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
845 lines
48 KiB
Python
845 lines
48 KiB
Python
"""Publication figures for the manuscript — unified, lettered, codename-free.
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Renders fig1 (the experimental-programme schematic) and re-plots every data panel directly from the
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committed results artifacts (figs/fig2.pdf .. fig5.pdf): no experiment codenames, no suptitles, bold panel
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letters, one consistent style. Since 2026-09-13 each data panel carries a short headline stating its
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finding (with the model and its size where relevant), legends say in words what is plotted, and
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Figs. 3 and 4 open with a schematic panel explaining the set-up, so a figure is readable without its
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caption. The per-experiment figures under results/ remain the exploratory versions; these are the
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manuscript's.
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Usage: python paper/pnas/make_figs.py
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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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ROOT = Path(__file__).resolve().parents[2]
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sys.path.insert(0, str(ROOT / "figures"))
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sys.path.insert(0, str(ROOT / "src"))
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import os
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os.chdir(ROOT) # load_bundle uses repo-relative paths
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from _figlib import load_bundle, load_seed_bundles, mean_ci # noqa: E402
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OUT = ROOT / "paper" / "pnas" / "figs"
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plt.rcParams.update({
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"font.size": 8, "axes.labelsize": 8.5, "legend.fontsize": 7, "legend.frameon": False,
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"lines.markersize": 3.6, "axes.spines.top": False, "axes.spines.right": False,
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})
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def letter(ax, s, x=-0.14):
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ax.text(x, 1.02, s, transform=ax.transAxes, fontsize=12, fontweight="bold", va="bottom")
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def save(fig, name):
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OUT.mkdir(exist_ok=True)
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fig.savefig(OUT / f"{name}.pdf", bbox_inches="tight")
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plt.close(fig)
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print("wrote", OUT / f"{name}.pdf")
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def headline(ax, text, sub=None, x0=0):
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"""A short bold finding above the panel, with an optional grey line naming model and size.
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Both lines are wrapped to the panel's own width (so a headline never runs into its neighbour)
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and set clear of the axes: the grey line 7 pt above the frame, the headline above that.
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"""
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import textwrap
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fig = ax.figure
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width_pt = fig.get_figwidth() * ax.get_position().width * 72 - x0
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wrap = lambda s, fs: "\n".join(textwrap.fill(par, max(20, int(width_pt / (fs * 0.5))))
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for par in s.split("\n"))
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text = wrap(text, 8.2)
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dy = 7
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if sub:
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sub = wrap(sub, 7)
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ax.annotate(sub, xy=(0, 1), xycoords="axes fraction", xytext=(x0, dy), textcoords="offset points",
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fontsize=7, color="#555", ha="left", va="bottom", annotation_clip=False, linespacing=1.15)
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dy += 9.5 * (sub.count("\n") + 1) + 3
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ax.annotate(text, xy=(0, 1), xycoords="axes fraction", xytext=(x0, dy), textcoords="offset points",
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fontsize=8.2, fontweight="bold", ha="left", va="bottom", annotation_clip=False, linespacing=1.15)
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def paired_p(df, a, b, metric):
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"""Paired per-seed t-test between two models on one metric (the brackets' p-value)."""
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from scipy.stats import ttest_rel
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piv = (df[df["metric"] == metric].pivot_table(index="seed", columns="model", values="accuracy",
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aggfunc="mean")[[a, b]].dropna())
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return float(ttest_rel(piv[a], piv[b]).pvalue) if len(piv) > 1 else float("nan")
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def stars(p):
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return "***" if p < 0.001 else "**" if p < 0.01 else "*" if p < 0.05 else "ns"
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def sig_brackets(ax, specs, top, step=0.055, h=0.012):
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"""Significance brackets packed into tiers. ``specs`` = [(x1, x2, p, color)]; brackets that
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overlap horizontally go to a higher tier, so the tallest span sits on top."""
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specs = sorted(specs, key=lambda s: (abs(s[1] - s[0]), s[3]))
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tiers: list[list[tuple[float, float]]] = []
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for x1, x2, p, c in specs:
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lo, hi = min(x1, x2) + 0.04, max(x1, x2) - 0.04
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k = next((i for i, tier in enumerate(tiers) if all(hi < a or lo > b for a, b in tier)), None)
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if k is None:
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tiers.append([]); k = len(tiers) - 1
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tiers[k].append((lo, hi))
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y = top + k * step
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ax.plot([x1, x1, x2, x2], [y, y + h, y + h, y], color=c, lw=0.8, clip_on=False)
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ax.text((x1 + x2) / 2, y + h + 0.004, stars(p), ha="center", va="bottom", fontsize=6.5, color=c)
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return top + len(tiers) * step
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def _icon(svg_name: str):
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"""Rasterise a committed icon SVG at 2048 px (print-lossless at the ~0.3 in placed size).
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Requires ``rsvg-convert`` (librsvg). The SVGs are the committed source of truth; no derived
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PNGs are kept in the repo.
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"""
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import subprocess
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import tempfile
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svg = OUT / "icons" / svg_name
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with tempfile.NamedTemporaryFile(suffix=".png") as f:
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try:
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subprocess.run(["rsvg-convert", "-w", "1024", "-h", "1024", "-o", f.name, str(svg)],
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check=True, capture_output=True)
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except FileNotFoundError as e:
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raise RuntimeError("rsvg-convert (librsvg) is required to rasterise the icon SVGs "
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"for fig1a") from e
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return plt.imread(f.name)
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# ---------------------------------------------------------------- fig 1: experimental programme
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def fig1a():
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from matplotlib.patches import FancyBboxPatch
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# (name, architecture, guarantee, edge, cell face, header fill, header text colour, icon)
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# Icons: Flaticon #2347052 (green pea, for Mendel) and #10479785 (robot) as committed SVGs,
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# used under GG's paid Flaticon licence; rasterised at build time by _icon().
