diag(#40): z-norm scores within family, winsorized 2-threshold Otsu zones, --feats offline mode

Synthetic and live scores share an axis with meaningful zero (raw scores carry a
common <mu,v> offset since v = mean diff is not orthogonal to the family mean).
Zones come from label-free online stats (EMA mean/std + Otsu valley), replacing
mean+k*sd which placed both cuts beyond every distribution. Winsorize at 1/99%
before Otsu: variance-maximizing cuts otherwise buy a class for one outlier.
Fresh-eyes review verified z-norm is affine (AUROCs unchanged), zones label-free,
P/R recompute from parquet matches titles.

Co-Authored-By: Claudypoo <288921227+claudypoo@users.noreply.github.com>

scripts/diag_pinning.py

@@ -36,11 +36,17 @@ v for each representation comes only from authored pairs (mean hack-minus-clean,
 normalized per module). Ground-truth labels from training rollouts are used only for
 diagnostic AUROC and precision measurements, never for routing.
 
-PINNING. Each panel shades the three zones the online gate rule would give on this
+DISPLAY + PINNING. Scores are plotted Z-NORMALIZED WITHIN FAMILY: live scores by the
-window: keep (bulk) | absorb (score > mean + k_mid*sd) | rout (>= mean + k_rout*sd),
+mean/std of all valid live rollouts, synthetic scores by the mean/std of the joint
-plus the oracle best hack-vs-rest split for reference. k's default to the real-run
+clean+hack pair scores. Affine per family, so every AUROC is unchanged; it puts both
-Config values (2/3), not the checkpoint's preset, so the plot answers "where WOULD
+families on one axis with a meaningful zero. (Raw scores share an offset <mu, v>:
-the cuts fall", overridable via --k-mid/--k-rout.
+v = mean(hack-clean) guarantees only the GAP between sides, not its location, and the
+authored-pair common mean is not orthogonal to v, so uncentered both pair sides land
+positive.) Zones keep | absorb | rout come from two-threshold Otsu on the live
+z-scores -- the label-free valley cuts an online gate could compute from a rolling
+score window (EMA mean/std + valley search). The previous mean+k*sd rule modeled
+hacks as a rare outlier tail and put both cuts beyond every distribution (hack share
+in these windows is 35-43%); the oracle hack-vs-rest split is drawn for reference.
 
 CAVEAT. Live advantages are reconstructed from rollouts.jsonl students only (teachers
 absent, zero-variance groups included, and skipped/empty completions missing from the
@@ -53,7 +59,9 @@ downstream (subset vectors, 4 scores, zones, table) is offline re-projection of
 cached features.
 
     uv run python scripts/diag_pinning.py --run-dir out/runs/<vanilla_lora2r_run>
-    uv run python scripts/diag_pinning.py --replot out/diag/pinning_data.parquet  # no GPU
+    uv run python scripts/diag_pinning.py --feats out/diag/pinning_feats.pt   # no GPU:
+                                          # recompute scores/table/plot from cached feats
+    uv run python scripts/diag_pinning.py --replot out/diag/pinning_data.parquet  # plot only
 outputs (out/diag/): pinning_q2.png (3x2 headline), pinning_data.parquet (per-rollout
 scores), pinning_pairset.parquet + printed table (subsets x 6 AUROCs),
 pinning_feats.pt (raw features, for offline re-analysis).
@@ -105,11 +113,10 @@ class Cfg:
     step_lo: int = 2
     step_hi: int = 9
     max_rollouts: int = 240
-    k_mid: float = 2.0    # absorb onset: score > mean + k_mid*sd  (real-run Config default)
-    k_rout: float = 3.0   # rout onset:   score >= mean + k_rout*sd
     adv_eps: float = 1e-6  # |A| below this = no update exists -> dropped from zones/AUROC
     resid_layers: tuple[int, ...] = (12, 18, 24)  # residual-stream capture depths (of 36)
     random_v_seed: int | None = None      # Haar placebo (sanity: nothing should separate)
+    feats: Path | None = None             # cached pinning_feats.pt -> full offline re-analysis
     replot: Path | None = None            # load parquet and re-plot only (no model, no GPU)
     out_dir: Path = Path("out/diag")
 
@@ -209,13 +216,35 @@ def _kde(x: np.ndarray, grid: np.ndarray) -> np.ndarray:
     return np.exp(-0.5 * z ** 2).sum(1) / (len(x) * bw * np.sqrt(2 * np.pi))
 
