78 lines
3.6 KiB
Python
78 lines
3.6 KiB
Python
"""Phase diagram of frozen-band recurrence: dynamics dial vs fidelity.
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x: spectral radius rho(A) of the trained state map (log scale)
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y: substrate fidelity = easy-bucket pass@1 at k=4 (free-running generation)
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label: hard-bucket pass@1 at k=4 (the gain every regime buys)
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All points: same frozen E2B band, same data, same 250-item eval, e400.
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"""
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from pathlib import Path
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import matplotlib
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matplotlib.use("Agg")
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import matplotlib.pyplot as plt
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OUT = Path(__file__).resolve().parent.parent / "results-loop"
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# name rho easy hard color
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# name rho(plot x) easy hard color dy
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PTS = [
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("untrained α-merge\n(training-free)\nhard 14%", 0.40, 0.885, 0.143, "#8a8f98", -52),
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("trained merge\n(anchored B, curriculum)", 0.26, 0.885, 0.464, "#2b6cb0", -60),
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("per-depth merges\n(time-varying, anchored)\nhard 36% (depth-stranded)", 0.325, 0.893, 0.357, "#805ad5", 18),
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("Parcae rec\n(ρ<1 enforced, learned B)", 0.292, 0.713, 0.429, "#2f855a", -58),
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("unconstrained rec\n(learned A,B)", 4.5, 0.697, 0.393, "#c53030", 16),
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]
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# x jittered around true rho=0.3 for the three anchored arms (visibility)
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# untrained merge x offset for visibility (true rho = 0.30)
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fig, ax = plt.subplots(figsize=(7.6, 5.2))
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ax.set_xscale("log")
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ax.axvspan(1.0, 20, color="#fff5f5", zorder=0)
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ax.axvline(1.0, color="#c53030", lw=1.2, ls="--")
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ax.text(1.06, 0.99, "ρ = 1 stability boundary", rotation=90, fontsize=8,
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color="#c53030", va="top")
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ax.text(3.1, 0.615, "norm projection converts\nexplosion → stationary churn\n"
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"(training survives, substrate pays)", fontsize=8, color="#c53030",
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ha="center")
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for name, rho, easy, hard, c, dy in PTS:
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ax.scatter(rho, easy, s=90 + 900 * hard, color=c, alpha=0.85, zorder=3,
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edgecolor="white", linewidth=1.5)
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lbl = name if ("stranded" in name or "14%" in name) else f"{name}\nhard {hard:.0%}"
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dx = 62 if "14%" in name else 0
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ax.annotate(lbl,
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(rho, easy), textcoords="offset points", xytext=(dx, dy),
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ha="center", fontsize=8.5, color=c)
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ax.annotate("", xy=(0.278, 0.735), xytext=(0.288, 0.862),
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arrowprops=dict(arrowstyle="->", color="#2f855a", lw=1.3))
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ax.text(0.46, 0.775, "learned B + no curriculum:\nfixed point leaves the\n"
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"substrate manifold", fontsize=8, color="#2f855a", ha="left")
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ax.set_xlim(0.2, 12)
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ax.set_ylim(0.58, 1.0)
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ax.set_xlabel("ρ(A) — spectral radius of the trained state map (dynamics dial)")
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ax.set_ylabel("substrate fidelity — easy-bucket pass@1 at k=4")
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ax.set_title("Frozen-band recurrence phase diagram: stability ≠ fidelity\n"
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"(marker size ∝ hard-bucket gain; every regime buys the same "
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"~40–46%, only one keeps the substrate)", fontsize=10.5)
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ax.grid(True, color="#ececec", lw=0.7, which="both")
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ax.set_axisbelow(True)
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for s in ("top", "right"):
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ax.spines[s].set_visible(False)
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fig.text(0.13, -0.06,
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"Same frozen gemma-4-E2B band (L14–30), same MBPP data, same "
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"250-item eval, e400 checkpoints. ρ from checkpoints (power "
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"iteration / diag max). Dynamics (x) and fixed-point location "
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"(y) are independent dials: contraction guarantees convergence "
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"and certified tail gradients, but only anchored content — fixed "
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"B=(1−α)I, zero-init correction, difficulty→depth curriculum — "
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"keeps the fixed point substrate-preserving.", fontsize=7.5,
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color="#555", wrap=True)
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fig.tight_layout()
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fig.savefig(OUT / "fig_phase.png", dpi=140, facecolor="white",
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bbox_inches="tight")
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print("wrote", OUT / "fig_phase.png")
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