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TIERS = [
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("Inheritance model\n(reference)", "Wright\u2013Fisher simulator (NumPy)",
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"closed forms \u00b7 sets the expectation",
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"#4e8d4e", "#eef6ec", "#c5e0bd", "#2d5b2d", "pea.svg"),
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("Trained networks", "RNN \u00b7 MLP \u00b7 VAE\non a synthetic oracle;\nconvolutional VAE on MNIST",
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"sign-level tests \u00b7 exact oracles", "#5b9bc9", "#eff6fb", "#c9e2f2", "#1f4e79",
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"robot.svg"),
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("Language models", "LoRA specialists on Qwen\n0.5B, 1.5B & 7B; exact-match\nand execution verifiers",
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"seed-replicated signs", "#3c6ea5", "#e7eef8", "#adc8e8", "#1d3f66", "robot.svg"),
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]
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ROWS = [
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("Grounding = immigration",
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"fresh verified samples from a\nfixed external source enter the\ntraining mix every generation",
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["immigration\u2013drift equilibrium:\n$g \\approx 0.05$ retains $\\geq$95% diversity;\nobservation floor $1-e^{-mp}$",
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"collapse & rescue in every\narchitecture; MNIST: dry 30$\\to$1 modes,\n10% grounding holds 30/30;\nestimator-bias learning kernel",
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"LIT:established at LLM scale in\nprior work (refs. 23, 33);\nnot re-run here"]),
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("Recombination = sex",
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"a child inherits from several\nparents, reassembling variants\nthat arose in different lineages",
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["blending conservation law\n(first-order cancellation);\nunion-operator gain; Fisher\u2013Muller",
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"merge rescues two forgetting\nspecialists ($\\approx$0.50 $\\to$ 0.955)",
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"merged specialists beat every parent\n(5 seeds at 0.5B; 7B); routing vs\naveraging: the headroom rule"]),
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("Epistasis (entangled skills)",
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"a variant's fitness contribution\ndepends on the variants present\nat the other loci",
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["reference values only: outbreeding\ndepression, the recombination-rate\noptimum, mate-pool breadth (SI)",
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None,
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"bred-and-screened offspring beat\nthe blind blend in every seed\n(hard, unsaturated tasks)"]),
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("The composed society",
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"selection, recombination,\ndiversity preservation and\ngrounding on one population",
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["four-arm ablation: grounding, sex,\ndiversity each removed\n$\\to$ three distinct failures",
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None,
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"6 generations $\\times$ 3 lineages:\nobligate merging collapses,\na declinable merge tracks\npartner complementarity"]),
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("Speciation",
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"reproductive isolation: diverged\nlineages no longer produce\nviable (mergeable) offspring",
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["BDM incompatibility model:\nisolation cliff; quadratic snowball",
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"barrier decomposition under\npermutation+rescaling; conflict\nsweep 0.97$\\to$0.03; emergent null",
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"convention conflict $\\to$ hybrid\nbreakdown; duration null; pre-merge\npredictive test (13 cond. $\\times$ 3 seeds)"]),
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]
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TAGS = [("Fig. 2B", "Fig. 2A", None),
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("SI", "Table S2", "Fig. 3B\u2013C"),
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("SI", None, "Table S2"),
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("Fig. 4D\u2013F", None, "Fig. 4B\u2013C"),
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("Fig. 5E\u2013F", "Fig. 5A\u2013B", "Figs. 5C\u2013D, 3D\u2013E")]
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fig, ax = plt.subplots(figsize=(11.4, 5.3))
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ax.set_axis_off()
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ax.set_xlim(0, 1)
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ax.set_ylim(0, 1)
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ax.text(0.0, 0.995, "A", fontsize=13, fontweight="bold", va="top")
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x0, gap, sep = 0.205, 0.008, 0.02 # sep: extra gutter between theory and the AI pair
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cw = (1.0 - x0 - sep) / 3
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xs = [x0, x0 + cw + sep, x0 + 2 * cw + sep]
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row_h, row_top = 0.157, 0.805
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for j2, (name, arch, guarantee, edge, face, headfill, textcol, icon) in enumerate(TIERS):
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x = xs[j2]
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xc = x + cw / 2 - 0.02 # text centred left of the icon slot
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ax.add_patch(FancyBboxPatch((x + gap, 0.825), cw - 2 * gap, 0.170,
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boxstyle="round,pad=0.004", fc=headfill, ec=edge, lw=1.6))
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ax.text(xc, 0.988, name, ha="center", va="top", fontsize=9.5,
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fontweight="bold", color=textcol, linespacing=1.0)
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# Reason: a two-line tier name needs its (single-line) subtitle pushed down.
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arch_y = 0.918 if "\n" in name else 0.944
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ax.text(x + cw / 2 - 0.030, arch_y, arch, ha="center", va="top", fontsize=6.6,
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linespacing=1.25, color=textcol)
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ax.text(x + cw / 2 - 0.030, 0.831, guarantee, ha="center", va="bottom", fontsize=6.4,
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style="italic", color=textcol, alpha=0.85)
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# Reason: imshow + interpolation="none" embeds the icon unsampled in the PDF (an
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# OffsetImage is always composited at figure dpi, i.e. ~39 px, whatever the source).
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img = _icon(icon)
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iw = 56.0 / 1140.0 # 56 display px on an 11.4in/100dpi fig
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ih = iw * 11.4 / 5.3
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icx, icy = x + cw - gap - 0.030, 0.906
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ax.imshow(img, extent=(icx - iw / 2, icx + iw / 2, icy - ih / 2, icy + ih / 2),
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interpolation="none", aspect="auto", zorder=5)
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ax.set_xlim(0, 1)
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ax.set_ylim(0, 1)
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for i2, (label, definition, cells) in enumerate(ROWS):
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tags = TAGS[i2]
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y1 = row_top - i2 * row_h
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y0 = y1 - row_h + 2 * gap
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yc = (y0 + y1) / 2
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ax.text(0.0, y1 - 0.014, label, ha="left", va="top", fontsize=8, fontweight="bold")
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ax.text(0.0, y1 - 0.054, definition, ha="left", va="top", fontsize=6.2,
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style="italic", color="#555", linespacing=1.35)
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for j2, cell in enumerate(cells):
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x = xs[j2]
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edge = TIERS[j2][3]
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face = TIERS[j2][4]
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if cell is None:
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ax.add_patch(FancyBboxPatch((x + gap, y0), cw - 2 * gap, y1 - y0,
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boxstyle="round,pad=0.004", fc="#f3f3f3", ec="none"))
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ax.text(x + cw / 2, yc, "adds no discriminating test\nat this tier", ha="center",
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va="center", fontsize=6.4, style="italic", color="#999", linespacing=1.35)
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elif cell.startswith("LIT:"):
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ax.add_patch(FancyBboxPatch((x + gap, y0), cw - 2 * gap, y1 - y0,
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boxstyle="round,pad=0.004", fc="#f3f3f3", ec="none"))
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ax.text(x + cw / 2, yc, cell[4:], ha="center", va="center",
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fontsize=6.4, style="italic", color="#777", linespacing=1.35)
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else:
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ax.add_patch(FancyBboxPatch((x + gap, y0), cw - 2 * gap, y1 - y0,
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boxstyle="round,pad=0.004", fc=face, ec="none"))
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ax.text(x + cw / 2, yc + 0.008, cell, ha="center", va="center",
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fontsize=6.4, linespacing=1.35)
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if tags[j2]: # where the result lives (the ToC role)
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ax.text(x + cw - gap - 0.005, y0 + 0.006, tags[j2], ha="right", va="bottom",
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fontsize=5.6, style="italic", color=edge)
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save(fig, "fig1a")
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# ------------------------------------------------------- fig 1B: society in space -> in time
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BLUE, GREEN, GOLD = "#4292c6", "#41ab5d", "#d4a017"
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def _robot(ax, x, y, img, dots=(), lost=(), size=0.62):
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"""The robot icon (the same Flaticon asset as Fig. 1A) with capability dots beneath."""