 
-def plot_q2(df: pl.DataFrame, k_mid: float, k_rout: float, subtitle: str, out_png: Path) -> dict:
+def _otsu3(x: np.ndarray) -> tuple[float, float]:
-    """2x2 figure ({grad,act} x {cos,dot}) from the saved per-rollout scores -- no GPU.
+    """Two-threshold Otsu: the pair of cuts maximizing 3-class between-class variance.
+    Label-free -- an online gate can compute this from a rolling window of scores, so
+    using it here is not oracle leakage. O(n^2), fine for a few hundred scores.
+    Scores are winsorized at 1/99% first: Otsu maximizes variance, so on heavy-tailed
+    scores a single extreme point otherwise buys a whole class (seen on grad_dot)."""
+    x = np.clip(x, *np.quantile(x, [0.01, 0.99]))
+    s = np.sort(np.asarray(x, float))
+    n = len(s)
+    c = np.concatenate([[0.0], np.cumsum(s)])
+    best, best_ij = -np.inf, (1, 2)
+    for i in range(1, n - 1):
+        for j in range(i + 1, n):
+            obj = c[i] ** 2 / i + (c[j] - c[i]) ** 2 / (j - i) + (c[n] - c[j]) ** 2 / (n - j)
+            if obj > best:
+                best, best_ij = obj, (i, j)
+    i, j = best_ij
+    return float((s[i - 1] + s[i]) / 2), float((s[j - 1] + s[j]) / 2)
+
+
+def plot_q2(df: pl.DataFrame, subtitle: str, out_png: Path) -> dict:
+    """3x2 figure ({grad,act,resid} x {cos,dot}) from the saved per-rollout scores -- no GPU.
 
     Per panel: live solve/fail/hack+ KDEs (+ thin hack- if n>=3), synthetic pair sides
-    dashed, three shaded zones keep|absorb|rout from mean + k*sd over the VALID live
+    dashed, all Z-NORMALIZED WITHIN FAMILY (live by valid-live mean/std, synthetic by
-    scores (|A|>eps; pop 'on_drop' excluded), oracle split, AUROC + P/R at the rout cut.
+    joint clean+hack mean/std; affine, AUROC unchanged) so both families share one axis
-    Returns the per-case stats dict for logging."""
+    with a meaningful zero. Three shaded zones keep|absorb|rout from two-threshold Otsu
+    on the live z-scores (label-free, online-computable), oracle split, AUROC + P/R at
+    the rout cut. Returns the per-case stats dict for logging."""
     pops = {p: df.filter(pl.col("pop") == p) for p in df["pop"].unique().to_list()}
     live_pops = ["on_solve", "on_fail", "on_hackpos", "on_hackneg"]
     live = df.filter(pl.col("pop").is_in(live_pops))
@@ -232,10 +261,16 @@ def plot_q2(df: pl.DataFrame, k_mid: float, k_rout: float, subtitle: str, out_pn
     fig, axes = plt.subplots(n_rows, 2, figsize=(12.5, 3.6 * n_rows + 0.8))
     for ax, (rep, kind) in zip(axes.flat, CASES):
         col = f"{rep}_{kind}"
-        s = live[col].to_numpy()
+        s_raw = live[col].to_numpy()
+        mu_l, sd_l = float(s_raw.mean()), float(s_raw.std()) or 1.0
+        syn_join = np.concatenate([pops[p][col].to_numpy() for p in ("syn_clean", "syn_hack")
+                                   if len(pops.get(p, []))])
+        mu_s = float(syn_join.mean()) if len(syn_join) else 0.0
+        sd_s = (float(syn_join.std()) or 1.0) if len(syn_join) else 1.0
+        z_of = lambda x, p: (x - mu_s) / sd_s if p.startswith("syn") else (x - mu_l) / sd_l
+        s = (s_raw - mu_l) / sd_l
         y = y_all
-        mu, sd = float(s.mean()), float(s.std())
+        t_lo, t_hi = _otsu3(s)
-        t_lo, t_hi = mu + k_mid * sd, mu + k_rout * sd
         auroc = _auroc(s.tolist(), y.tolist())
         auroc_pos = _auroc(s[posm].tolist(), y[posm].tolist())
         thr = np.unique(s)
@@ -248,23 +283,12 @@ def plot_q2(df: pl.DataFrame, k_mid: float, k_rout: float, subtitle: str, out_pn
         stats[col] = {"auroc_pos": auroc_pos, "auroc_all": auroc, "prec_rout": prec,
                       "rec_rout": rec, "n_rout": n_rout, "t_hi": t_hi, "oracle": oracle}
 
