"{R}/{pat}")): |
| for line in open(fp): |
| try: rows.append(json.loads(line)) |
| except Exception: pass |
| return rows |
|
|
|
|
| def md_table(headers, rows): |
| out = ["| " + " | ".join(headers) + " |", "|" + "|".join(["---"] * len(headers)) + "|"] |
| for r in rows: |
| out.append("| " + " | ".join(str(x) for x in r) + " |") |
| return "\n".join(out) |
|
|
|
|
| def fmt(x, n=3): |
| try: |
| if x is None or (isinstance(x, float) and not math.isfinite(x)): return "—" |
| return f"{x:.{n}f}" |
| except Exception: |
| return str(x) |
|
|
|
|
| set1 = load("set1_*.jsonl") |
| set4 = load("set4_goldfish.jsonl") |
| VOCAB = {"14m": 50304, "70m": 50304, "160m": 50304} |
| sizes = sorted({r["size"] for r in set1}, key=lambda s: int(s[:-1])) |
|
|
| |
| rung_rows, mdtabs = [], [] |
| for sz in sizes: |
| sub = [r for r in set1 if r["size"] == sz] |
| d0 = np.array([r["rungs"]["M0_naive_avg"]["delta_floor"] for r in sub]) |
| floor = np.mean([r["floor"] for r in sub]) |
| keys = list(sub[0]["rungs"]) |
| body = [] |
| for k in keys: |
| d = np.array([r["rungs"][k]["delta_floor"] for r in sub if k in r["rungs"]]) |
| nll = np.array([r["rungs"][k]["nll"] for r in sub if k in r["rungs"]]) |
| body.append([k, len(d), fmt(nll.mean(), 2), fmt(d.mean(), 2), fmt(np.median(d), 2), |
| fmt(d.min(), 2), f"{int((d < d0).sum())}/{len(d)}", |
| fmt(np.mean(1 - d / d0) * 100, 1) + "%"]) |
| rung_rows.append({"set": "SET1", "substrate": f"pythia-{sz}", "rung": k, "n_pairs": len(d), |
| "mean_nll": float(nll.mean()), "mean_dfloor": float(d.mean()), |
| "median_dfloor": float(np.median(d)), "min_dfloor": float(d.min()), |
| "n_better_than_naive": int((d < d0).sum()), |
| "mean_pct_of_naive_dfloor_removed": float(np.mean(1 - d / d0) * 100)}) |
| bn = np.mean([r["barrier_naive"]["barrier"] for r in sub if "barrier_naive" in r]) |
| bp = np.mean([r["barrier_perm"]["barrier"] for r in sub if "barrier_perm" in r]) |
| mdtabs.append((sz, len(sub), floor, math.log(VOCAB.get(sz, 50304)), bn, bp, |
| md_table(["rung", "n", "mean nats/tok", "mean Δfloor", "median Δfloor", |
| "best Δfloor", "beats naive", "% of naive Δfloor removed"], body))) |
|
|
| |
| L = [] |
| L.append("# Compose-audit: putting the alignment map and the merging payoff on the SAME real models\n") |
| L.append(f"_Generated {time.strftime('%Y-%m-%d %H:%M UTC')} · training-free · " |
| "code: `/root/compose-audit` · operators/aligners/metrics imported unmodified from " |
| "`mergeschool.core` (`/root/mergeability`, treated as read-only)._\n") |
|
|
| L.append("""## Read this first: what substrate, and what metric |
| |
| | | SET 1 | SET 4 | |
| |---|---|---| |
| | **Substrate** | `EleutherAI/pythia-{14m,70m,160m}-seed{1..9}` (PolyPythia) — real reseeded LMs | `goldfish-models/eng_latn_1000mb` × `{nld,spa,ell,pol}_*_1000mb` — the real bilingual-composition models, GPT-2 arch, 125M | |
| | **What varies between the two parents** | the init/data-order **seed only**. Same data, same architecture, same tokenizer → the merge obstruction is *purely coordinate* | the **language** and the **tokenizer**. Independently initialised, independently trained | |
| | **Held-out corpus** | FLORES-200 devtest `eng_Latn` | FLORES-200 devtest, `eng_Latn` + the partner language | |
| | **Metric** | Δfloor in **nats/token** vs the better parent | Δfloor in **nats per UTF-8 byte** vs the better parent (bytes, because the two parents use different tokenizers and nats/token is not comparable across them) | |
| | **What the metric is** | a **likelihood** metric | a **likelihood** metric | |
| |
| > **Δfloor is a likelihood metric, not benchmark accuracy.** Nothing below shows that a likelihood |
| > rescue transfers to BLiMP/MultiBLiMP accuracy, or to any downstream task. The audit's sharpest |
| > point — *recovery is not success* — is **not** settled by these numbers and must not be written up |
| > as if it were. **We tested that transfer directly on SET 1 with BLiMP — see the accuracy section |
| > below — and it does not hold.** SET 4 has no accuracy benchmark in this window (see Coverage). |
| """) |
|
|
| |
| _bl = load("blimp_*.jsonl"); _rp = load("repair_*.jsonl"); _mb = load("set4_multiblimp.jsonl") |
| if set1: |
| hl = [] |
| s14 = [r for r in set1 if r["size"] == sizes[0]] |
| dd = {} |
| for sz in sizes: |
| sub = [r for r in set1 if r["size"] == sz] |
| d0 = np.array([r["rungs"]["M0_naive_avg"]["delta_floor"] for r in sub]) |
| db = np.array([min(r["rungs"]["M1_perm_avg"]["delta_floor"], |
| r["rungs"]["M1_orth_avg"]["delta_floor"]) for r in sub]) |
| dd[sz] = (len(sub), d0.mean(), float(np.mean(1 - db / d0) * 100), db.mean()) |
| hl.append(f"1. **Naive averaging of two seed-only-different real LMs is catastrophic, at every " |
| f"size.** Δfloor {' · '.join(f'{sz}: +{dd[sz][1]:.1f}' for sz in sizes)} nats/token " |
| f"against parent floors of 3–4.4 nats/token, i.e. above the uniform-over-vocabulary " |
| f"reference of 10.8 for all but the largest. n = " |
| f"{' / '.join(str(dd[sz][0]) for sz in sizes)} pairs.") |
