Giorgio Gilestro
84124de143
Clarity pass over the main text (36-item audit), Discussion rewrite and cut, acknowledgements, Souly et al. as ref 62, lettered SI panels, model section moved under Results; plus the untracked curriculum/society/compose/smol configs, runners, figures, stats and tests that the SI already cites. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Y64o8FKP7rCuXzC48pxpMm
78 lines
3.2 KiB
Python
78 lines
3.2 KiB
Python
"""E4 figure: multi-teacher recombination — supply vs realisation.
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Three panels tell the honest story: (A) union coverage rises with K_T and decorrelation,
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matching the exact closed form (recombination *supplies* the tail); (B) that supply is
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realised in the pupil only under a union-preserving merge — mean-mixture distillation
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dilutes it away (flat in K_T) while max-merge keeps it; (C) the union-surviving gap.
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Usage: python figures/plot_E4.py [results/E4]
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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, savefig, letter_axes # 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/E4") -> 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 = sorted(df["K_T"].unique())
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rhos = sorted(df["rho"].unique())
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g0 = df[df["g"] == 0.0]
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colors = plt.cm.viridis(np.linspace(0, 0.85, len(K_Ts)))
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fig, axes = plt.subplots(1, 3, figsize=(15, 4.3))
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# Panel A: union coverage vs rho per K_T, with closed-form overlay
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ax = axes[0]
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for K, c in zip(K_Ts, colors):
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sub = g0[g0["K_T"] == K].groupby("rho")["union_coverage"].mean()
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ax.plot(sub.index, sub.values, "o", color=c, label=f"$K_T$={K}")
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ax.plot(rhos, [U_closed(K, r, q) for r in rhos], "-", color=c, lw=1)
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ax.set(xlabel=r"parent correlation $\rho$", ylabel="union tail coverage",
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title=r"Supply: union matches $U(K_T,\rho,q)$")
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ax.legend(frameon=False, fontsize=8)
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# Panel B: surviving coverage vs rho per K_T — mean (dashed) vs max (solid)
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ax = axes[1]
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for K, c in zip(K_Ts, colors):
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sub = g0[g0["K_T"] == K].groupby("rho")
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ax.plot(sub["surviving_max"].mean().index, sub["surviving_max"].mean().values,
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"-o", color=c, label=f"$K_T$={K}", ms=4)
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ax.plot(sub["surviving_mean"].mean().index, sub["surviving_mean"].mean().values,
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"--", color=c, lw=1, alpha=0.7)
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ax.set(xlabel=r"parent correlation $\rho$", ylabel="surviving tail coverage",
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title="Realised: max-merge (solid) rises;\nmean-mixture (dashed) stays flat")
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ax.legend(frameon=False, fontsize=8)
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# Panel C: surviving vs K_T at rho=0, both operators — the recombination benefit
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ax = axes[2]
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r0 = g0[g0["rho"] == 0.0]
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mx = r0.groupby("K_T")["surviving_max"].agg(["mean", "sem"])
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mn = r0.groupby("K_T")["surviving_mean"].agg(["mean", "sem"])
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ax.errorbar(mx.index, mx["mean"], yerr=1.96 * mx["sem"], fmt="-o",
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color="#1f77b4", capsize=3, label="max-merge (union-preserving)")
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ax.errorbar(mn.index, mn["mean"], yerr=1.96 * mn["sem"], fmt="--s",
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color="#d62728", capsize=3, label="mean-mixture distillation")
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ax.set(xlabel="number of parents $K_T$", ylabel="surviving tail coverage",
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title=r"Benefit needs a union-preserving merge ($\rho=0$)",
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xticks=K_Ts)
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ax.legend(frameon=False, fontsize=9)
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fig.tight_layout()
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letter_axes(fig)
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savefig(fig, results_dir, "E4")
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if __name__ == "__main__":
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main(*sys.argv[1:])
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