Fig. 1 revision: pop-gen definitions as row labels, title into the caption, solid header row
Row labels now teach the vocabulary (grounding = immigration, recombination = sex, epistasis, the composed society, speciation = reproductive isolation), each with a two-to-three-line definition in the left margin, replacing the question taglines. The in-figure title/arrow is removed (the caption carries it); the tier header row is now solid-colour with white text so the model-nature band reads as a header rather than a content row. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01BkRLcc18rwT2Lysu6PbG7v
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5 changed files with 39 additions and 36 deletions
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@ -20,7 +20,7 @@ An operator of a model population faces recurring decisions for which there is n
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\begin{figure*}[p]\centering % fig1
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\includegraphics[width=\textwidth]{figs/fig1.pdf}
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\caption{The experimental programme. Each population-genetic abstraction (Table 1) is tested at up to three tiers of model architecture, ordered left to right by increasing realism: an exact Wright--Fisher simulator over knowledge distributions (closed forms; bitwise-reproducible), trained neural networks measured against exact oracles (recurrent, feedforward, and variational-autoencoder generators on a synthetic mode universe, and a convolutional VAE on MNIST), and language models (LoRA specialists on Qwen bases at 0.5B and 7B, scored by an exact-match verifier). Rows are the paper's five questions; filled cells name the experiments run at each tier; dashed cells were not tested, and the composed society at language-model scale is the paper's stated gap.}\label{fig1}
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\caption{The experimental programme. Each population-genetic abstraction (Table 1) is tested at up to three tiers of model architecture, ordered left to right by increasing realism: an exact Wright--Fisher simulator over knowledge distributions (closed forms; bitwise-reproducible), trained neural networks measured against exact oracles (recurrent, feedforward, and variational-autoencoder generators on a synthetic mode universe, and a convolutional VAE on MNIST), and language models (LoRA specialists on Qwen bases at 0.5B and 7B, scored by an exact-match verifier). The same population-genetic abstractions are carried across the three tiers. Rows are the framework's mechanisms, each defined at the left margin; filled cells name the experiments run at each tier; dashed cells were not tested, and the composed society at language-model scale is the paper's stated gap.}\label{fig1}
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\end{figure*}
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\section*{The minimal model, and where its exactness ends}
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@ -28,9 +28,10 @@ FIGURES: dict[str, tuple[list[str], str]] = {
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"trained neural networks measured against exact oracles (recurrent, feedforward, and "
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"variational-autoencoder generators on a synthetic mode universe, and a convolutional VAE on "
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"MNIST), and language models (LoRA specialists on Qwen bases at 0.5B and 7B, scored by an "
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"exact-match verifier). Rows are the paper's five questions; filled cells name the "
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"experiments run at each tier; dashed cells were not tested, and the composed society at "
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"language-model scale is the paper's stated gap."),
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"exact-match verifier). The same population-genetic abstractions are carried across the "
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"three tiers. Rows are the framework's mechanisms, each defined at the left margin; filled "
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"cells name the experiments run at each tier; dashed cells were not tested, and the composed "
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"society at language-model scale is the paper's stated gap."),
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"fig2": (["paper/pnas/figs/fig2.pdf"],
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"Grounding is immigration. (A) Stationary diversity against the grounding fraction in the "
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"minimal inheritance model: simulation (points, 95\\% CI) matches the exact immigration--drift "
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@ -48,66 +48,69 @@ def fig1():
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TIERS = [
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("Exact model", "Wright\u2013Fisher simulator (NumPy)", "closed forms \u00b7 bitwise-reproducible",
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"#4292c6", "#eaf2fa"),
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"#3d7eb8", "#eaf2fa"),
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("Trained networks", "RNN \u00b7 MLP \u00b7 VAE on a synthetic oracle;\nconvolutional VAE on MNIST",
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"sign-level tests \u00b7 exact oracles", "#41ab5d", "#edf8ea"),
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"sign-level tests \u00b7 exact oracles", "#3f8f4f", "#edf8ea"),
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("Language models", "LoRA specialists on Qwen 0.5B & 7B;\nexact-match verifier",
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"seed-replicated signs", "#e6550d", "#fdf0e6"),
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"seed-replicated signs", "#d9650f", "#fdf0e6"),
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]
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ROWS = [
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("Grounding", "how much real data?",
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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$1 modes,\n10% grounding holds 30/30;\nestimator-bias learning kernel",