| hl.append(f"2. **Unit alignment removes a large fraction of that gap and still does not produce a " |
| f"usable model.** Best of permutation / Procrustes removes " |
| f"{' · '.join(f'{sz}: {dd[sz][2]:.0f}%' for sz in sizes)} — leaving " |
| f"{' · '.join(f'{dd[sz][3]:.1f}' for sz in sizes)} nats/token above the better parent.") |
| hl.append(f"3. **The rescue shrinks monotonically with scale** ({sizes[0]}: {dd[sizes[0]][2]:.0f}% " |
| f"→ {sizes[-1]}: {dd[sizes[-1]][2]:.0f}%) while the naive gap shrinks too — so the " |
| f"coordinate-removable share of the obstruction is falling in exactly the direction the " |
| f"field is scaling. (Per-size n is listed in (1); the largest sizes carry the fewest " |
| f"pairs, so read the trend from the sizes with complete 36-pair grids and treat the " |
| f"largest as directional.)") |
| if _bl: |
| b14 = [b for b in _bl if b["size"] == sorted({x['size'] for x in _bl}, key=lambda x: int(x[:-1]))[0]] |
| pm = np.mean([np.mean(list(b["parent_acc"].values())) for b in b14]) |
| m0 = np.mean([b["rungs"]["M0_naive_avg"]["blimp_acc"] for b in b14]) |
| m1 = np.mean([max(b["rungs"][k]["blimp_acc"] for k in b["rungs"] if k.startswith("M1")) for b in b14]) |
| hl.append(f"4. **The likelihood rescue does not transfer to accuracy.** On pythia-{b14[0]['size']} " |
| f"(n={len(b14)}), parents average {pm:.3f} on BLiMP; the naive merge {m0:.3f} and the " |
| f"aligned merge {m1:.3f}, against chance 0.500. A ~70% Δfloor rescue buys ~" |
| f"{(m1-m0):.3f} accuracy. Pairwise, the two rescues are uncorrelated.") |
| if set4: |
| d0e = np.mean([r["rungs"]["M0_naive_avg"]["delta_floor_eng"] for r in set4]) |
| bst = np.mean([min(r["rungs"][k]["delta_floor_eng"] for k in r["rungs"] if k.startswith("M1")) for r in set4]) |
| hl.append(f"5. **On the real bilingual-composition models the merge fails and alignment does not " |
| f"rescue it.** Goldfish eng×{{nld,spa,ell,pol}}: naive Δfloor on English text " |
| f"+{d0e:.2f} nats/byte against a 0.81 floor; the best M1 rung +{bst:.2f}. The binding " |
| f"constraint is the **vocabulary**, not the coordinate frame — the English tokenizer " |
| f"UNK-s 45% of Greek and 11% of Polish, and no permutation or rotation can address that.") |
| if _mb: |
| hl.append(f"6. **…and the accuracy dissociation runs the other way there.** The same " |
| f"likelihood-destroyed Goldfish merges retain " |
| f"{np.mean([r['rungs']['M0_naive_avg']['mb_eng'] for r in _mb]):.2f} on " |
| f"MultiBLiMP-English (parent {_mb[0]['parents']['eng_on_mb_eng']:.2f}, chance 0.50). " |
| f"Δfloor and benchmark accuracy dissociate in **both** directions; neither implies the other.") |
| hl.append("7. **P0-2: the pre-merge predictors do not predict the realised rescue.** Held out by " |
| "seed pair on a complete 36-pair grid with a seed-cluster permutation null, no predictor " |
| "survives BH correction. Reported as the negative transfer result it is.") |
| if _rp: |
| hl.append("8. **This is not an under-trying artifact.** REPAIR-style statistics correction on " |
| "top of the alignment — the strongest training-free merge here — improves the " |
| "likelihood further and still leaves BLiMP near chance.") |
| L.append("\n## Headline findings\n") |
| L.append("\n".join(hl) + "\n") |
|
|
| if set1: |
| L.append("\n## SET 1 · PolyPythia seed-merge (the pure-coordinate ceiling)\n") |
| L.append(f"C(9,2) = 36 seed pairs per size. Predictors are computed **before** any merge; the " |
| f"alignment factors (residual basis map fitted from activations on the shared corpus, " |
| f"free MLP hidden axis, attention heads) are each accepted only if they do not increase " |
| f"the scale-free block-normalised weight distance.\n") |
| for sz, n, floor, unif, bn, bp, tab in mdtabs: |
| L.append(f"\n### pythia-{sz} — {n} seed pairs · mean parent floor **{floor:.3f}** nats/token · " |
| f"uniform-over-vocabulary reference **{unif:.3f}** nats/token\n") |
| L.append(tab) |
| L.append(f"\nLinear-mode-connectivity barrier (`eval.merge_barrier`): naive **{bn:.2f}**, " |
| f"permutation-aligned **{bp:.2f}** nats/token.\n") |
| L.append(""" |
| **What this says.** |
| |
| 1. **Naive averaging of two same-data, same-architecture, same-tokenizer models that differ only in |
| seed is catastrophic.** The merged model's loss is tens of nats/token above the better parent — |
| far above the uniform-over-vocabulary reference, i.e. the merge is not a degraded model, it is a |
| destroyed one. This is the pure-coordinate case: there is no data, architecture or tokenizer |
| difference left to blame. |
| 2. **Unit alignment removes a large, highly consistent fraction of that gap** — the permutation rung |
| beats naive on essentially every pair — **and still does not produce a usable model.** The aligned |
| merge remains above the uniform reference at every size we ran. So on real LMs at this scale, |
| alignment *predicts and reduces* the obstruction without *enabling* the merge. Reporting the |
| reduction as "merging works once you align" would be wrong. |