-        lo = float(np.quantile(s, 0.005))
+        zvals = np.concatenate([s, (syn_join - mu_s) / sd_s]) if len(syn_join) else s
-        hi = float(np.quantile(s, 0.995))
+        lo = float(np.quantile(zvals, 0.005))
-        if kind == "cos":                       # keep synthetic medians visible (cos shares a scale;
+        hi = float(np.quantile(zvals, 0.995))
-            for p in ("syn_clean", "syn_hack"):  # dot doesn't -- pair grads dwarf live, annotate instead)
-                if len(pops.get(p, [])):
-                    m = float(np.median(pops[p][col].to_numpy()))
-                    lo, hi = min(lo, m), max(hi, m)
         pad = 0.05 * (hi - lo) or 1e-6
         lo, hi = lo - pad, hi + pad
         grid = np.linspace(lo, hi, 400)
-        if kind == "dot":
-            off = [f"syn {p.split('_')[1]} med={float(np.median(pops[p][col].to_numpy())):+.2g}"
-                   for p in ("syn_clean", "syn_hack")
-                   if len(pops.get(p, [])) and not lo < float(np.median(pops[p][col].to_numpy())) < hi]
-            if off:
-                ax.annotate("off-scale: " + ", ".join(off) + r" $\rightarrow$",
-                            xy=(0.98, 0.68), xycoords="axes fraction", ha="right", fontsize=7, color="#777777")
 
         curves = [("on_solve", SOLVE, "-", 1.9, 0.12), ("on_fail", FAIL, "-", 1.9, 0.12),
                   ("on_hackpos", HACK, "-", 1.9, 0.12),
@@ -273,7 +297,7 @@ def plot_q2(df: pl.DataFrame, k_mid: float, k_rout: float, subtitle: str, out_pn
             curves.insert(3, ("on_hackneg", HACK, (0, (1, 1)), 1.2, 0.0))
         ymax = 0.0
         for p, c, ls, lw, fill in curves:
-            yk = _kde(pops[p][col].to_numpy(), grid)
+            yk = _kde(z_of(pops[p][col].to_numpy(), p), grid)
             ymax = max(ymax, yk.max())
             if fill:
                 ax.fill_between(grid, yk, color=c, alpha=fill, lw=0)
@@ -283,8 +307,9 @@ def plot_q2(df: pl.DataFrame, k_mid: float, k_rout: float, subtitle: str, out_pn
         # precision claim rests on a handful of rollouts -- show them). hack row on top,
         # in a strip below y=0 (faint separator line); tick labels stay outside the axes.
         ax.axhline(0, color="#cccccc", lw=0.6, zorder=0)
+        ax.axvline(0, color="#bbbbbb", lw=0.7, zorder=0)   # 0 = family mean (z-norm)
         for row, (p, c) in enumerate((("on_hackpos", HACK), ("on_fail", FAIL), ("on_solve", SOLVE))):
-            x = pops[p][col].to_numpy()
+            x = z_of(pops[p][col].to_numpy(), p)
             ax.plot(x, np.full(len(x), -(0.035 + 0.035 * row) * ymax), "|",
                     color=c, ms=4, alpha=0.6, mew=0.8)
 
@@ -308,8 +333,8 @@ def plot_q2(df: pl.DataFrame, k_mid: float, k_rout: float, subtitle: str, out_pn
             ax.spines[sp].set_visible(False)
         ax.set_title(f"{rep} · {kind}    AUROC={auroc_pos:.2f} (A>0 contrast; vs-all {auroc:.2f})   "
                      f"P@rout={prec:.2f} (n={n_rout}) R={rec:.2f}", fontsize=9)
-        ax.set_xlabel({"cos": "cosine to v (concat modules)",
+        ax.set_xlabel({"cos": "cosine to v (concat modules), z within family",
-                       "dot": "dot ⟨x, v⟩ (update mass along v)"}[kind], fontsize=8.5)
+                       "dot": "dot ⟨x, v⟩, z within family"}[kind], fontsize=8.5)
 