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None]),
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("Recombination", "blend or merge?",
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("Recombination = sex",
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"a child inherits from several\nparents, reassembling variants\nthat arose in different lineages",
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["blending conservation law\n(first-order cancellation);\nunion-operator gain; Fisher\u2013Muller",
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"merge rescues two forgetting\nspecialists ($\\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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("Entangled skills", "who merges with whom?",
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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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["NK landscapes: outbreeding\ndepression; directed sex restores\nthe gain; mate-pool breadth optimum",
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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", "can the loop sustain itself?",
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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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"OPEN"]),
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("Speciation & prediction", "when does merging fail?",
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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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fig, ax = plt.subplots(figsize=(11.4, 5.4))
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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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x0, gap = 0.16, 0.008
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x0, gap = 0.205, 0.008
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cw = (1.0 - x0) / 3
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row_h, row_top = 0.152, 0.79
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row_h, row_top = 0.157, 0.805
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ax.annotate("", xy=(0.995, 0.975), xytext=(x0 + 0.02, 0.975),
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arrowprops=dict(arrowstyle="->", color="#555", lw=1.1))
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ax.text(x0 + (1 - x0) / 2, 0.988, "the same population-genetic abstractions (Table 1), increasing realism",
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ha="center", va="bottom", fontsize=8, style="italic", color="#333")
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for j2, (name, arch, guarantee, edge, face) in enumerate(TIERS):
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x = x0 + j2 * cw
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ax.add_patch(FancyBboxPatch((x + gap, 0.825), cw - 2 * gap, 0.155,
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boxstyle="round,pad=0.004", fc=edge, ec=edge, lw=1.4))
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ax.text(x + cw / 2, 0.966, name, ha="center", va="top", fontsize=9.5,
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fontweight="bold", color="white")
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ax.text(x + cw / 2, 0.922, arch, ha="center", va="top", fontsize=6.8,
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linespacing=1.3, color="white")
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ax.text(x + cw / 2, 0.833, guarantee, ha="center", va="bottom", fontsize=6.4,
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style="italic", color="white", alpha=0.92)
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for j, (name, arch, guarantee, edge, face) in enumerate(TIERS):
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x = x0 + j * cw
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ax.add_patch(FancyBboxPatch((x + gap, 0.795), cw - 2 * gap, 0.16,
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boxstyle="round,pad=0.004", fc=face, ec=edge, lw=1.4))
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ax.text(x + cw / 2, 0.944, name, ha="center", va="top", fontsize=9, fontweight="bold", color=edge)
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ax.text(x + cw / 2, 0.902, arch, ha="center", va="top", fontsize=6.8, linespacing=1.3)
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ax.text(x + cw / 2, 0.803, guarantee, ha="center", va="bottom", fontsize=6.4,
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style="italic", color="#555")
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for i, (label, question, cells) in enumerate(ROWS):
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y1 = row_top - i * row_h
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for i2, (label, definition, cells) in enumerate(ROWS):
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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, yc + 0.012, label, ha="left", va="center", fontsize=8, fontweight="bold")
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ax.text(0.0, yc - 0.022, question, ha="left", va="center", fontsize=6.8, style="italic", color="#555")
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for j, cell in enumerate(cells):
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x = x0 + j * cw
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edge, face = TIERS[j][3], TIERS[j][4]
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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 = x0 + j2 * cw
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edge, face = TIERS[j2][3], 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="white", ec="#bbbbbb",
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@ -126,7 +129,6 @@ def fig1():
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ax.text(x + cw / 2, yc, cell, ha="center", va="center", fontsize=6.4, linespacing=1.35)
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save(fig, "fig1")
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# ---------------------------------------------------------------- fig 2: grounding + MNIST
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def fig2():
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from knowledge.analysis import critical_grounding, reduce_to_stationary
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