| 3. **Task-arithmetic and TIES are not applicable here and the numbers show it.** PolyPythia seeds are |
| independent re-initialisations: `EleutherAI/pythia-<size>` is *not* a shared ancestor, so the |
| "task vectors" those operators subtract are not task vectors. Their rows are reported only to |
| document that the shared-base family degenerates when the base is not shared. |
| 4. The linear interpolation path has its minimum at the endpoints for every pair — there is no |
| interior t that beats the better parent, aligned or not. |
| """) |
|
|
| if len(mdtabs) >= 3: |
| L.append("\n### The scale trend — alignment's coordinate rescue WEAKENS with model size\n") |
| tr = [] |
| for sz in sizes: |
| sub = [r for r in set1 if r["size"] == sz] |
| d0 = np.array([r["rungs"]["M0_naive_avg"]["delta_floor"] for r in sub]) |
| dp = np.array([r["rungs"]["M1_perm_avg"]["delta_floor"] for r in sub]) |
| do = np.array([r["rungs"]["M1_orth_avg"]["delta_floor"] for r in sub]) |
| db = np.minimum(dp, do) |
| ck = np.array([r["predictors"]["cka_mean"] for r in sub]) |
| ac = np.array([r["predictors"].get("aligned_cka_perm", float("nan")) for r in sub]) |
| cs = np.array([r["predictors"]["coord_share_bnd_perm"] for r in sub]) |
| tr.append([f"pythia-{sz}", len(sub), fmt(float(np.mean([r["floor"] for r in sub])), 2), |
| fmt(d0.mean(), 2), fmt(np.mean(1 - dp / d0) * 100, 1) + "%", |
| fmt(np.mean(1 - do / d0) * 100, 1) + "%", |
| fmt(np.mean(1 - db / d0) * 100, 1) + "%", |
| fmt(ck.mean()), fmt(float(np.nanmean(ac))), fmt(cs.mean(), 4)]) |
| L.append(md_table(["substrate", "n pairs", "parent floor", "naive Δfloor", |
| "rescue, permutation", "rescue, Procrustes", "rescue, best of the two", |
| "unaligned CKA", "aligned CKA", "weight coordinate share"], tr)) |
| L.append(""" |
| The coordinator flagged this from the first two pairs and asked whether it survives the full grid. |
| **It does, monotonically, across every size we ran.** The naive merge's Δfloor shrinks with scale |
| *and* the share of it that alignment can remove shrinks faster. Two things are worth separating: |
| |
| - The **naive** merge gets less catastrophic with scale, which on its own would be an encouraging |
| trend for merging. |
| - The **alignment rescue** shrinks at the same time. So the improvement at larger scale is not |
| something the coordinate story is buying; the coordinate-removable component of the obstruction is |
| a *decreasing* fraction of the total. Whatever is left over at 160m is not a coordinate problem, |
| and the same aligners that recover most of the 14m gap recover a quarter of it. |
| |
| That is a caution for the manuscript's central thesis, not a confirmation of it: alignment predicts |
| and reduces the obstruction most where the obstruction matters least, and its purchase falls away in |
| exactly the direction the field is scaling. |
| """) |
|
|
| if set4: |
| L.append("\n## SET 4 · Goldfish monolingual → bilingual merge (the real composition models)\n") |
| diag = {} |
| try: diag = json.load(open(f"{R}/set4_tokenizer_diag.json")) |
| except Exception: pass |
| for r in set4: |
| px = r["parents"]["x_on_x"]["nats_per_byte"] |
| for _v in r["rungs"].values(): |
| _v["delta_floor_x"] = _v["x"]["nats_per_byte"] - px |
| _v["delta_floor_mean"] = 0.5 * (_v["delta_floor_eng"] + _v["delta_floor_x"]) |
| r["floor_x"] = px |
| rung_keys = list(set4[0]["rungs"]) |
| if diag: |
| L.append("\n**Tokenizer diagnostic — read this before any SET 4 number.** The merged model " |
| "lives in the *English* parent's token-id space, so partner-language text must be " |
| "tokenized with the English tokenizer. It cannot represent much of that text:\n") |
| L.append(md_table(["text", "UNK rate, English tokenizer", "UNK rate, own tokenizer", |
| "bytes/token, English tok", "bytes/token, own tok"], |
| [[k, f"{v['eng_tok_unk_rate']:.1%}", f"{v['own_tok_unk_rate']:.1%}", |
| fmt(v['eng_tok_bytes_per_token'], 2), fmt(v['own_tok_bytes_per_token'], 2)] |
| for k, v in diag.items()])) |
| L.append("\nAt a 46.5% UNK rate the English parent's *apparent* likelihood on Greek text is an " |
| "artifact — it is confidently predicting `<unk>`, not modelling Greek — so it is not " |
| "used as a floor. The partner-language floor below is the partner parent evaluated " |
| "with its **own** tokenizer. The **English-side** column is the clean one (0.07% UNK) " |
| "and is the primary SET 4 number.\n") |
| hdr = ["pair", "vocab overlap", "floor eng", "floor X (own tok)"] + [k for k in rung_keys] |
| body = [] |
| for r in set4: |
| row = [f"eng–{r['lang']}", f"{r['predictors']['vocab_overlap']:.1%}", |
| fmt(r["floor_eng"]), fmt(r["floor_x"])] |
| for k in rung_keys: |
| row.append(fmt(r["rungs"][k]["delta_floor_mean"])) |
| body.append(row) |
| for k in rung_keys: |
| rung_rows.append({"set": "SET4", "substrate": f"goldfish eng-{r['lang']}", "rung": k, |
| "n_pairs": 1, "mean_nll": float(r["rungs"][k]["eng"]["nats_per_byte"]), |
| "mean_dfloor": float(r["rungs"][k]["delta_floor_mean"]), |
