86 lines
3.9 KiB
Python
86 lines
3.9 KiB
Python
"""Phase diagram of frozen-band recurrence: dynamics dial vs fidelity.
|
||
|
||
x: spectral radius rho(A) of the trained state map (log scale)
|
||
y: substrate fidelity = easy-bucket pass@1 at k=4 (free-running generation)
|
||
label: hard-bucket pass@1 at k=4 (the gain every regime buys)
|
||
All points: same frozen E2B band, same data, same 250-item eval, e400.
|
||
"""
|
||
from pathlib import Path
|
||
|
||
import matplotlib
|
||
matplotlib.use("Agg")
|
||
import matplotlib.pyplot as plt
|
||
|
||
OUT = Path(__file__).resolve().parent.parent / "results-loop"
|
||
|
||
# name rho easy hard color
|
||
# name rho(plot x) easy hard color dy
|
||
PTS = [
|
||
("untrained 14%", 0.22, 0.885, 0.143, "#8a8f98", -26),
|
||
("merge ★ 46%", 0.26, 0.885, 0.464, "#2b6cb0", -40),
|
||
("per-depth 36%", 0.30, 0.893, 0.357, "#805ad5", 26),
|
||
("tied-α 43%", 0.35, 0.910, 0.429, "#0987a0", -32),
|
||
("rand-k 36%", 0.41, 0.918, 0.357, "#3182ce", 22),
|
||
("noise-s₀ 43%*", 0.48, 0.904, 0.429, "#b83280", -34),
|
||
("4×MLP 54%†", 0.56, 0.902, 0.536, "#5f6b7a", 20),
|
||
("Parcae rec 41%*\n(ρ<1 enforced, learned B)", 0.292, 0.722, 0.411, "#2f855a", -50),
|
||
("unconstrained rec 39%\n(learned A,B)", 4.5, 0.697, 0.393, "#c53030", 16),
|
||
]
|
||
# x jittered around true rho=0.3 for the three anchored arms (visibility)
|
||
# untrained merge x offset for visibility (true rho = 0.30)
|
||
|
||
fig, ax = plt.subplots(figsize=(7.6, 5.2))
|
||
ax.set_xscale("log")
|
||
ax.axvspan(1.0, 20, color="#fff5f5", zorder=0)
|
||
ax.axvline(1.0, color="#c53030", lw=1.2, ls="--")
|
||
ax.text(1.06, 0.99, "ρ = 1 stability boundary", rotation=90, fontsize=8,
|
||
color="#c53030", va="top")
|
||
ax.text(3.1, 0.615, "norm projection converts\nexplosion → stationary churn\n"
|
||
"(training survives, substrate pays)", fontsize=8, color="#c53030",
|
||
ha="center")
|
||
|
||
for name, rho, easy, hard, c, dy in PTS:
|
||
ax.scatter(rho, easy, s=90 + 900 * hard, color=c, alpha=0.85, zorder=3,
|
||
edgecolor="white", linewidth=1.5)
|
||
lbl = name
|
||
dx = 0
|
||
ax.annotate(lbl,
|
||
(rho, easy), textcoords="offset points", xytext=(dx, dy),
|
||
ha="center", fontsize=7.5, color=c)
|
||
|
||
ax.annotate("", xy=(0.285, 0.740), xytext=(0.29, 0.868),
|
||
arrowprops=dict(arrowstyle="->", color="#2f855a", lw=1.3))
|
||
ax.text(0.55, 0.79, "learned free B:\nfixed point leaves the\n"
|
||
"substrate manifold\n(curriculum, s₀, ρ, capacity\nall causally cleared)",
|
||
fontsize=8, color="#2f855a", ha="left")
|
||
ax.text(0.34, 0.972, "the anchored family — B tied to the anchor (labels: hard-bucket at k=4; * seed mean, † single seed)",
|
||
fontsize=7.8, color="#2b6cb0", ha="center", style="italic")
|
||
|
||
|
||
ax.set_xlim(0.17, 12)
|
||
ax.set_ylim(0.58, 1.0)
|
||
ax.set_xlabel("ρ(A) — spectral radius of the trained state map (dynamics dial)")
|
||
ax.set_ylabel("substrate fidelity — easy-bucket pass@1 at k=4")
|
||
ax.set_title("Frozen-band recurrence phase diagram: stability ≠ fidelity\n"
|
||
"(marker size ∝ hard-bucket gain at k=4; every regime buys "
|
||
"36–54% within seed noise; only anchored B keeps the substrate)",
|
||
fontsize=10.5)
|
||
ax.grid(True, color="#ececec", lw=0.7, which="both")
|
||
ax.set_axisbelow(True)
|
||
for s in ("top", "right"):
|
||
ax.spines[s].set_visible(False)
|
||
|
||
fig.text(0.13, -0.06,
|
||
"Same frozen gemma-4-E2B band (L14–30), same MBPP data, same "
|
||
"250-item eval, e400 checkpoints. ρ from checkpoints (power "
|
||
"iteration / diag max). Dynamics (x) and fixed-point location "
|
||
"(y) are independent dials: contraction guarantees convergence "
|
||
"and certified tail gradients, but only anchored content — fixed "
|
||
"B=(1−α)I, zero-init correction, difficulty→depth curriculum — "
|
||
"keeps the fixed point substrate-preserving.", fontsize=7.5,
|
||
color="#555", wrap=True)
|
||
fig.tight_layout()
|
||
fig.savefig(OUT / "fig_phase.png", dpi=140, facecolor="white",
|
||
bbox_inches="tight")
|
||
print("wrote", OUT / "fig_phase.png")
|