Giorgio Gilestro
b8da418034
Grounding refinement (18 reps): forward-KL is the operative neural
collapse metric, not H or tail-survival. The RNN's smoothing keeps
spurious tail modes alive, so tail_truth_mass_alive is flat/non-monotone
in g and H stays ~0.8 of H*; only forward-KL falls monotonically (dry
2.08 -> g=0.2: 0.75, paired t up to 3.3). The sharp g* << 1 is an
exact-operator feature carried by the histogram bridge (0.047); the
trained RNN confirms the SIGN and softens the sharpness (half the KL gap
closes by g~0.04, but full recovery needs g~0.19). Blueprint 3.5's
directional claim holds; the pre-registered 95%-of-H*/tail falsifier is
not met because those are the wrong metrics for a smoothing model.
Robustness: a fully-degenerate RNN can emit only invalid codewords, so
measure_distribution now returns a terminal-collapse sentinel (fixation
on the dominant mode) instead of crashing a long sweep. Edge test added
(94 tests green).
Figures: plot_{bridge,collapse,grounding,architectures,recombination}.py,
each a pure function of its committed bundle, wired into `make figures`
(glob plot_*.py minus plot_E[1-6]/_*). bridge sits on the exact H_eq
curve (g*=0.047); recombination shows max-merge rising while mean-distill
stays flat; architectures shows the collapse/rescue signs across
histogram/GRU/MLP.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
90 lines
4.2 KiB
Python
90 lines
4.2 KiB
Python
"""`recombination` figure — the E4 "merge, don't average" finding in REAL weights (↔ E4/C4).
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K_T specialist GRUs are trained on assignments from the exact shared-switch retention
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construction, so union coverage matches the closed form U(K_T,rho,q) exactly. The pupil then
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recombines the *measured* teacher distributions two ways: mean (naive pooling) vs oracle-guided
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max-merge (M2N2-style union). The Layer-1 conservation law — mean-mixture is flat in K_T while
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max-merge rises — is what must survive the move to trained weights.
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Four panels: (A) union coverage vs K_T with the closed-form overlay (recombination *supply*);
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(B) analytic teachers — max-merge rises, mean stays flat (the conservation law); (C) the same
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on *trained* teacher weights (same signs, compressed/noisier — the smoothing caveat); (D) the
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rho=1 control — identical teachers buy nothing under either operator. Reads only the bundle.
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Usage: python figures/plot_recombination.py [results/recombination]
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"""
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from __future__ import annotations
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import sys
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from pathlib import Path
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import matplotlib.pyplot as plt
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import numpy as np
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sys.path.insert(0, str(Path(__file__).parent))
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from _figlib import load_bundle, mean_ci, savefig # noqa: E402
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def U_closed(K_T, rho, q):
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return rho * q + (1 - rho) * (1 - (1 - q) ** K_T)
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def main(results_dir: str = "results/recombination") -> None:
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df, cfg = load_bundle(results_dir)
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q = cfg["coverage"]["q"]
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K_Ts = np.array(sorted(df["K_T"].unique()))
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fig, axes = plt.subplots(2, 2, figsize=(13, 9))
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# Panel A: union coverage vs K_T (rho=0 and rho=1) + closed-form overlay.
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ax = axes[0, 0]
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for rho, col in [(0.0, "#1f77b4"), (1.0, "#ff7f0e")]:
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sub = df[df["rho"] == rho]
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_, m, ci = mean_ci(sub, "K_T", "union_coverage")
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ax.errorbar(sorted(sub["K_T"].unique()), m, yerr=ci, fmt="o", color=col, capsize=3,
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label=fr"union ($\rho$={rho:g})")
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ax.plot(K_Ts, [U_closed(K, rho, q) for K in K_Ts], "-", color=col, lw=1)
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ax.set(xlabel="number of teachers $K_T$", ylabel="union tail coverage",
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title=r"Supply: union matches closed form $U(K_T,\rho,q)$")
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ax.legend(frameon=False, fontsize=9)
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# Panels B/C: mean vs max surviving coverage at rho=0, analytic then trained.
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def operator_panel(ax, mean_col, max_col, title):
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r0 = df[df["rho"] == 0.0]
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for col, style, lab, c in [(max_col, "-o", "max-merge (union)", "#2ca02c"),
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(mean_col, "--s", "mean-distill (pool)", "#d62728")]:
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_, m, ci = mean_ci(r0, "K_T", col)
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ax.errorbar(sorted(r0["K_T"].unique()), m, yerr=ci, fmt=style, color=c, capsize=3,
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label=lab)
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ax.set(xlabel="number of teachers $K_T$", ylabel="surviving tail coverage", title=title)
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ax.legend(frameon=False, fontsize=9)
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operator_panel(axes[0, 1], "surviving_mean_target", "surviving_max_target",
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r"Analytic teachers ($\rho$=0): max rises, mean flat"
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"\n(the conservation law)")
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operator_panel(axes[1, 0], "surviving_mean", "surviving_max",
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r"Trained GRU teachers ($\rho$=0): same signs"
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"\n(compressed + noisier — smoothing caveat)")
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# Panel D: rho=1 control — identical teachers, both operators flat.
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ax = axes[1, 1]
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r1 = df[df["rho"] == 1.0]
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for col, style, lab, c in [("surviving_max", "-o", "max-merge", "#2ca02c"),
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("surviving_mean", "--s", "mean-distill", "#d62728"),
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("union_coverage", ":^", "union", "#1f77b4")]:
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_, m, ci = mean_ci(r1, "K_T", col)
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ax.errorbar(sorted(r1["K_T"].unique()), m, yerr=ci, fmt=style, color=c, capsize=3, label=lab)
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ax.set(xlabel="number of teachers $K_T$", ylabel="tail coverage",
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title=r"Control ($\rho$=1, identical teachers):"
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"\nmore teachers buy nothing")
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ax.legend(frameon=False, fontsize=9)
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fig.suptitle("recombination — 'merge, don't average' holds in real weights: max-merge realises "
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"the multi-teacher tail benefit, mean-distill conserves collapse", y=1.0, fontsize=12)
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fig.tight_layout()
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savefig(fig, results_dir, "recombination")
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if __name__ == "__main__":
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main(*sys.argv[1:])
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