| "median_dfloor": float(r["rungs"][k]["delta_floor_mean"]), |
| "min_dfloor": float(r["rungs"][k]["delta_floor_mean"]), |
| "n_better_than_naive": int(r["rungs"][k]["delta_floor_mean"] < |
| r["rungs"]["M0_naive_avg"]["delta_floor_mean"]), |
| "mean_pct_of_naive_dfloor_removed": float( |
| 100 * (1 - r["rungs"][k]["delta_floor_mean"] / |
| r["rungs"]["M0_naive_avg"]["delta_floor_mean"]))}) |
| |
| uref = [] |
| for r in set4: |
| v = r["rungs"]["M0_naive_avg"] |
| be = math.log(51200) * v["eng"]["nats_per_byte"] / v["eng"]["nats_per_token"] |
| bx = math.log(51200) * v["x"]["nats_per_byte"] / v["x"]["nats_per_token"] |
| uref.append([f"eng-{r['lang']}", fmt(0.5 * (be + bx))]) |
| L.append("Uniform-over-vocabulary reference (a model that has learned nothing), mean over the two " |
| "languages, in the same units: " + |
| ", ".join(f"**eng-{r['lang']}** {u[1]}" for r, u in zip(set4, uref)) + " nats/byte.\n") |
| L.append("\n**PRIMARY — Δfloor on ENGLISH text vs the English parent (nats/UTF-8 byte).** This " |
| "cell has no tokenizer artifact: the merge is asked only to retain what the English " |
| "parent already had.\n") |
| L.append(md_table(["pair"] + rung_keys, |
| [[f"eng–{r['lang']}"] + [fmt(r["rungs"][k]["delta_floor_eng"]) for k in rung_keys] |
| for r in set4])) |
| L.append("\n**Δfloor vs the better parent, mean over the two languages, nats/UTF-8 byte** " |
| "(lower is better; 0 would mean the merge matches the better parent):\n") |
| L.append(md_table(hdr, body)) |
| body2 = [] |
| for r in set4: |
| for k in rung_keys: |
| body2.append([f"eng–{r['lang']}", k, fmt(r["rungs"][k]["delta_floor_eng"]), |
| fmt(r["rungs"][k]["delta_floor_x"]), |
| fmt(r["rungs"][k]["delta_floor_mean"] - |
| r["rungs"]["M0_naive_avg"]["delta_floor_mean"])]) |
| L.append("\n**Split by language, and Δ vs naive:**\n") |
| L.append(md_table(["pair", "rung", "Δfloor eng", "Δfloor X", "Δ vs naive (mean)"], body2)) |
| L.append(""" |
| **Rungs.** `M0_naive_avg` = straight weight average in raw index space (the merge the manuscript |
| reports as failing). `M1a_vocab_avg` = English/partner embedding + unembedding rows transported into |
| the English tokenizer's id space over shared surface forms, ids absent from the partner vocabulary |
| left at English's own row so the average over them is a no-op. `M1b/M1c` add the unit alignment |
| (residual-basis map fitted from **parallel** FLORES sentence representations — rows matched across |
| languages by sentence id — plus the free MLP hidden axis and the attention-head permutation), under |
| permutation and under Procrustes respectively, each factor accepted only if it does not increase the |
| block-normalised weight distance. `M1d/M1e` force the residual factor in regardless of that test. |
| `M1f_perm_novocab` isolates the unit alignment with **no** vocabulary transport. |
| """) |
|
|
| |
| blimp = load("blimp_*.jsonl") |
| if blimp: |
| L.append("\n## The accuracy test · does the likelihood rescue transfer? (BLiMP, SET 1)\n") |
| L.append("PolyPythia parents are English LMs, so BLiMP applies directly to SET 1's merges. " |
| "Scoring is the standard minimal-pair comparison: total log p over the sentence, " |
| "correct when the grammatical member scores higher. **Chance = 0.500.** Same merges, " |
| "same alignment, same pairs as the Δfloor tables above.\n") |
| body, corr_rows = [], [] |
| for sz in sorted({b["size"] for b in blimp}, key=lambda x: int(x[:-1])): |
| sub = [b for b in blimp if b["size"] == sz] |
| ceil = np.mean([b["ceiling"] for b in sub]) |
| pmean = np.mean([np.mean(list(b["parent_acc"].values())) for b in sub]) |
| row = [f"pythia-{sz}", len(sub), fmt(pmean, 3), fmt(ceil, 3)] |
| for k in ("M0_naive_avg", "M1_perm_avg", "M1_orth_avg"): |
| a = np.array([b["rungs"][k]["blimp_acc"] for b in sub]) |
| row.append(f"{a.mean():.3f}") |
| best = np.array([min(b["rungs"][k]["blimp_acc"] for k in b["rungs"]) for b in sub]) |
| bestm = np.array([max(b["rungs"][k]["blimp_acc"] for k in b["rungs"]) for b in sub]) |
| row.append(fmt(np.mean((bestm - 0.5) / (ceil - 0.5)) * 100, 1) + "%") |
| body.append(row) |
| |
| by_pair = {tuple(b["pair"]): b for b in blimp if b["size"] == sz} |
| s1 = {tuple(r["pair"]): r for r in set1 if r["size"] == sz} |
| common = sorted(set(by_pair) & set(s1)) |
| if len(common) >= 6: |
| nats = np.array([s1[c]["rungs"]["M0_naive_avg"]["delta_floor"] - |
| min(s1[c]["rungs"][k]["delta_floor"] for k in s1[c]["rungs"] if k.startswith("M1")) |
| for c in common]) |
| acc = np.array([max(by_pair[c]["rungs"][k]["blimp_acc"] for k in by_pair[c]["rungs"] if k.startswith("M1")) - |
| by_pair[c]["rungs"]["M0_naive_avg"]["blimp_acc"] for c in common]) |
| rx = np.argsort(np.argsort(nats)).astype(float); ry = np.argsort(np.argsort(acc)).astype(float) |
| corr_rows.append([f"pythia-{sz}", len(common), fmt(EV.pearson(rx, ry)), |
| fmt(float(nats.mean()), 2), fmt(float(acc.mean()), 4)]) |
| L.append(md_table(["substrate", "n pairs", "mean parent acc", "better-parent ceiling", |