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from matplotlib.patches import Circle
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ax.imshow(img, extent=(x - size / 2, x + size / 2, y - size / 2, y + size / 2),
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interpolation="none", zorder=2)
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marks = [(c, False) for c in dots] + [(c, True) for c in lost]
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n = len(marks)
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for i, (c, is_lost) in enumerate(marks):
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cx = x + (i - (n - 1) / 2) * 0.19
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cy = y - size / 2 - 0.13
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if is_lost:
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ax.add_patch(Circle((cx, cy), 0.07, fc="white", ec=c, lw=0.9, ls=(0, (2, 2))))
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ax.text(cx, cy - 0.005, "\u00d7", ha="center", va="center", fontsize=6, color=c)
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else:
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ax.add_patch(Circle((cx, cy), 0.07, fc=c, ec="none"))
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def fig1b():
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from matplotlib.patches import Circle, FancyArrowPatch
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W, H = 11.4, 4.75
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fig, ax = plt.subplots(figsize=(W, H))
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ax.set_xlim(0, W)
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ax.set_ylim(0, H)
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ax.set_aspect("equal")
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ax.set_axis_off()
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ax.text(0.05, H - 0.05, "B", fontsize=13, fontweight="bold", va="top")
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def arrow(p, q, color="#666", lw=1.2, style="-|>", shrink=2.0, ls="-"):
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ax.add_patch(FancyArrowPatch(p, q, arrowstyle=style, mutation_scale=10, color=color,
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lw=lw, linestyle=ls, shrinkA=shrink, shrinkB=shrink))
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rob = _icon("robot.svg")
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# ---------------- left: a society in space (contemporaries exchanging messages)
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cx, cy, r = 2.45, 2.95, 0.95
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dotsets = [(BLUE, GOLD), (GREEN,), (BLUE, GREEN), (GOLD, GREEN), (BLUE,)]
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pos = []
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for i, ds in enumerate(dotsets):
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a = np.pi / 2 + i * 2 * np.pi / 5
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x, y = cx + r * np.cos(a) * 1.4, cy + r * np.sin(a) * 0.95
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pos.append((x, y))
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_robot(ax, x, y, rob, dots=ds)
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for i, j2 in [(0, 2), (1, 3), (2, 4), (0, 3), (1, 4)]:
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arrow(pos[i], pos[j2], color="#99a", lw=0.9, style="<|-|>", shrink=26, ls=(0, (4, 2)))
|
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ax.text(pos[0][0] + 0.72, pos[0][1] + 0.38, "hi!", fontsize=8, ha="center",
|
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bbox=dict(boxstyle="round,pad=0.25", fc="white", ec="#99a", lw=0.8))
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clk = (0.55, 4.33)
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ax.add_patch(Circle(clk, 0.21, fc="white", ec="#445", lw=1.1))
|
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ax.plot([clk[0], clk[0]], [clk[1], clk[1] + 0.13], color="#445", lw=1.0)
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ax.plot([clk[0], clk[0] + 0.10], [clk[1], clk[1]], color="#445", lw=1.0)
|
||
ax.text(clk[0], clk[1] - 0.34, "one moment", ha="center", fontsize=7, style="italic",
|
||
color="#555")
|
||
ax.text(2.45, 0.80, "a society in space", ha="center", fontsize=11, fontweight="bold")
|
||
ax.text(2.45, 0.50, "contemporaries exchanging messages \u2014 multi-agent systems, agent economies",
|
||
ha="center", fontsize=7.2, style="italic", color="#555")
|
||
ax.text(2.45, 0.24, "information is passed on, but not easily stored: it fades with the conversation",
|
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ha="center", fontsize=7.2, style="italic", color="#555")
|
||
|
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# ---------------- middle: the shift of perspective
|
||
arrow((4.60, 2.75), (5.95, 2.75), color="#445", lw=2.0, style="-|>")
|
||
ax.text(5.27, 2.91, "the same ecosystem,\nseen along its time axis", ha="center",
|
||
va="bottom", fontsize=8, style="italic", color="#334", linespacing=1.3)
|
||
|
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# ---------------- right: a society in time (a pedigree)
|
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axx = 6.8
|
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arrow((axx, 4.55), (axx, 1.25), color="#445", lw=1.3)
|
||
for gy, lab in [(4.05, "gen 0"), (2.80, "gen 1"), (1.60, "gen 2")]:
|
||
ax.text(axx - 0.12, gy, lab, ha="right", va="center", fontsize=7.5, color="#445")
|
||
|
||
p1, p2 = (8.0, 4.05), (9.5, 4.05)
|
||
c1, c2 = (7.5, 2.80), (9.0, 2.80)
|
||
g2 = (9.0, 1.60)
|
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_robot(ax, *p1, rob, dots=(BLUE, GOLD))
|
||
_robot(ax, *p2, rob, dots=(GREEN, BLUE))
|
||
_robot(ax, *c1, rob, dots=(BLUE,), lost=(GOLD,))
|
||
_robot(ax, *c2, rob, dots=(BLUE, GREEN, GOLD))
|
||
_robot(ax, *g2, rob, dots=(BLUE, GREEN, GOLD))
|
||
arrow((7.87, 3.51), (7.56, 3.29), color="#666")
|
||
ax.text(7.42, 3.41, "inherit", ha="right", fontsize=7, style="italic", color="#555")
|
||
arrow((8.15, 3.49), (8.85, 3.29), color="#666")
|
||
arrow((9.40, 3.49), (9.13, 3.29), color="#666")
|
||
ax.text(9.0, 3.39, "merge (sex)", ha="center", fontsize=7, style="italic", color="#555",
|
||
bbox=dict(boxstyle="round,pad=0.12", fc="white", ec="none"))
|
||
ax.text(7.5, 2.08, "rare skill lost", ha="center", fontsize=6.8, style="italic",
|
||
color="#a33")
|
||
arrow((9.0, 2.24), (9.0, 2.06), color="#666")
|
||
globe = (10.55, 2.10)
|
||
