1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
|
"""Analyze the HRM diagnostic output: stats + plots."""
import numpy as np
import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
from scipy import stats
import argparse
ap = argparse.ArgumentParser()
ap.add_argument("--in", dest="inp", required=True)
ap.add_argument("--out-dir", default="/home/yurenh2/rrm/research/flossing/plots")
args = ap.parse_args()
import os
os.makedirs(args.out_dir, exist_ok=True)
d = np.load(args.inp)
print("keys:", list(d.keys()))
lyap = d["lyap_max"] # (N,)
exact = d["exact_correct"].astype(bool) # (N,)
drift_zH = d["drift_zH"] # (N, T) ACT-step level drift
drift_zL = d["drift_zL"] # (N, T)
q_halt = d["q_halt"] # (N, T)
q_continue = d["q_continue"] # (N, T)
halted_at = d["halted_at"] # (N,) — ACT step at which q_halt>q_continue first
N = len(lyap)
print(f"N={N}, exact_acc={exact.mean():.3f}")
succ = lyap[exact]; fail = lyap[~exact]
print(f"\n=== Lyapunov max ===")
print(f" success: mean={succ.mean():+.4f} std={succ.std():.4f} n={succ.size}")
print(f" failure: mean={fail.mean():+.4f} std={fail.std():.4f} n={fail.size}")
# Stats tests
t, p = stats.ttest_ind(succ, fail, equal_var=False)
print(f" Welch t-test: t={t:.3f} p={p:.2e}")
u, p_u = stats.mannwhitneyu(succ, fail, alternative="two-sided")
print(f" Mann-Whitney U: U={u:.0f} p={p_u:.2e}")
# Effect size (Cohen's d)
pooled_std = np.sqrt(((succ.size-1)*succ.var() + (fail.size-1)*fail.var()) / (succ.size+fail.size-2))
d_cohen = (succ.mean() - fail.mean()) / pooled_std
print(f" Cohen's d: {d_cohen:.3f}")
# AUC: lyap predicts failure
# Failure tends to have higher (less negative) lyap.
auc = stats.mannwhitneyu(fail, succ, alternative="greater").statistic / (fail.size * succ.size)
print(f" AUROC (lyap predicting failure): {auc:.3f}")
# ----- plot 1: histogram of lyap by success/failure -----
fig, ax = plt.subplots(1, 1, figsize=(6,4))
bins = np.linspace(min(lyap.min(),-1.5), max(lyap.max(), -0.1), 40)
ax.hist(succ, bins=bins, alpha=0.55, label=f"success (n={succ.size})", color="C0", density=True)
ax.hist(fail, bins=bins, alpha=0.55, label=f"failure (n={fail.size})", color="C3", density=True)
ax.axvline(succ.mean(), color="C0", ls="--", lw=1)
ax.axvline(fail.mean(), color="C3", ls="--", lw=1)
ax.set_xlabel(r"$\lambda_{max}$ (top Lyapunov exponent, per inner cycle)")
ax.set_ylabel("density")
ax.set_title(f"HRM Sudoku 1k @ step_26040: λ_max distribution\nCohen's d={d_cohen:.2f}, Welch p={p:.1e}, AUROC={auc:.2f}")
ax.legend()
fig.tight_layout()
fig.savefig(f"{args.out_dir}/lyap_hist.png", dpi=130)
plt.close()
# ----- plot 2: drift trajectory means -----
fig, axes = plt.subplots(1, 2, figsize=(11,4), sharey=False)
for ax, drift, name in [(axes[0], drift_zH, r"$\|z_H^{(t+1)} - z_H^{(t)}\|$"),
(axes[1], drift_zL, r"$\|z_L^{(t+1)} - z_L^{(t)}\|$")]:
mean_s = drift[exact].mean(0); std_s = drift[exact].std(0)
mean_f = drift[~exact].mean(0); std_f = drift[~exact].std(0)
x = np.arange(drift.shape[1])
ax.fill_between(x, mean_s-std_s, mean_s+std_s, color="C0", alpha=0.25)
ax.plot(x, mean_s, "C0", label="success")
ax.fill_between(x, mean_f-std_f, mean_f+std_f, color="C3", alpha=0.25)
ax.plot(x, mean_f, "C3", label="failure")
ax.set_xlabel("ACT step")
ax.set_title(f"drift per ACT step: {name}")
ax.legend()
ax.set_yscale("log")
fig.tight_layout()
fig.savefig(f"{args.out_dir}/drift_per_act.png", dpi=130)
plt.close()
# ----- plot 3: Q-halt gating dynamics -----
fig, ax = plt.subplots(1, 1, figsize=(6,4))
diff = q_halt - q_continue
mean_s = diff[exact].mean(0); std_s = diff[exact].std(0)
mean_f = diff[~exact].mean(0); std_f = diff[~exact].std(0)
x = np.arange(diff.shape[1])
ax.fill_between(x, mean_s-std_s, mean_s+std_s, color="C0", alpha=0.25)
ax.plot(x, mean_s, "C0", label="success")
ax.fill_between(x, mean_f-std_f, mean_f+std_f, color="C3", alpha=0.25)
ax.plot(x, mean_f, "C3", label="failure")
ax.axhline(0, color="k", ls=":", lw=0.6)
ax.set_xlabel("ACT step")
ax.set_ylabel("q_halt − q_continue")
ax.set_title("ACT Q-head gating signal over ACT steps")
ax.legend()
fig.tight_layout()
fig.savefig(f"{args.out_dir}/q_gating.png", dpi=130)
plt.close()
# ----- plot 4: lyap vs token_acc scatter -----
token_acc = d["token_acc"]
fig, ax = plt.subplots(1, 1, figsize=(6,4))
ax.scatter(lyap[exact], token_acc[exact], s=8, alpha=0.3, color="C0", label="exact-correct")
ax.scatter(lyap[~exact], token_acc[~exact], s=8, alpha=0.3, color="C3", label="exact-fail")
ax.set_xlabel(r"$\lambda_{max}$")
ax.set_ylabel("token-level accuracy")
ax.legend()
ax.set_title("λ_max vs token accuracy")
fig.tight_layout()
fig.savefig(f"{args.out_dir}/lyap_vs_tokenacc.png", dpi=130)
plt.close()
print(f"\nplots saved to {args.out_dir}/")
|