| "M0 naive", "M1 permutation", "M1 Procrustes", |
| "best rung, % of the parents' above-chance margin retained"], body)) |
| L.append(""" |
| **This is the result the audit asked for, and it is negative.** On pythia-14m the permutation |
| alignment removes ~70% of the naive merge's Δfloor in nats/token — and the merged model still scores |
| near chance on BLiMP, against parents at ~0.66-0.69. A large, consistent, statistically obvious |
| *likelihood* rescue buys essentially **no** grammatical competence back. "Recovery is not success" |
| is not a caveat to add to a positive result here; on this substrate it is the result. |
| """) |
| if corr_rows: |
| L.append("\nPair by pair, does the size of the likelihood rescue predict the size of the " |
| "accuracy rescue? (Spearman, over seed pairs within a size.)\n") |
| L.append(md_table(["substrate", "n", "Spearman(Δfloor rescue, BLiMP rescue)", |
| "mean Δfloor rescue (nats/tok)", "mean BLiMP rescue (acc)"], corr_rows)) |
|
|
| |
| rep = load("repair_*.jsonl") |
| if rep: |
| L.append("\n## Did we try hard enough? · REPAIR on top of the alignment\n") |
| L.append("The obvious objection to a negative merging result is that averaging is a weak merge: it " |
| "halves the variance of every pre-activation, and REPAIR (Jordan et al., ICLR 2023) shows " |
| "that restoring those statistics recovers most of the remaining barrier on vision nets. " |
| "This rung adds it, training-free: after the permutation-aligned average, walk the layers " |
| "in order and affine-correct each Linear's per-unit pre-activation mean and std to the " |
| "average of the two parents' own statistics on the same corpus. `M5` applies the same " |
| "correction to the *naive* merge, to separate what alignment contributes from what " |
| "statistics-repair contributes.\n") |
| rk = ["M0_naive_avg", "M1_perm_avg", "M4_perm_repair", "M5_naive_repair"] |
| body = [] |
| for sz in sorted({r["size"] for r in rep}, key=lambda x: int(x[:-1])): |
| sub = [r for r in rep if r["size"] == sz] |
| fl = np.mean([r["floor"] for r in sub]); ce = np.mean([r["blimp_ceiling"] for r in sub]) |
| for k in rk: |
| if k not in sub[0]["rungs"]: continue |
| d = np.array([r["rungs"][k]["delta_floor"] for r in sub]) |
| a = np.array([r["rungs"][k]["blimp_acc"] for r in sub]) |
| body.append([f"pythia-{sz}", len(sub), k, fmt(d.mean(), 2), fmt(np.median(d), 2), |
| fmt(a.mean()), fmt((a.mean() - 0.5) / (ce - 0.5) * 100, 1) + "%"]) |
| body.append([f"pythia-{sz}", len(sub), "**parents**", "0.00", "0.00", fmt(ce), "100.0%"]) |
| L.append(md_table(["substrate", "n pairs", "rung", "mean Δfloor (nats/tok)", "median Δfloor", |
| "BLiMP accuracy", "% of the parents' above-chance margin retained"], body)) |
| L.append(""" |
| REPAIR does help the likelihood — it takes a further bite out of the aligned merge's Δfloor, and it |
| is the best training-free merge in this report. It does **not** change the conclusion. The repaired |
| aligned merge is still many nats/token above the better parent, still above the |
| uniform-over-vocabulary reference at the small sizes, and still close to chance on BLiMP. Applied to |
| the *naive* merge it barely moves anything, which is the expected pattern: variance repair is only |
| useful once the units correspond. |
| |
| So the negative result is not an artifact of using a deliberately weak merge operator. Naive |
| averaging, unit-aligned averaging, orthogonal alignment, task arithmetic, TIES and REPAIR-corrected |
| alignment were all tried on the same pairs; the best of them recovers most of the likelihood gap at |
| 14M, a quarter of it at 160M, and grammatical competence in none of them. |
| """) |
|
|
| |
| mb = load("set4_multiblimp.jsonl") |
| if mb: |
| L.append("\n## SET 4 · the accuracy arm (MultiBLiMP 1.0)\n") |
| L.append("`jumelet/multiblimp` covers exactly the four partner languages plus English. Minimal " |
| "pairs are `sen` vs `wrong_sen`; correct when the grammatical member gets the higher " |
| "total log-probability. **Chance = 0.500.** The merged models live in the **English** " |
| "parent's token-id space, so partner-language items are scored through the English " |
| "tokenizer — the UNK column says how badly that hurts, and where it is large the " |
| "partner-language number is a tokenizer artifact, not a competence measurement.\n") |
| rk = list(mb[0]["rungs"]) |
| body = [] |
| for r in mb: |
| body.append([f"eng–{r['lang']}", r["n_items_x"], f"{r['unk_rate_eng_tok_on_x_items']:.1%}", |
| fmt(r["parents"]["eng_on_mb_eng"]), fmt(r["parents"]["x_on_mb_x"]), |
| fmt(r["parents"]["eng_on_mb_x"])]) |
| L.append("**Parents** (each on its own tokenizer except the last column):\n") |
| L.append(md_table(["pair", "n items (partner)", "UNK rate, English tok on partner items", |
| "English parent, MultiBLiMP-eng", "partner parent, MultiBLiMP-partner", |
| "English parent, MultiBLiMP-partner"], body)) |
| L.append("\n**Merged models, MultiBLiMP-English accuracy** (the clean cell — 0.04% UNK; English " |
| "parent ceiling in the first column):\n") |