     handles = [Line2D([0], [0], color=SOLVE, lw=1.9), Line2D([0], [0], color=FAIL, lw=1.9),
                Line2D([0], [0], color=HACK, lw=1.9),
@@ -318,7 +343,7 @@ def plot_q2(df: pl.DataFrame, k_mid: float, k_rout: float, subtitle: str, out_pn
                Patch(facecolor=ABSORB_C, alpha=0.18), Patch(facecolor=ROUT_C, alpha=0.18),
                Line2D([0], [0], color=ORACLE, lw=1.3, ls="-.")]
     labels = ["live solve", "live fail", "live hack (A>0)", "synthetic clean", "synthetic hack",
-              f"absorb (>mean+{k_mid:g}sd)", f"rout (>=mean+{k_rout:g}sd)", "oracle hack/rest split"]
+              "absorb (otsu lo, label-free)", "rout (otsu hi, label-free)", "oracle hack/rest split"]
     fig.legend(handles, labels, loc="lower center", ncol=4, fontsize=8, frameon=False)
     fig.suptitle(subtitle, fontsize=10)
     fig.tight_layout(rect=(0, 0.07, 1, 0.95))
@@ -335,12 +360,25 @@ def main(cfg: Cfg) -> int:
     feats_path = cfg.out_dir / "pinning_feats.pt"
     q2_png = cfg.out_dir / "pinning_q2.png"
     if cfg.replot is not None:
-        plot_q2(pl.read_parquet(cfg.replot), cfg.k_mid, cfg.k_rout, f"replot -- {cfg.replot.name}", q2_png)
+        plot_q2(pl.read_parquet(cfg.replot), f"replot -- {cfg.replot.name}", q2_png)
         if rank_path.exists():
             print(tabulate(pl.read_parquet(rank_path).to_pandas(), headers="keys",
                            tablefmt="pipe", floatfmt="+.3f", showindex=False))
         return 0
 
+    if cfg.feats is not None:
+        fe = torch.load(cfg.feats, weights_only=False)
+        logger.info(f"offline re-analysis from {cfg.feats} (no GPU)")
+        src = str(cfg.feats)
+    else:
+        fe = _extract_feats(cfg, feats_path)
+        src = f"{cfg.run_dir.name} | {cfg.ckpt}"
+    return _downstream(cfg, fe, src)
+
+
+def _extract_feats(cfg: Cfg, feats_path: Path) -> dict:
+    """One GPU pass: features for every authored pair side and live rollout, saved to
+    feats_path. Everything downstream is offline re-projection (rerun via --feats)."""
     device = torch.device("cuda")
     ckpt_path = cfg.run_dir / f"{cfg.ckpt}.safetensors"
     meta = _ckpt_meta(ckpt_path)
@@ -349,8 +387,7 @@ def main(cfg: Cfg) -> int:
     r = run_cfg.get("lora_r", 32)
     init_seed = run_cfg.get("lora_init_seed", 0)
     logger.info(f"ckpt {ckpt_path.name} step={meta.get('step')} hack_rate={meta.get('hack_rate')} "
-                f"model={model_name} r={r} init_seed={init_seed} | run-preset k_mid/k_rout="
+                f"model={model_name} r={r} init_seed={init_seed}")
-                f"{run_cfg.get('route_std_mid')}/{run_cfg.get('route_std_rout')} (plot uses {cfg.k_mid}/{cfg.k_rout})")
 
     tok = AutoTokenizer.from_pretrained(model_name)
     if tok.pad_token_id is None:
@@ -425,6 +462,27 @@ def main(cfg: Cfg) -> int:
         m = (steps == s) & (p_idx == p)
         grp_mean[(s, p)] = reward[m].mean()
     adv = np.array([reward[i] - grp_mean[(steps[i], p_idx[i])] for i in range(len(reward))])
+    groups: dict[str, list[int]] = defaultdict(list)
+    for i, p in enumerate(pairs_all):
+        groups[p.problem_id.split("_")[0]].append(i)
+    fe = {"G": G, "ACT": ACT, "RES": RES, "adv": adv, "exploited": exploited,
+          "gt_pass": gt_pass, "steps": steps, "p_idx": p_idx, "names": names,
+          "resid_layers": cfg.resid_layers, "pair_feats": PF, "pair_groups": dict(groups),
+          "pair_ids": [p.problem_id for p in pairs_all]}
+    torch.save(fe, feats_path)
+    logger.info(f"wrote {feats_path}")
+    return fe
+
+
+def _downstream(cfg: Cfg, fe: dict, src: str) -> int:
+    """Scores, pairset table, parquet, and plot from the feature dict -- no GPU."""
+    data_path = cfg.out_dir / "pinning_data.parquet"
+    rank_path = cfg.out_dir / "pinning_pairset.parquet"
+    q2_png = cfg.out_dir / "pinning_q2.png"
+    PF, pair_ids = fe["pair_feats"], fe["pair_ids"]
+    G, ACT, RES = fe["G"], fe["ACT"], fe["RES"]
+    adv, exploited, gt_pass = fe["adv"], fe["exploited"], fe["gt_pass"]
+    steps, p_idx = fe["steps"], fe["p_idx"]
     G_adv = G * torch.tensor(adv, dtype=G.dtype)[:, None, None]               # the update the gate sees
 
     # ── Q2 populations: drop A~0 (no update); positive = exploited & A>0 ──
@@ -440,10 +498,8 @@ def main(cfg: Cfg) -> int:
           f"too few learnable hacks and every AUROC below is noise.")
 