ax.add_patch(Circle(globe, 0.32, fc="#eaf4fb", ec="#2c7fb8", lw=1.2))
|
||
from matplotlib.patches import Arc as _Arc
|
||
ax.add_patch(_Arc(globe, 0.32, 0.64, theta1=90, theta2=270, ec="#2c7fb8", lw=0.8))
|
||
ax.add_patch(_Arc(globe, 0.32, 0.64, theta1=270, theta2=90, ec="#2c7fb8", lw=0.8))
|
||
ax.plot([globe[0] - 0.32, globe[0] + 0.32], [globe[1], globe[1]], color="#2c7fb8", lw=0.8)
|
||
ax.text(globe[0], globe[1] - 0.44, "reality\n(verifier)", ha="center", va="top", fontsize=7,
|
||
color="#2c7fb8", linespacing=1.2)
|
||
arrow((10.22, 1.95), (9.38, 1.70), color="#2c7fb8", lw=1.2)
|
||
ax.text(9.82, 2.03, "ground\n(immigrate)", ha="center", va="bottom", fontsize=7,
|
||
style="italic", color="#2c7fb8", linespacing=1.2)
|
||
ax.text(8.9, 0.80, "a society in time", ha="center", fontsize=11, fontweight="bold")
|
||
ax.text(8.9, 0.50, "information is inherited, evolutionarily selected, and passed on again \u2014",
|
||
ha="center", fontsize=7.2, style="italic", color="#555")
|
||
ax.text(8.9, 0.24, "from parent model to child model \u2014 where population genetics applies",
|
||
ha="center", fontsize=7.2, style="italic", color="#555")
|
||
ax.set_xlim(0, W)
|
||
ax.set_ylim(0, H)
|
||
save(fig, "fig1b")
|
||
|
||
# ---------------------------------------------------------------- fig 2: grounding + MNIST
|
||
def fig2():
|
||
from knowledge.analysis import critical_grounding, reduce_to_stationary
|
||
from knowledge.metrics import heterozygosity
|
||
from knowledge.truth import make_true_distribution
|
||
|
||
df, cfg = load_bundle("results/E2")
|
||
n = cfg["dynamics"]["n"]
|
||
td = make_true_distribution(cfg["truth"]["K"], 1, "zipf", cfg["truth"]["tail_frac"],
|
||
cfg["truth"]["zipf_s"], 0, tail_threshold=cfg["truth"]["tail_threshold"])
|
||
H_star = heterozygosity(td.p_star)
|
||
last = int(cfg["generations"] * 0.8)
|
||
stat = df[df["generation"] >= last]
|
||
|
||
fig, axes = plt.subplots(1, 2, figsize=(10.6, 4.3), gridspec_kw={"width_ratios": [1.35, 1], "wspace": 0.28})
|
||
fig.subplots_adjust(top=0.8)
|
||
|
||
ax = axes[1]
|
||
st = reduce_to_stationary(stat, value_col="heterozygosity", replicate_col="replicate", last_frac=1.0)
|
||
gg, Hm, Hci = mean_ci(stat, "g", "heterozygosity")
|
||
nz = gg > 0
|
||
ax.errorbar(gg[nz], Hm[nz], yerr=Hci[nz], fmt="o", color="#1f77b4", capsize=2,
|
||
label="simulation (mean, 95% CI over 100 lineages)")
|
||
ax.plot(gg[~nz], Hm[~nz], "o", mfc="white", mec="#1f77b4")
|
||
m_of_g = stat.groupby("g")["m"].first().to_numpy()
|
||
m_grid = np.linspace(0, m_of_g.max(), 400)
|
||
|
||
def H_eq(m):
|
||
m = np.asarray(m, float)
|
||
return np.where(m <= 0, 0.0, H_star * m * (2 * n + m - 1) / (n + 2 * n * m + m * m))
|
||
|
||
ax.plot(m_grid / (n + m_grid), H_eq(m_grid), "k--", lw=1, label="exact prediction (immigration–drift equilibrium)")
|
||
ax.axhline(H_star, ls=":", color="gray", lw=1, label="diversity of the real data itself")
|
||
r = critical_grounding(st, H_star=H_star, frac=0.95, seed=7)
|
||
ax.axvspan(r["ci_low"], r["ci_high"], color="#d62728", alpha=0.15)
|
||
ax.axvline(r["g_star"], color="#d62728", lw=1.1,
|
||
label=f"threshold: 95% of real-data diversity kept ($g\\approx{r['g_star']:.3f}$)")
|
||
ax.set(xlabel="share of real data in each generation's training sample, $g$",
|
||
ylabel="diversity the population settles at, $H$")
|
||
ax.legend(loc="lower right", fontsize=6.4)
|
||
headline(ax, "About 5% real data per generation keeps 95% of the diversity", "inheritance model (simulation): 1,000 knowledge items, 100 lineages")
|
||
letter(ax, "B")
|
||
|
||
ax = axes[0]
|
||
from PIL import Image
|
||
im = np.asarray(Image.open("results/mnist_collapse/mnist_montage.png"))
|
||
# Strip the baked-in title band and left label margin (raster text is unreadable at panel
|
||
# size); measured on the committed montage: boxes span y >= 69, x >= 75, row centres below.
|
||
top, left = 60, 68
|
||
ax.imshow(im[top:, left:], interpolation="bilinear")
|
||
for yc, g in zip((101.5, 191.5, 282.0, 372.5, 462.5), (0, 4, 8, 12, 15)):
|
||
ax.text(-10, yc - top, str(g), ha="right", va="center", fontsize=8.5)
|
||
ax.text(-0.055, 0.5, "generation", transform=ax.transAxes, rotation=90,
|
||
ha="center", va="center", fontsize=8.5)
|
||
ax.set_axis_off()
|
||
ax.text(0.5, -0.03, "each row is a later generation; every column a randomly drawn digit; no real data added",
|
||
transform=ax.transAxes, ha="center", va="top", fontsize=7, color="#555", style="italic")
|
||
headline(ax, "Trained only on its own output, an image model collapses to one shape",
|
||
"image generator (VAE) re-trained each generation on its own drawings", x0=16)
|
||
letter(ax, "A", x=-0.02)
|
||
save(fig, "fig2")
|
||
|
||
|
||
# ---------------------------------------------------------------- fig 6: the society
|
||
def _load_curriculum():
|
||
"""The six-generation language-model population, all curricula and seeds, one long-form frame.
|
||
|
||
Delegates to figures/stats_llm_curriculum.py, the single place where arm labels are assigned by
|
||
experiment directory (the veto arm is recorded as `society`; never trust the arm column alone).
|
||
"""
|
||
from stats_llm_curriculum import load_curriculum
|
||
return load_curriculum()
|
||
|
||
|
||
def fig4():
|
||
import pandas as pd
|
||
from matplotlib.patches import FancyArrowPatch, FancyBboxPatch
|
||
|
||
df, _ = load_bundle("results/E11")
|
||
arms = [("full", "#2ca02c", "full system"),
|
||
("no_sex", "#ff7f0e", "no recombination"),
|
||
("no_diversity", "#9467bd", "no diversity preservation"),
|
||
("no_grounding", "#d62728", "no grounded evaluation")]
|
||
arms = [a for a in arms if a[0] in set(df["arm"].unique())]
|
||
g_opt = df["global_opt"].mean()
|
||
|
||
fig = plt.figure(figsize=(11.4, 11.4))
|
||
gs = fig.add_gridspec(3, 6, height_ratios=[1.25, 1, 1], hspace=0.62, wspace=0.6)
|
||
|
||
cur = _load_curriculum()
|
||
acc = cur[(cur["metric"] == "all_families") & (cur["generation"] >= 0)]
|
||
best = acc.groupby(["arm", "seed", "generation"])["value"].max().reset_index() # best lineage
|
||
comp = (cur[(cur["arm"] == "veto") & (cur["metric"] == "complementarity")]
|
||
.groupby("generation")["value"].mean())
|
||
gens = sorted(comp.index)
|
||
llm_arms = [("isolated", "#1f77b4", "-o", "never merge"),
|
||
("veto", "#2ca02c", "-o", "merge only if it beats keeping the parent"),
|
||
("society_stop3", "#ff7f0e", "--s", "merge through generation 2, then stop (control)"),
|
||
("society", "#d62728", "-o", "always merge with a contemporary")]
|
||
|
||
# ---- A: how the population works (a schematic strip; the syllabus is read from the data)
|
||
axB, axC = fig.add_subplot(gs[1, 0:4]), fig.add_subplot(gs[1, 4:6])