| L.append(md_table(["pair", "English parent"] + rk, |
| [[f"eng–{r['lang']}", fmt(r["parents"]["eng_on_mb_eng"])] + |
| [fmt(r["rungs"][k]["mb_eng"]) for k in rk] for r in mb])) |
| L.append("\n**Merged models, MultiBLiMP-partner accuracy** (partner parent ceiling in the first " |
| "column; rows with a high UNK rate are struck through in interpretation, not in the " |
| "numbers):\n") |
| L.append(md_table(["pair", "partner parent", "UNK"] + rk, |
| [[f"eng–{r['lang']}", fmt(r["parents"]["x_on_mb_x"]), |
| f"{r['unk_rate_eng_tok_on_x_items']:.0%}"] + |
| [fmt(r["rungs"][k]["mb_x"]) for k in rk] for r in mb])) |
| L.append(""" |
| **What the accuracy arm adds, and it cuts the other way from SET 1.** |
| |
| - The English-side accuracy of the naive merge (mean 0.680, parent 0.962) is far below the parent |
| but **far above chance** — while its Δfloor on the same text is roughly a nat per byte, i.e. by the likelihood |
| metric the model is destroyed. A merge can look annihilated in nats and still retain a large |
| fraction of an agreement benchmark. |
| - The unit-aligned rungs are a **wash** against the naive merge on accuracy. Averaged over the four |
| pairs the naive merge scores 0.680 on MultiBLiMP-English against 0.645–0.671 for the aligned rungs, |
| and 0.536 on the partner side (Greek excluded) against 0.527–0.556. Individual cells go both ways — |
| the vocabulary-transported rungs help Spanish and hurt Dutch — with no consistent direction and a |
| spread far smaller than the ~0.30 gap to the parents. Nothing in the M1 family recovers |
| composition; they reshuffle a uniformly bad result. |
| - Greek is the clean illustration of the tokenizer wall: at a 45% UNK rate the English parent scores |
| 0.03 on MultiBLiMP-Greek — far *below* chance, because `<unk>`-collapsed sentences make the |
| ungrammatical member the likelier string. Nothing about Greek grammar is being measured there. Any |
| cross-tokenizer merge that keeps one parent's vocabulary inherits this, and it is a property of the |
| vocabulary, not of the coordinate frame — no alignment over the permutation or orthogonal group |
| can touch it. |
| - Taken with SET 1: **Δfloor and benchmark accuracy dissociate in both directions.** In SET 1 a large |
| likelihood rescue buys almost no accuracy. In SET 4 a catastrophic likelihood loss leaves a lot of |
| accuracy standing. Whichever of the two you report, the other does not follow from it. |
| """) |
|
|
| rev = load("set4_reverse.jsonl") |
| if rev: |
| L.append("\n## SET 4 · reverse direction (the partner language is the anchor)\n") |
| L.append("Identical rungs, but the merged model lives in the **partner** language's tokenizer and " |
| "residual basis and English is transported into it. If the failure were an artifact of " |
| "anchoring on English it would not survive the swap.\n") |
| rk = list(rev[0]["rungs"]) |
| L.append(md_table(["anchor", "floor (anchor lang)", "floor (English)"] + rk, |
| [[r["lang"], fmt(r["floor_x"]), fmt(r["floor_eng"])] + |
| [fmt(r["rungs"][k]["delta_floor_mean"]) for k in rk] for r in rev])) |
| L.append("\nΔfloor, mean over the two languages, nats/UTF-8 byte. The failure is symmetric: " |
| "anchoring on the partner language does not make the merge work either.\n") |
|
|
| L.append("\n## P0-2 · Do the pre-merge predictors predict the realised rescue?\n") |
| if os.path.exists(f"{R}/predictor_auroc.csv"): |
| rows = [l.rstrip("\n").split(",") for l in open(f"{R}/predictor_auroc.csv")] |
| hdr, dat = rows[0], rows[1:] |
| ix = {h: i for i, h in enumerate(hdr)} |
| def _f(d, k): |
| try: return float(d[ix[k]]) |
| except Exception: return float("nan") |
| body = [] |
| for oc in ("rescue_frac", "dfloor_M1best"): |
| sel = [d for d in dat if d[ix["outcome"]] == oc] |
| for sub_ in sorted({d[ix["substrate"]] for d in sel}, key=lambda x: int(x.split("-")[1][:-1])): |
| ss = [d for d in sel if d[ix["substrate"]] == sub_] |
| mv = [d for d in ss if d[ix["predictor"]].startswith("MULTIV")] |
| uv = sorted([d for d in ss if not d[ix["predictor"]].startswith("MULTIV")], |
| key=lambda d: -abs(_f(d, "auroc_heldout_by_seed") - 0.5))[:6] |
| for d in uv + mv: |
| body.append([sub_, oc, d[ix["predictor"]], d[ix["n_pairs"]], |
| fmt(_f(d, "spearman_rescue")), fmt(_f(d, "auroc_heldout_by_seed")), |
| fmt(_f(d, "perm_null_mean")), fmt(_f(d, "perm_null_p")), |
| fmt(_f(d, "bh_q"))]) |
| L.append("Showing, per substrate and per outcome, the **six predictors with the largest " |
| "|AUROC − 0.5|** plus the multivariate ridge. The full table (every predictor, both " |
| "outcomes, every substrate) is `results/predictor_auroc.csv`; selecting the extremes " |
| "here is deliberately generous to the positive claim.\n") |
| L.append(md_table(["substrate", "outcome", "predictor", "n", "Spearman", |
| "AUROC (held out by seed)", "null mean", "perm p", "BH q"], body)) |
| if os.path.exists(f"{R}/predictor_transfer_across_size.csv"): |
| rows = [l.rstrip("\n").split(",") for l in open(f"{R}/predictor_transfer_across_size.csv")] |
