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Diffstat (limited to 'research/flossing/analyze_halt_bucket.py')
| -rw-r--r-- | research/flossing/analyze_halt_bucket.py | 122 |
1 files changed, 122 insertions, 0 deletions
diff --git a/research/flossing/analyze_halt_bucket.py b/research/flossing/analyze_halt_bucket.py new file mode 100644 index 0000000..2ad80fc --- /dev/null +++ b/research/flossing/analyze_halt_bucket.py @@ -0,0 +1,122 @@ +"""Validate codex's λ*(h, β) = (1/h) log β framework using halted_at buckets. + +If the framework is right, then across halt buckets: +- success samples should all satisfy λ_1 × h_micro × halted_at ≈ log(β_target) (a constant ≪ 0) +- equivalently: success λ_1 should scale as ~1/halted_at + +We use halted_at as a proxy for "effective computation budget" (h in codex's notation). +For each ACT step we have cycles_per_act micro-Lyapunov-steps: + HRM (H=2, L=2): 2*(2+1) = 6 + TRM (H=3, L=6): 3*(6+1) = 21 +""" +import numpy as np +import matplotlib +matplotlib.use("Agg") +import matplotlib.pyplot as plt + +ROOT = "/home/yurenh2/rrm/research/flossing" + +cases = { + "HRM_step26040": dict(npz=f"{ROOT}/diag_joint_1k.npz", cycles_per_act=6), + "TRM_step13020": dict(npz=f"{ROOT}/diag_trm_step13020_512.npz", cycles_per_act=21), +} + +fig, axes = plt.subplots(2, 3, figsize=(15, 9)) + +for row, (name, meta) in enumerate(cases.items()): + d = np.load(meta["npz"]) + cpa = meta["cycles_per_act"] + lam = d["lyap_spec"][:, 0] # top-1 Lyap per sample (per micro step) + succ = d["exact_correct"] > 0.5 + halted = d["halted_at"].copy() + halted[halted == 0] = 16 # never-halt → used full 16 ACT steps + + h_micro = halted * cpa # effective micro-step horizon + logbeta = lam * h_micro # log of cumulative decay over h_micro + beta = np.exp(np.clip(logbeta, -20, 20)) # implied β + + print(f"\n=== {name} ===") + print(f" N={len(lam)} acc={succ.mean():.3f} cycles/ACT={cpa}") + print(f" λ_1 mean: succ={lam[succ].mean():+.4f} fail={lam[~succ].mean():+.4f}") + print(f" halted_at: succ={halted[succ].mean():.2f} fail={halted[~succ].mean():.2f}") + print(f" log β implied succ={logbeta[succ].mean():+.3f} fail={logbeta[~succ].mean():+.3f}") + print(f" β implied: succ={beta[succ].mean():.3f} fail={beta[~succ].mean():.3f}") + + # By halt bucket + print(f" bucket n_succ n_fail λ_succ λ_fail logβ_succ logβ_fail") + buckets = sorted(set(halted.tolist())) + for b in buckets: + ms = (halted == b) & succ + mf = (halted == b) & ~succ + if ms.sum() + mf.sum() < 5: continue + lam_s = lam[ms].mean() if ms.sum() > 0 else np.nan + lam_f = lam[mf].mean() if mf.sum() > 0 else np.nan + lb_s = lam_s * b * cpa + lb_f = lam_f * b * cpa + print(f" h={b:>3} {ms.sum():>4} {mf.sum():>4} " + f"{lam_s:+7.4f} {lam_f:+7.4f} {lb_s:+8.3f} {lb_f:+8.3f}") + + # ----- Panel A: λ vs halted_at, succ vs fail ----- + ax = axes[row, 0] + ax.scatter(halted[succ] + np.random.uniform(-0.15, 