|
||
# Reason: the strip is placed by hand so that it is flush with the B/D frames on the left, spans
|
||
# to C's right edge, and sits a fixed 0.75 in above B's headline (a gridspec row would leave a
|
||
# gap that scales with the row height). Its height follows the content's designed aspect.
|
||
W, H = 11.4, 3.1
|
||
pb, pc = axB.get_position(), axC.get_position()
|
||
w_frac = pc.x1 - pb.x0
|
||
h_frac = (w_frac * fig.get_figwidth()) * (H / W) / fig.get_figheight()
|
||
ax = fig.add_axes([pb.x0, pb.y1 + 0.75 / fig.get_figheight(), w_frac, h_frac])
|
||
ax.set_xlim(0, W); ax.set_ylim(0, H); ax.set_aspect("equal"); ax.set_axis_off()
|
||
|
||
def box(x, y, w, h, text, fc="#eef3f8", ec="#7a93ad", fs=6.3, bold_first=True):
|
||
ax.add_patch(FancyBboxPatch((x, y), w, h, boxstyle="round,pad=0.04", fc=fc, ec=ec, lw=1.0))
|
||
lines = text.split("\n")
|
||
ax.text(x + w / 2, y + h - 0.1, lines[0], ha="center", va="top", fontsize=fs + 0.9,
|
||
fontweight="bold" if bold_first else "normal")
|
||
ax.text(x + w / 2, y + h - 0.1 - 0.27, "\n".join(lines[1:]), ha="center", va="top", fontsize=fs,
|
||
color="#333", linespacing=1.25)
|
||
|
||
def arrow(p, q, color="#555", style="-|>", ls="-", lw=1.1):
|
||
ax.add_patch(FancyArrowPatch(p, q, arrowstyle=style, mutation_scale=9, color=color, lw=lw,
|
||
linestyle=ls, shrinkA=1, shrinkB=1))
|
||
|
||
ax.text(0.05, H - 0.02, "each generation, every lineage:", fontsize=8.0, fontweight="bold", va="top")
|
||
bw, bh, by = 1.78, 1.2, 0.9
|
||
bx = (0.05, 0.05 + bw + 0.12, 0.05 + 2 * (bw + 0.12))
|
||
box(bx[0], by, bw, bh, "1 learn a new skill\ncontinue the parent's\nadapter: 300 new +\n150 replay examples")
|
||
box(bx[1], by, bw, bh, "2 merge? (arm rule)\naverage weights with\na partner, ratio chosen\non validation data")
|
||
box(bx[2], by, bw, bh, "3 test all six skills\na verifier marks each\nanswer; the child is\nthe next parent")
|
||
arrow((bx[0] + bw + 0.05, by + bh / 2), (bx[1] - 0.05, by + bh / 2))
|
||
arrow((bx[1] + bw + 0.05, by + bh / 2), (bx[2] - 0.05, by + bh / 2))
|
||
ax.plot([bx[2] + bw / 2, bx[2] + bw / 2, bx[0] + bw / 2, bx[0] + bw / 2], [by - 0.05, by - 0.3, by - 0.3, by - 0.12],
|
||
color="#555", lw=1.0)
|
||
arrow((bx[0] + bw / 2, by - 0.14), (bx[0] + bw / 2, by - 0.06))
|
||
ax.text(bx[1] + bw / 2, by - 0.42, "next generation (six in all)", ha="center", va="top", fontsize=6.8, style="italic", color="#555")
|
||
|
||
# the syllabus grid (from the config, so it matches the data)
|
||
fams = ["mnli", "arc", "hellaswag", "squad", "boolq", "winogrande"]
|
||
short = {"mnli": "NLI", "arc": "science", "hellaswag": "common\nsense", "squad": "reading",
|
||
"boolq": "yes/no", "winogrande": "pronoun"}
|
||
fam_col = {"mnli": "#c6dbef", "arc": "#c7e9c0", "hellaswag": "#fdd0a2", "squad": "#dadaeb",
|
||
"boolq": "#fcbba1", "winogrande": "#fee391"}
|
||
orders = [[fams[(i * 2 + k) % 6] for k in range(6)] for i in range(3)]
|
||
gx0, gy0, cw, ch = 6.95, 0.9, 0.5, 0.4
|
||
ax.text(gx0 + 3 * cw, H - 0.02, "the syllabus (six skills, rotated)",
|
||
ha="center", va="top", fontsize=8.0, fontweight="bold")
|
||
for k in range(6):
|
||
ax.text(gx0 + (k + 0.5) * cw, gy0 + 3 * ch + 0.05, f"gen {k + 1}", ha="center", va="bottom", fontsize=6.4, color="#333")
|
||
for i, o in enumerate(orders):
|
||
yy = gy0 + (2 - i) * ch
|
||
ax.text(gx0 - 0.06, yy + ch / 2, f"lineage {i + 1}", ha="right", va="center", fontsize=6.8, color="#333")
|
||
for k, f in enumerate(o):
|
||
ax.add_patch(FancyBboxPatch((gx0 + k * cw + 0.02, yy + 0.02), cw - 0.04, ch - 0.04,
|
||
boxstyle="round,pad=0.01", fc=fam_col[f], ec="none"))
|
||
ax.text(gx0 + (k + 0.5) * cw, yy + ch / 2, short[f], ha="center", va="center", fontsize=5.4, linespacing=0.95)
|
||
ax.text(gx0 - 0.06, gy0 - 0.14, "complementarity:", ha="right", va="center", fontsize=6.8, color="#333")
|
||
for k, g in enumerate(gens):
|
||
ax.text(gx0 + (k + 0.5) * cw, gy0 - 0.14, f"{comp[g]:.2f}", ha="center", va="center", fontsize=6.8, color="#333")
|
||
ax.text(gx0 + 3 * cw, gy0 - 0.3, "(partner complementarity: the share of a partner's skills\na lineage does not yet have; high early, zero at the end)",
|
||
ha="center", va="top", fontsize=6.4, style="italic", color="#555", linespacing=1.2)
|
||
|
||
# the arms
|
||
ax.text(10.0, H - 0.02, "the arms", fontsize=8.0, fontweight="bold", va="top")
|
||
short_arm = {"isolated": "never merge", "veto": "merge only if it helps the child",
|
||
"society_stop3": "merge until gen 2, then stop", "society": "always merge (contemporary)"}
|
||
for r, (name, c, style, lab) in enumerate(llm_arms):
|
||
yy = H - 0.5 - r * 0.36
|
||
ax.plot([10.05, 10.35], [yy, yy], style[:-1] if style.endswith(("o", "s")) else style, color=c, lw=1.6)
|
||
ax.plot([10.2], [yy], style[-1], color=c, ms=4.5)
|
||
ax.text(10.43, yy, short_arm[name], ha="left", va="center", fontsize=6.6)
|
||
headline(ax, "How the six-generation language-model population works",
|
||
"3 lineages \u00b7 6 generations \u00b7 3 training seeds; Qwen2.5-1.5B base (1.5 billion parameters)")
|
||
letter(ax, "A", x=-0.03)
|
||
|
||
# ---- B: the population's outcome
|
||
ax = axB
|
||
for name, c, style, lab in llm_arms:
|
||
g, m, ci = mean_ci(best[best["arm"] == name], "generation", "value")
|
||
ax.plot(g, m, style, color=c, lw=1.6, ms=4 if "s" in style else 6, label=lab)
|
||
ax.fill_between(g, m - ci, m + ci, color=c, alpha=0.15)
|
||
seq = best[best["arm"] == "sequential"]["value"].mean()
|
||
ax.plot([gens[-1]], [seq], "D", color="gray", ms=5, label="one model taught the whole syllabus alone")
|
||
ax.set(xlabel="generation\npartner complementarity", ylabel="accuracy on all six skills\n(best lineage)", ylim=(0.15, 0.9))
|
||
ax.set_xticks(gens)
|
||
ax.set_xticklabels([f"{g + 1}\n{comp[g]:.2f}" for g in gens])
|
||
ax.legend(loc="lower left")
|
||
headline(ax, "Forced merging collapses once partners stop knowing different things;\n"
|
||
"optional merging stays level with never merging", "best lineage; mean over 3 seeds, 95% CI shaded")
|
||
letter(ax, "B", x=-0.08)
|
||
|
||
# ---- C: merges declined under two syllabi with different complementarity schedules
|
||
ax = axC
|
||
w = 0.38
|
||
for arm, off, cbar, cline, ls, lab in (("veto", -w / 2, "#2ca02c", "#1b5e20", "-", "rotated syllabus (as in A)"),
|
||