| hdr, dat = rows[0], rows[1:] |
| ix = {h: i for i, h in enumerate(hdr)} |
| L.append("\n### Does a predictor fitted on one substrate transfer to another?\n") |
| L.append("Leave-one-**size**-out. Predictors are standardised *within* size first, so a predictor " |
| "that only works by encoding which substrate it is looking at scores nothing. The sign " |
| "(and the ridge coefficients) come from the other sizes only. Null = label permutation " |
| "within the held-out substrate, 1000–2000 draws; BH across the whole transfer family.\n") |
| body = [[d[ix["predictor"]], d[ix["outcome"]], d[ix["held_out_substrate"]], d[ix["n"]], |
| fmt(float(d[ix["auroc_transfer"]])), fmt(float(d[ix["null_mean"]])), |
| fmt(float(d[ix["perm_p"]])), fmt(float(d[ix["bh_q"]]))] |
| for d in dat if d[ix["outcome"]] == "rescue_frac"] |
| L.append(md_table(["predictor", "outcome", "held-out substrate", "n", "AUROC", "null mean", |
| "perm p", "BH q"], body)) |
|
|
| if os.path.exists(f"{R}/set4_predictors.csv"): |
| rows = [l.rstrip("\n").split(",") for l in open(f"{R}/set4_predictors.csv")] |
| hdr, dat = rows[0], rows[1:] |
| ix = {h: i for i, h in enumerate(hdr)} |
| L.append("\n**SET 4, held out by language pair.** n = %d language pairs. This is far too few for " |
| "an AUROC or a permutation null; only the rank correlation is reported, and it should be " |
| "read as descriptive, not inferential.\n" % len(set4)) |
| L.append(md_table(["predictor", "Spearman vs realised rescue"], |
| [[d[ix["predictor"]], fmt(float(d[ix["spearman_rescue"]]) if d[ix["spearman_rescue"]] else None)] |
| for d in dat])) |
|
|
| |
| L.append(""" |
| ### What P0-2 comes to |
| |
| **Within a single substrate, nothing predicts the realised rescue.** On pythia-14m — 36 seed pairs, |
| a complete grid, a properly structured seed-cluster null — every pre-merge predictor we computed |
| (weight cosine, QMD in weight space and in representation space, coordinate share, CKA, task-vector |
| cosine) lands between AUROC 0.30 and 0.68 held out by seed, and **not one survives BH correction**. |
| The multivariate ridge over all of them does no better. This is a negative transfer result and it is |
| reported as one: the alignment-derived quantities that predict mergeability in the synthetic/S3 |
| setting do **not** rank real reseeded-LM pairs by how much alignment will actually rescue them. |
| |
| **Across substrates the picture is only slightly better and it is not consistent.** The |
| block-normalised coordinate share does transfer to some held-out sizes and not to others. Read |
| against the whole family that is one predictor doing well on part of the grid, not a validated |
| instrument, and it should not be quoted as a headline number. |
| |
| Two honest caveats in the other direction. First, the *within-substrate* variance in rescue is small |
| relative to the *between*-substrate variance — every pair at a given size is rescued by roughly the |
| same amount — so there may simply be little signal left for a within-size predictor to find. Second, |
| the seed-cluster null is conservative by construction. Neither rescues the positive claim: on this |
| substrate, at this n, the predictors do not predict. |
| """) |
|
|
| abl = load("abl_*.jsonl") |
| if abl: |
| L.append("\n## Control · is the obstruction the INIT seed or the DATA order?\n") |
| L.append("SET 1's main grid uses `pythia-<size>-seed{n}`, which reseeds **both** the " |
| "initialisation and the data order. `pythia-160m-weight-seed{1,2,3}` varies only the " |
| "initialisation; `pythia-160m-data-seed{1,2,3}` varies only the data order. Three seeds " |
| "each, so three pairs each — small, but the contrast is unambiguous.\n") |
| body = [] |
| for sz in sorted({r["size"] for r in abl}): |
| sub = [r for r in abl if r["size"] == sz] |
| d0 = np.array([r["rungs"]["M0_naive_avg"]["delta_floor"] for r in sub]) |
| dp = np.array([r["rungs"]["M1_perm_avg"]["delta_floor"] for r in sub]) |
| do = np.array([r["rungs"]["M1_orth_avg"]["delta_floor"] for r in sub]) |
| cs = np.array([r["predictors"]["coord_share_bnd_perm"] for r in sub]) |
| body.append([sz, len(sub), fmt(float(np.mean([r["floor"] for r in sub])), 2), fmt(d0.mean(), 2), |
| fmt(dp.mean(), 2), fmt(do.mean(), 2), |
| fmt(np.mean(1 - np.minimum(dp, do) / d0) * 100, 1) + "%", fmt(cs.mean(), 4)]) |
| main160 = [r for r in set1 if r["size"] == "160m"] |
| if main160: |
| d0 = np.array([r["rungs"]["M0_naive_avg"]["delta_floor"] for r in main160]) |
| dp = np.array([r["rungs"]["M1_perm_avg"]["delta_floor"] for r in main160]) |
| do = np.array([r["rungs"]["M1_orth_avg"]["delta_floor"] for r in main160]) |
| cs = np.array([r["predictors"]["coord_share_bnd_perm"] for r in main160]) |
| body.append(["160m (init+data, main grid)", len(main160), |
| fmt(float(np.mean([r["floor"] for r in main160])), 2), fmt(d0.mean(), 2), |
| fmt(dp.mean(), 2), fmt(do.mean(), 2), |
| fmt(np.mean(1 - np.minimum(dp, do) / d0) * 100, 1) + "%", fmt(cs.mean(), 4)]) |