0.15, succ.sum()), lam[succ], + s=5, alpha=0.35, c="C2", label=f"succ (n={succ.sum()})") + ax.scatter(halted[~succ] + np.random.uniform(-0.15, 0.15, (~succ).sum()), lam[~succ], + s=5, alpha=0.35, c="C3", label=f"fail (n={(~succ).sum()})") + # Per-bucket mean + means_s, means_f, bs = [], [], [] + for b in buckets: + ms = (halted == b) & succ + mf = (halted == b) & ~succ + if ms.sum() >= 3: means_s.append((b, lam[ms].mean())) + if mf.sum() >= 3: means_f.append((b, lam[mf].mean())) + if means_s: + xs, ys = zip(*means_s); ax.plot(xs, ys, "C2o-", lw=2, ms=8, label="succ mean") + if means_f: + xf, yf = zip(*means_f); ax.plot(xf, yf, "C3o-", lw=2, ms=8, label="fail mean") + # 1/h reference: codex prediction λ ∝ 1/h + if means_s: + h_ref = np.array([b for b, _ in means_s]) + # fit constant = mean of λ*h*cpa over succ + c = (lam[succ] * halted[succ] * cpa).mean() + ref = c / (h_ref * cpa) + ax.plot(h_ref, ref, "k--", lw=1, alpha=0.5, label=f"λ=1/h·log β (log β={c:.2f})") + ax.axhline(0, color="k", lw=0.5, ls=":") + ax.set_xlabel("halted_at (ACT steps)"); ax.set_ylabel("λ_1 (per micro-step)") + ax.set_title(f"{name}: λ_1 vs halt step") + ax.legend(fontsize=7); ax.grid(alpha=0.3) + + # ----- Panel B: log β = λ × h_micro by halt bucket ----- + ax = axes[row, 1] + ax.scatter(halted[succ] + np.random.uniform(-0.15, 0.15, succ.sum()), logbeta[succ], + s=5, alpha=0.35, c="C2", label="succ") + ax.scatter(halted[~succ] + np.random.uniform(-0.15, 0.15, (~succ).sum()), logbeta[~succ], + s=5, alpha=0.35, c="C3", label="fail") + if means_s: + xs = [b for b, _ in means_s] + ys = [lam[(halted==b)&succ].mean() * b * cpa for b in xs] + ax.plot(xs, ys, "C2o-", lw=2, ms=8, label="succ mean") + if means_f: + xf = [b for b, _ in means_f] + yf = [lam[(halted==b)&~succ].mean() * b * cpa for b in xf] + ax.plot(xf, yf, "C3o-", lw=2, ms=8, label="fail mean") + ax.axhline(0, color="k", lw=0.5, ls=":") + ax.set_xlabel("halted_at"); ax.set_ylabel("log β = λ_1 × halt × cycles/ACT") + ax.set_title(f"{name}: implied log β (constant ⇒ 1/h scaling holds)") + ax.legend(fontsize=8); ax.grid(alpha=0.3) + + # ----- Panel C: histogram of implied β by succ/fail ----- + ax = axes[row, 2] + bins = np.linspace(-6, 4, 50) + ax.hist(logbeta[succ], bins=bins, alpha=0.6, color="C2", label=f"succ μ={logbeta[succ].mean():+.2f}") + ax.hist(logbeta[~succ], bins=bins, alpha=0.6, color="C3", label=f"fail μ={logbeta[~succ].mean():+.2f}") + ax.axvline(0, color="k", lw=0.5, ls=":") + ax.set_xlabel("log β implied"); ax.set_ylabel("count") + ax.set_title(f"{name}: log β distribution") + ax.legend(fontsize=8); ax.grid(alpha=0.3) + +fig.suptitle("Codex's λ*(h, β) = (1/h) log β prediction: across halt buckets, " + "λ should scale as 1/h with constant log β", fontsize=11) +fig.tight_layout() +out = f"{ROOT}/plots_halt_bucket.png" +fig.savefig(out, dpi=130) +print(f"\n→ {out}") |