("decor_veto", w / 2, "#ff7f0e", "#a04000", "--", "syllabus with complementarity\npeaking mid-way")):
|
||
v = cur[(cur["arm"] == arm) & (cur["metric"] == "veto_used")]
|
||
rate = v.groupby(["seed", "generation"])["value"].mean().groupby("generation").mean()
|
||
c = cur[(cur["arm"] == arm) & (cur["metric"] == "complementarity")].groupby("generation")["value"].mean()
|
||
ax.bar(np.array(gens) + 1 + off, rate.loc[gens], w, color=cbar, alpha=0.55, label=f"merges declined, {lab}")
|
||
ax.plot(np.array(gens) + 1, c.loc[gens], ls, color=cline, lw=1.4, label=f"partner complementarity, {lab}")
|
||
ax.set(xlabel="generation", ylabel="fraction", ylim=(0, 1.9), yticks=[0, 0.25, 0.5, 0.75, 1.0])
|
||
ax.set_xticks(np.array(gens) + 1)
|
||
ax.legend(loc="upper left", fontsize=5.6, ncol=1) # ylim headroom keeps it off the bars
|
||
headline(ax, "Lineages decline merges more often\nas generations pass, whatever the partner offers",
|
||
"declinable-merge arm, 3 seeds per syllabus")
|
||
letter(ax, "C", x=-0.2)
|
||
|
||
# ---- D-F: the simulated society (the inheritance-model reference)
|
||
axes = [fig.add_subplot(gs[2, 0:2]), fig.add_subplot(gs[2, 2:4]), fig.add_subplot(gs[2, 4:6])]
|
||
panels = [("best_fitness", "real fitness of the best agent", "D", "the best agent's real fitness"),
|
||
("diversity", "population diversity", "E", "how different the agents are from one another"),
|
||
("conformity_true_gap", "conformity − true fitness", "F", "how far the crowd's consensus sits from the truth")]
|
||
for ax, (col, ylab, L, sub) in zip(axes, panels):
|
||
for name, c, lab in arms:
|
||
sub_df = df[df["arm"] == name]
|
||
g, m, ci = mean_ci(sub_df, "generation", col)
|
||
ax.plot(g, m, "-", color=c, lw=1.6, label=lab)
|
||
ax.fill_between(g, m - ci, m + ci, color=c, alpha=0.15)
|
||
if col == "best_fitness":
|
||
ax.axhline(g_opt, ls=":", color="gray", lw=1, label="best possible (global optimum)")
|
||
ax.legend(fontsize=6.4)
|
||
headline(ax, "Simulated society: remove one mechanism and it fails in its own way", sub)
|
||
else:
|
||
headline(ax, " ", sub)
|
||
ax.set(xlabel="generation", ylabel=ylab)
|
||
letter(ax, L)
|
||
save(fig, "fig4")
|
||
|
||
|
||
# ------------------------------------------------- fig 5: merge failure across the two real tiers
|
||
def fig5():
|
||
# wspace: panel B carries a right-hand twin axis whose label would otherwise collide with C
|
||
fig, axes = plt.subplots(2, 3, figsize=(11.4, 8.4), gridspec_kw={"wspace": 0.45, "hspace": 0.75})
|
||
fig.subplots_adjust(top=0.9)
|
||
|
||
bdm, _ = load_bundle("results/E12")
|
||
rhos = sorted(bdm["rho"].unique())
|
||
colors = plt.cm.viridis(np.linspace(0.15, 0.85, len(rhos)))
|
||
|
||
def agg(df, keys, value):
|
||
g = df.groupby(keys)[value].agg(["mean", "std", "count"]).reset_index()
|
||
g["se"] = g["std"] / np.sqrt(g["count"].clip(lower=1))
|
||
return g
|
||
|
||
ax = axes[1, 1]
|
||
par = agg(bdm, "divergence", "parent_fitness")
|
||
ax.plot(par["divergence"], par["mean"], "k--", lw=1.3, label="parents")
|
||
for rho, c in zip(rhos, colors):
|
||
g = agg(bdm[bdm["rho"] == rho], "divergence", "offspring_fitness")
|
||
ax.plot(g["divergence"], g["mean"], "-o", color=c, label=f"hybrid, density {rho:g}")
|
||
ax.fill_between(g["divergence"], g["mean"] - g["se"], g["mean"] + g["se"], color=c, alpha=0.15)
|
||
ax.axhline(0, color="#999", lw=0.7, ls=":")
|
||
ax.set(xlabel="parental divergence (substitutions)", ylabel="fitness of the hybrid")
|
||
ax.legend()
|
||
headline(ax, "Simulation: hybrids fail once\nlineages diverge far enough", "20-locus genotypes with incompatibilities")
|
||
letter(ax, "E")
|
||
|
||
ax = axes[1, 2]
|
||
for rho, c in zip(rhos, colors):
|
||
g = agg(bdm[bdm["rho"] == rho], "divergence", "isolation")
|
||
ax.plot(g["divergence"], g["mean"], "-o", color=c, label=f"{rho:g}")
|
||
ax.set(xlabel="parental divergence (substitutions)", ylabel="probability the hybrid is non-viable", ylim=(-0.02, 1.02))
|
||
ax.legend(title="incompatibility density")
|
||
headline(ax, "Denser incompatibilities\nbring the cliff earlier", "same simulation")
|
||
letter(ax, "F")
|
||
|
||
dec, _ = load_bundle("results/speciation_real")
|
||
order = [c for c in ["shared", "independent", "conflict"] if c in set(dec["condition"])]
|
||
g = dec.groupby("condition").agg(naive=("barrier_naive", "mean"),
|
||
res=("residual_scale", "mean")).reindex(order)
|
||
ax = axes[0, 0]
|
||
x = np.arange(len(order)); w = 0.38
|
||
ax.bar(x - w / 2, g["naive"], w, color="#9ecae1", label="barrier as trained")
|
||
ax.bar(x + w / 2, g["res"], w, color="#d62728", label="barrier after undoing unit relabelling\n(what remains is functional conflict)")
|
||
ax.set_xticks(x)
|
||
ax.set_xticklabels(["same task,\nshared start", "same task,\ndifferent start", "conflicting\ntasks"])
|
||
ax.set(ylabel="merge error barrier\n(how much worse the average is than its parents)")
|
||
ax.legend(fontsize=6.4)
|
||
headline(ax, "Alignment removes the barrier for compatible networks, not for conflicting ones",
|
||
"pairs of small image classifiers forked from one base")
|
||
letter(ax, "A")
|
||
|
||
cliff, _ = load_bundle("results/speciation_real_cliff")
|
||
cg = cliff.groupby("conflict_frac").agg(res=("residual_scale", "mean"),
|
||
hyb=("acc_merge_scale", "mean")).reset_index()
|
||
ax = axes[0, 1]
|
||
ax.plot(cg["conflict_frac"], cg["res"], "-o", color="#d62728", label="barrier left after alignment")
|
||
ax2 = ax.twinx()
|
||
ax2.plot(cg["conflict_frac"], cg["hyb"], "-s", color="#2c7fb8", label="accuracy of the merged model")
|
||
ax2.set_ylabel("merged accuracy", color="#2c7fb8")
|
||
ax2.tick_params(axis="y", labelcolor="#2c7fb8")
|
||
ax2.spines["right"].set_visible(True)
|
||
ax.set(xlabel="share of classes the parents label differently", ylabel="barrier left after alignment")
|
||
l1, la1 = ax.get_legend_handles_labels(); l2, la2 = ax2.get_legend_handles_labels()
|
||
ax.legend(l1 + l2, la1 + la2, loc="center left")
|
||
headline(ax, "The more classes in conflict, the worse the merge", "same classifier pairs; conflict swept")
|
||
letter(ax, "B")
|
||
|
||
rep, _ = load_seed_bundles("results/llm_speciation") # s{seed}/ layout; seeds 2-3 from CX3
|
||
|
||
def series(df, mode, model, metric):
|
||
"""Seed mean and 95% CI half-width per x (a single seed gives a zero-width band)."""
