| 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. No accuracy benchmark was run inside this window (see Coverage). |
| """) |
|
|
| 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 set4: |
| L.append("\n## SET 4 · Goldfish monolingual → bilingual merge (the real composition models)\n") |
| rung_keys = list(set4[0]["rungs"]) |
| hdr = ["pair", "vocab overlap", "floor eng", "floor X"] + [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("**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. |
| """) |
|
|
| 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)} |
| body = [] |
| for d in dat: |
| body.append([d[ix["substrate"]], d[ix["predictor"]], d[ix["n_pairs"]], |
| fmt(float(d[ix["spearman_rescue"]]) if d[ix["spearman_rescue"]] else None), |
| fmt(float(d[ix["auroc_heldout_by_seed"]]) if d[ix["auroc_heldout_by_seed"]] else None), |
| fmt(float(d[ix["perm_null_mean"]]) if d[ix["perm_null_mean"]] else None), |
| fmt(float(d[ix["perm_null_p"]]) if d[ix["perm_null_p"]] else None), |
| fmt(float(d[ix["bh_q"]]) if d[ix["bh_q"]] else None)]) |
| L.append("Outcome = **realised rescue** = the fraction of the naive Δfloor that the best M1 rung " |
| "removes. Label = above the within-size median. Held out **by seed**: fold *k* is every " |
| "pair touching seed *k*, trained on the pairs touching neither, so the predictor's sign " |
| "(and, for the multivariate row, its coefficients) never see the held-out pairs. Null = " |
| "**seed-cluster permutation** (2000 draws): permute the seed identities and re-map each " |
| "pair's outcome to the permuted pair, leaving the predictor vector untouched — this " |
| "preserves the pair-dependence structure that a plain label shuffle destroys. " |
| "BH-corrected across the predictor family.\n") |
| L.append(md_table(["substrate", "predictor", "n", "Spearman", "AUROC (held out by seed)", |
| "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("\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"]) |
| cov.append(["BLiMP / MultiBLiMP accuracy", "0", "**NOT RUN**", |
| "No benchmark harness was close to wired inside this window. Deliberately not built from scratch. The Δfloor results below therefore 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") |
|
|