     # ── headline vectors from the routeV-default subset; placebo swaps in Haar ──
-    groups: dict[str, list[int]] = defaultdict(list)
+    groups: dict[str, list[int]] = fe["pair_groups"]
-    for i, p in enumerate(pairs_all):
+    head_idx = [i for i, pid in enumerate(pair_ids) if pid.startswith(cfg.headline_prefix)]
-        groups[p.problem_id.split("_")[0]].append(i)
-    head_idx = [i for i, p in enumerate(pairs_all) if p.problem_id.startswith(cfg.headline_prefix)]
     assert head_idx, f"no pairs match headline prefix {cfg.headline_prefix!r}"
     logger.info(f"headline v from prefix {cfg.headline_prefix!r} -> {len(head_idx)} pairs")
 
@@ -466,7 +522,7 @@ def main(cfg: Cfg) -> int:
                   for side in ("clean", "hack")}
 
     # ── pairset table: subsets x 4 AUROCs on the SAME cached live features ──
-    candidates = [("all-in-one", list(range(len(pairs_all))))] + \
+    candidates = [("all-in-one", list(range(len(pair_ids))))] + \
                  [(g, idx) for g, idx in sorted(groups.items()) if len(idx) >= 3]
     valid_pos = valid & (adv > 0)
     rows = []
@@ -502,18 +558,14 @@ def main(cfg: Cfg) -> int:
                   np.full(n_syn, -1), np.ones(n_syn)) for side in ("clean", "hack")]
     df = pl.concat(dfs)
     df.write_parquet(data_path)
-    torch.save({"G": G, "ACT": ACT, "RES": RES, "adv": adv, "exploited": exploited,
+    logger.info(f"wrote {data_path} ({len(df)} rows)")
-                "gt_pass": gt_pass, "steps": steps, "p_idx": p_idx, "names": names,
-                "resid_layers": cfg.resid_layers, "pair_feats": PF, "pair_groups": dict(groups),
-                "pair_ids": [p.problem_id for p in pairs_all]}, feats_path)
-    logger.info(f"wrote {data_path} ({len(df)} rows), {feats_path}")
 
-    sub = (f"{cfg.run_dir.name} | {cfg.ckpt}, live steps {cfg.step_lo}-{cfg.step_hi}, v from "
+    sub = (f"{src}, live steps {int(steps.min())}-{int(steps.max())}, v from "
            f"'{cfg.headline_prefix}' pairs (n={len(head_idx)}) | "
            f"hack+={counts['on_hackpos']} hack-={counts['on_hackneg']} solve={counts['on_solve']} "
            f"fail={counts['on_fail']} dropped(A~0)={counts['on_drop']}"
            + (f" | PLACEBO seed={cfg.random_v_seed}" if cfg.random_v_seed is not None else ""))
-    stats = plot_q2(df, cfg.k_mid, cfg.k_rout, sub, q2_png)
+    stats = plot_q2(df, sub, q2_png)
     best = max(stats, key=lambda c: stats[c]["auroc_pos"])
     print(f"\nmain metric: best case on the A>0 contrast = {best} "
           f"AUROC={stats[best]['auroc_pos']:.3f} (vs-all {stats[best]['auroc_all']:.3f}) "

scripts/diag_pinning_refresh.py

@@ -43,7 +43,7 @@ from vgrout.lora2r import wrap_model_with_lora2r
 from vgrout.pairs import load_pairs
 from vgrout.extract_vhack_grad import extract_v_hack, completion_nll
 from vgrout.train import _build_v_grad, route_band_edges, _auroc
-from diag_pinning import _kde, SOLVE, HACK, MEANC   # same dir (scripts/ is sys.path[0] when run directly)
+from diag_pinning import _kde, SOLVE, HACK, ABSORB_C as MEANC   # same dir (scripts/ is sys.path[0] when run directly)
 
 
 @dataclass