|
||
sub = df[(df["mode"] == mode) & (df["model"] == model) & (df["metric"] == metric)]
|
||
per_seed = sub.groupby(["x", "seed"])["accuracy"].mean().reset_index()
|
||
x, m, h = mean_ci(per_seed, "x", "accuracy")
|
||
return x, m, np.nan_to_num(h)
|
||
|
||
def band(ax, x_, y_, h_, style, color, label):
|
||
ax.plot(x_, y_, style, color=color, label=label)
|
||
ax.fill_between(x_, y_ - h_, y_ + h_, color=color, alpha=0.18, linewidth=0)
|
||
|
||
ax = axes[0, 2]
|
||
band(ax, *series(rep, "conflict", "parent_a", "ambig_asc"), "--o", "#9ecae1", "parent A, graded by its own convention")
|
||
band(ax, *series(rep, "conflict", "parent_b", "ambig_desc"), "--o", "#a1d99b", "parent B, graded by its own convention")
|
||
band(ax, *series(rep, "conflict", "merge_soup", "coherence"), "-s", "#d62728", "merged model, graded by whichever\nconvention it follows best")
|
||
ax.set(xlabel="training share on the conflicting convention",
|
||
ylabel="accuracy on the shared, ambiguous questions", ylim=(-0.02, 0.4))
|
||
ax.legend(fontsize=6.0, loc="upper left")
|
||
headline(ax, "Language models: contradictory\nconventions break the merged model", "Qwen2.5-0.5B specialists; 3 seeds, 95% CI shaded")
|
||
letter(ax, "C")
|
||
|
||
ax = axes[1, 0]
|
||
band(ax, *series(rep, "duration", "merge_soup", "mean_private"), "-o", "#d62728", "merged model, on both parents' tasks")
|
||
band(ax, *series(rep, "duration", "parent_a", "strings"), "--o", "#9ecae1", "parent A, on its own task")
|
||
band(ax, *series(rep, "duration", "parent_b", "arith"), "--o", "#a1d99b", "parent B, on its own task")
|
||
ax.set(xlabel="how long each specialist was trained (epochs)", ylabel="accuracy", ylim=(0, 1.02))
|
||
ax.legend(loc="lower right", fontsize=6.4)
|
||
headline(ax, "Training specialists longer, apart,\ndoes not break merging", "same language models; parents share no data")
|
||
letter(ax, "D")
|
||
save(fig, "fig5")
|
||
|
||
|
||
# ---------------------------------------------------------------- fig 3: the language-model tier
|
||
def fig3():
|
||
import matplotlib.transforms as mtrans
|
||
import pandas as pd
|
||
from matplotlib.patches import Circle, FancyArrowPatch, FancyBboxPatch
|
||
from scipy.stats import spearmanr
|
||
|
||
from stats_llm_7b_seeds import with_best_specialist
|
||
|
||
fig = plt.figure(figsize=(11.4, 12.4))
|
||
gs = fig.add_gridspec(3, 2, height_ratios=[1.0, 1, 1], hspace=0.9, wspace=0.34)
|
||
|
||
# ---- A: how the compared models are built (schematic), placed flush with B/D on the left and a
|
||
# fixed 0.75 in above B's headline (see fig4 for the same rule)
|
||
axB, axC = fig.add_subplot(gs[1, 0]), fig.add_subplot(gs[1, 1])
|
||
W, H = 10.6, 3.2
|
||
pb, pc = axB.get_position(), axC.get_position()
|
||
w_frac = pc.x1 - pb.x0
|
||
h_frac = (w_frac * fig.get_figwidth()) * (H / W) / fig.get_figheight()
|
||
ax = fig.add_axes([pb.x0, pb.y1 + 0.75 / fig.get_figheight(), w_frac, h_frac])
|
||
ax.set_xlim(0, W); ax.set_ylim(0, H); ax.set_aspect("equal"); ax.set_axis_off()
|
||
rob = _icon("robot.svg")
|
||
FAM = [GOLD, GREEN, BLUE] # lists, strings, arithmetic
|
||
|
||
def robot(x, y, size, dots=(), alpha=1.0, crossed=False):
|
||
ax.imshow(rob, extent=(x - size / 2, x + size / 2, y - size / 2, y + size / 2),
|
||
interpolation="none", zorder=2)
|
||
n = len(dots)
|
||
for k, c in enumerate(dots):
|
||
cx, cy = x + (k - (n - 1) / 2) * 0.17, y - size / 2 - 0.11
|
||
ax.add_patch(Circle((cx, cy), 0.065, fc=c, ec="none", alpha=alpha))
|
||
if crossed:
|
||
ax.plot([cx - 0.04, cx + 0.04], [cy - 0.04, cy + 0.04], color="white", lw=0.8, zorder=3)
|
||
|
||
def caption(x, y, title, body):
|
||
ax.text(x, y, title, ha="center", va="top", fontsize=8.0, fontweight="bold")
|
||
ax.text(x, y - 0.22, body, ha="center", va="top", fontsize=7.0, color="#333", linespacing=1.25)
|
||
|
||
def arrow(p, q, color="#555"):
|
||
ax.add_patch(FancyArrowPatch(p, q, arrowstyle="-|>", mutation_scale=9, color=color, lw=1.1,
|
||
shrinkA=1, shrinkB=1))
|
||
|
||
ry, rs = 2.0, 0.66
|
||
xb, xs, xa, xt, xr = 0.65, (2.05, 2.7, 3.35), 5.05, 7.4, 9.65
|
||
robot(xb, ry, rs)
|
||
caption(xb, 1.32, "base model", "the shared “textbook”;\nno extra training")
|
||
arrow((xb + 0.45, ry), (xs[0] - 0.4, ry))
|
||
for k, x in enumerate(xs):
|
||
robot(x, ry, 0.52, dots=(FAM[k],))
|
||
caption(xs[1], 1.32, "three specialists", "the base plus one small adapter each,\ntrained on one task family\n(lists · strings · arithmetic)")
|
||
ax.text(xs[1], 0.46, "“best specialist” = the best of the three,\nchosen per seed",
|
||
ha="center", va="top", fontsize=6.8, style="italic", color="#555", linespacing=1.2)
|
||
# the three ways of combining them
|
||
ax.plot([xs[1], xs[1], xr, xr], [ry + 0.38, ry + 0.78, ry + 0.78, ry + 0.4], color="#555", lw=1.0)
|
||
ax.text((xs[1] + xr) / 2, ry + 0.82, "combine the three specialists, three ways", ha="center", va="bottom",
|
||
fontsize=7.4, style="italic", color="#555")
|
||
for x in (xa, xt):
|
||
ax.plot([x, x], [ry + 0.78, ry + 0.5], color="#555", lw=1.0)
|
||
arrow((x, ry + 0.52), (x, ry + rs / 2 + 0.02))
|
||
arrow((xr, ry + 0.52), (xr, ry + 0.26 + 0.02))
|
||
robot(xa, ry, rs, dots=FAM, alpha=0.45)
|
||
caption(xa, 1.32, "merged (average)", "the adapters averaged;\nevery parent's contribution\nis diluted")
|
||
robot(xt, ry, rs, dots=FAM, crossed=True)
|
||
caption(xt, 1.32, "merged (interference-aware)", "changes on which the parents\nconflict are dropped, then\nthe rest averaged (TIES)")
|
||
for k, x in enumerate((xr - 0.46, xr, xr + 0.46)):
|
||
robot(x, ry + 0.02, 0.44, dots=(FAM[k],))
|
||
ax.add_patch(FancyBboxPatch((xr - 0.2, 1.36), 0.4, 0.2, boxstyle="round,pad=0.02", fc="white", ec="#555", lw=0.9))
|
||
ax.text(xr, 1.46, "router", ha="center", va="center", fontsize=6.6)