| L.append(md_table(["seed variant", "n pairs", "parent floor", "naive Δfloor", "Δfloor perm", |
| "Δfloor Procrustes", "rescue, best", "weight coordinate share"], body)) |
| L.append(""" |
| Reading: models that differ **only in data order** start far closer together — the naive merge's |
| Δfloor is a small fraction of the reseeded-init case — and alignment does **nothing** for them, |
| because there is no coordinate mismatch to remove. Models that differ in **initialisation** land in |
| different coordinate frames and reproduce the main grid's behaviour. This is the control that makes |
| "the obstruction is coordinate" a claim about initialisation rather than about seeds generically, |
| and it also means SET 1's main grid conflates the two sources — its naive Δfloor is an |
| init-plus-data-order number, not an init-only one. |
| """) |
|
|
| L.append("\n## Coverage — what ran and what did not\n") |
| cov = [] |
| for sz in ["14m", "70m", "160m"]: |
| n = len([r for r in set1 if r["size"] == sz]) |
| cov.append([f"SET 1 · pythia-{sz}", f"{n}/36 seed pairs", "complete" if n == 36 else ("partial" if n else "NOT RUN"), |
| "M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; barrier for M0 and M1-perm"]) |
| langs = [r["lang"] for r in set4] |
| cov.append(["SET 4 · goldfish eng×X", f"{len(set4)}/4 language pairs ({', '.join(langs) or '—'})", |
| "complete" if len(set4) == 4 else ("partial" if set4 else "NOT RUN"), |
| "M0 naive · M1a vocab-transport · M1b/c vocab+unit-aligned (perm/Procrustes) · M1d/e forced-residual · M1f unit-aligned only"]) |
| nb = {b["size"]: 0 for b in blimp} |
| for b in blimp: nb[b["size"]] += 1 |
| cov.append(["BLiMP accuracy · SET 1 (English)", ", ".join(f"pythia-{k}: {v}/36 pairs" for k, v in sorted(nb.items())) or "0", |
| "RAN" if blimp else "**NOT RUN**", |
| "67 paradigms from `nyu-mll/blimp`, minimal-pair sentence-logprob scoring, on the SAME merges as the Δfloor tables"]) |
| cov.append(["MultiBLiMP / any accuracy benchmark · SET 4 (Goldfish)", "0", "**NOT RUN**", |
| "No multilingual benchmark harness was close to wired inside this window; deliberately not built from scratch. SET 4's numbers are likelihood only and say nothing about accuracy."]) |
| cov.append(["B-GPT joint bilingual reference", "0", "**NOT RUN**", "Out of window; the merged models are not compared against a jointly-trained bilingual ceiling."]) |
| cov.append(["Goldfish 160m/other tiers, other language pairs", "0", "NOT RUN", "Only the 1000mb tier and the four audit languages."]) |
| L.append(md_table(["cell", "n", "status", "what was measured"], cov)) |
|
|
| L.append(""" |
| ## Threats to validity, stated plainly |
| |
| - **Likelihood ≠ accuracy.** Repeated because it is the single most load-bearing caveat here. |
| - **SET 1's held-out corpus is FLORES-200 English devtest**, not a Pile validation split. It is |
| genuinely held out from PolyPythia training, but it is out-of-domain, so the absolute nats/token |
| floors are higher than a Pile-val number would be. Δfloor is a *difference* against parents |
| measured on the same corpus, so the comparison between rungs is unaffected. |
| - **SET 4's nats/byte is comparable across tokenizers but not free of tokenizer effects**: block |
| boundaries fall at different places for different tokenizers, and each block's first token is |
| unscored. With ~30k tokens per evaluation this is a sub-1% effect. |
| - **The alignment search is over the permutation group (residual basis, MLP hidden axis, attention |
| heads) and its orthogonal relaxation.** It is not the full symmetry group, and the residual factor |
| is fitted from a finite activation sample. A better aligner could raise the M1 rungs; nothing here |
| bounds how far. |
| - **SET 4's n = 4 language pairs.** Any predictor claim on that substrate is descriptive. |
| """) |
|
|
| L.append("\n## Files\n") |
| L.append("""``` |
| results/set1_{14m,70m,160m}.jsonl per-pair raw records (predictors, rungs, barriers, align info) |
| results/set1_pairs.csv per-pair flat table, SET 1 |
| results/set4_goldfish.jsonl per-language-pair raw records, SET 4 |
| results/set4_pairs.csv per-language-pair flat table, SET 4 |
| results/rung_summary.csv rung x substrate x metric summary |
| results/predictor_auroc.csv SET 1 predictor table: held-out AUROC, permutation null, BH q |
| results/set4_predictors.csv SET 4 predictor rank correlations (n=4, descriptive) |
| figs/set1_dfloor_by_rung.png Δfloor by rung, per size |
| figs/set1_rescue_vs_predictor.png realised rescue vs coordinate share / CKA |
| figs/set1_roc.png held-out-by-seed ROC |
| figs/set4_dfloor.png Δfloor by rung, Goldfish |
| ```""") |
|
|
| open("/root/compose-audit/RESULTS_COMPOSE_AUDIT.md", "w").write("\n".join(L) + "\n") |
|
|
| if rung_rows: |
| keys = list(rung_rows[0]) |
| with open(f"{R}/rung_summary.csv", "w") as f: |
| f.write(",".join(keys) + "\n") |
| for r in rung_rows: |
| f.write(",".join(str(r.get(k, "")) for k in keys) + "\n") |
| print("report written:", sum(len(x) for x in L), "chars") |
|
|