|
||
for x in (xr - 0.46, xr, xr + 0.46):
|
||
ax.plot([xr, x], [1.56, ry - 0.22 - 0.09], color="#555", lw=0.7, ls=(0, (2, 1.5)))
|
||
caption(xr, 1.16, "routed (kept separate)", "each question goes to the\nspecialist that owns it;\nnothing is averaged")
|
||
ax.text(W / 2, 0.02, "All models share the same frozen base; only the small adapters differ. "
|
||
"A verifier marks every answer right or wrong; accuracy is the share marked right.",
|
||
ha="center", va="bottom", fontsize=7.4, color="#333")
|
||
headline(ax, "How the models compared in B and C are built")
|
||
letter(ax, "A", x=-0.03)
|
||
|
||
# ---- B, C: bars with per-seed CIs and paired-test brackets
|
||
METRICS = ((-0.19, "overall", "#2c7fb8", "accuracy, mean over all task families"),
|
||
(0.19, "worst_family", "#d62728", "accuracy on the model's weakest task family"))
|
||
|
||
def seed_bars(ax, df, models, labels, pairs):
|
||
x = np.arange(len(models))
|
||
tops = []
|
||
for off, metric, c, lab in METRICS:
|
||
vals, errs = [], []
|
||
for m in models:
|
||
v = df[(df["model"] == m) & (df["metric"] == metric)].groupby("seed")["accuracy"].mean()
|
||
vals.append(v.mean())
|
||
errs.append(1.96 * v.std(ddof=1) / np.sqrt(len(v)) if len(v) > 1 else 0.0)
|
||
ax.bar(x + off, vals, 0.36, yerr=errs, capsize=2, color=c, label=lab)
|
||
tops.append(max(v + e for v, e in zip(vals, errs)))
|
||
specs = []
|
||
for a, b in pairs:
|
||
for off, metric, c, _ in METRICS:
|
||
specs.append((models.index(a) + off, models.index(b) + off, paired_p(df, a, b, metric), c))
|
||
ymax = sig_brackets(ax, specs, top=max(tops) + 0.035)
|
||
ax.set_ylim(0, ymax + 0.02)
|
||
ax.set_xticks(x); ax.set_xticklabels(labels, fontsize=7)
|
||
ax.set(ylabel="verifier accuracy")
|
||
ax.legend(loc="upper center", bbox_to_anchor=(0.5, -0.2), ncol=2, fontsize=6.4)
|
||
ax.text(0.5, -0.33, "brackets: paired t-test over seeds; * p<0.05 ** p<0.01 *** p<0.001 ns not significant",
|
||
transform=ax.transAxes, ha="center", va="top", fontsize=5.8, color="#555")
|
||
|
||
ax = axB
|
||
dfm = with_best_specialist(load_bundle("results/llm_merge_seeds")[0])
|
||
seed_bars(ax, dfm, ["base", "best_specialist", "merge_soup", "merge_ties"],
|
||
["base", "best\nspecialist", "merged\n(average)", "merged\n(interference-aware)"],
|
||
[("best_specialist", "merge_soup"), ("best_specialist", "merge_ties"), ("merge_soup", "merge_ties")])
|
||
headline(ax, "Merged specialists beat the best single specialist",
|
||
"Qwen2.5-0.5B (0.5 billion parameters), easy tasks, 5 training seeds")
|
||
letter(ax, "B")
|
||
|
||
ax = axC
|
||
df7 = with_best_specialist(load_seed_bundles("results/llm_moe_hard_hpc")[0])
|
||
seed_bars(ax, df7, ["best_specialist", "merge_soup", "merge_ties", "moe_oracle"],
|
||
["best\nspecialist", "merged\n(average)", "merged\n(interference-aware)", "routed\n(kept separate)"],
|
||
[("best_specialist", "merge_soup"), ("merge_soup", "moe_oracle"), ("best_specialist", "moe_oracle")])
|
||
headline(ax, "On hard tasks, keeping specialists separate beats averaging them",
|
||
"Qwen2.5-7B (7 billion parameters), hard tasks, 3 training seeds")
|
||
letter(ax, "C")
|
||
|
||
# ---- D: pre-merge disagreement predicts merge damage
|
||
a = pd.read_parquet("results/llm_epistasis/results.parquet")
|
||
b = pd.read_parquet("results/llm_epistasis_compat/results.parquet")
|
||
dfe = pd.concat([a, b], ignore_index=True)
|
||
ax = fig.add_subplot(gs[2, 0])
|
||
for mode, c, mk, lab in (("conflict", "#d62728", "o", "parents taught contradictory conventions"),
|
||
("duration", "#2c7fb8", "s", "parents merely trained longer, apart"),
|
||
("compat", "#41ab5d", "^", "parents share training data, no conflict")):
|
||
sub = dfe[dfe["mode"] == mode]
|
||
ax.scatter(sub["epi_conf"], sub["merge_penalty"], c=c, marker=mk, s=26, alpha=0.75, label=lab)
|
||
ax.axhline(0, color="#999", lw=0.6)
|
||
ax.set(xlabel="how often the two parents confidently disagree (measured before merging)",
|
||
ylabel="merge penalty\n(accuracy lost relative to using each\nparent for its own task)")
|
||
ax.legend(loc="upper left", fontsize=6.4)
|
||
headline(ax, "Disagreement between parents, measured\nbefore merging, predicts merge damage",
|
||
"39 specialist pairs (13 conditions × 3 seeds), Qwen2.5-0.5B")
|
||
letter(ax, "D")
|
||
|
||
# ---- E: which pre-merge measures carry the signal
|
||
preds = [("dis_raw", "disagreement\n(raw)", "#fc9272"), ("epi_conf", "disagreement\n(confident)", "#d62728"),
|
||
("cross_perf", "cross-task\naccuracy", "#fcbba1"),
|
||
("grad_cos", "gradient\nalignment", "#9ecae1"), ("delta_cos", "weight\ncosine", "#9ecae1"),
|
||
("delta_l2", "weight\ndistance", "#9ecae1")]
|
||
ax = fig.add_subplot(gs[2, 1])
|
||
rhos_ = [abs(spearmanr(dfe[c], dfe["merge_penalty"])[0]) for c, _, _ in preds]
|
||
ax.bar(np.arange(len(preds)), rhos_, 0.6, color=[c for _, _, c in preds])
|
||
ax.set_xticks(np.arange(len(preds)))
|
||
ax.set_xticklabels([l for _, l, _ in preds], fontsize=6.2)
|
||
ax.set(ylabel="association with merge penalty\n(|Spearman ρ|)", ylim=(0, 0.8))
|
||
tr = mtrans.blended_transform_factory(ax.transData, ax.transAxes)
|
||
for (x1, x2, lab) in ((-0.3, 2.3, "measured by asking the parents questions"), (2.7, 5.3, "measured on the parents' weights")):
|
||
ax.plot([x1, x2], [-0.27, -0.27], transform=tr, color="#555", lw=0.9, clip_on=False)
|
||
ax.text((x1 + x2) / 2, -0.30, lab, transform=tr, ha="center", va="top", fontsize=6.4, color="#333")
|
||
headline(ax, "Behavioural measures predict the damage;\nweight-geometry measures do not",
|
||
"same 39 pairs; rank correlation with the merge penalty")
|
||
letter(ax, "E")
|
||
save(fig, "fig3")
|
||
|
||
|
||
if __name__ == "__main__":
|
||
for f in (fig1a, fig1b, fig2, fig3, fig4, fig5):
|
||
f()
|