"""Publication figures for the PNAS draft — unified, lettered, codename-free. Renders fig1 (the experimental-programme schematic) and re-plots every data panel directly from the committed results artifacts (figs/fig2.pdf .. fig7.pdf): no experiment codenames, no suptitles, no per-panel headline titles (interpretation lives in the captions), bold panel letters, one consistent style. The per-experiment figures under results/ remain the exploratory versions; these are the manuscript's. Usage: python paper/pnas/make_figs.py """ from __future__ import annotations import sys from pathlib import Path import matplotlib.pyplot as plt import numpy as np ROOT = Path(__file__).resolve().parents[2] sys.path.insert(0, str(ROOT / "figures")) sys.path.insert(0, str(ROOT / "src")) import os os.chdir(ROOT) # load_bundle uses repo-relative paths from _figlib import load_bundle, mean_ci # noqa: E402 OUT = ROOT / "paper" / "pnas" / "figs" plt.rcParams.update({ "font.size": 8, "axes.labelsize": 8.5, "legend.fontsize": 7, "legend.frameon": False, "lines.markersize": 3.6, "axes.spines.top": False, "axes.spines.right": False, }) def letter(ax, s, x=-0.14): ax.text(x, 1.02, s, transform=ax.transAxes, fontsize=12, fontweight="bold", va="bottom") def save(fig, name): OUT.mkdir(exist_ok=True) fig.savefig(OUT / f"{name}.pdf", bbox_inches="tight") plt.close(fig) print("wrote", OUT / f"{name}.pdf") def _icon(svg_name: str): """Rasterise a committed icon SVG at 2048 px (print-lossless at the ~0.3 in placed size). Requires ``rsvg-convert`` (librsvg). The SVGs are the committed source of truth; no derived PNGs are kept in the repo. """ import subprocess import tempfile svg = OUT / "icons" / svg_name with tempfile.NamedTemporaryFile(suffix=".png") as f: try: subprocess.run(["rsvg-convert", "-w", "1024", "-h", "1024", "-o", f.name, str(svg)], check=True, capture_output=True) except FileNotFoundError as e: raise RuntimeError("rsvg-convert (librsvg) is required to rasterise the icon SVGs " "for fig1a") from e return plt.imread(f.name) # ---------------------------------------------------------------- fig 1: experimental programme def fig1a(): from matplotlib.patches import FancyBboxPatch # (name, architecture, guarantee, edge, cell face, header fill, header text colour, icon) # Icons: Flaticon #2347052 (green pea, for Mendel) and #10479785 (robot) as committed SVGs, # used under GG's paid Flaticon licence; rasterised at build time by _icon(). TIERS = [ ("Biological model", "Wright\u2013Fisher simulator (NumPy)", "closed forms \u00b7 bitwise-reproducible", "#4e8d4e", "#eef6ec", "#c5e0bd", "#2d5b2d", "pea.svg"), ("Trained networks", "RNN \u00b7 MLP \u00b7 VAE on a synthetic oracle;\nconvolutional VAE on MNIST", "sign-level tests \u00b7 exact oracles", "#5b9bc9", "#eff6fb", "#c9e2f2", "#1f4e79", "robot.svg"), ("Language models", "LoRA specialists on Qwen 0.5B & 7B;\nexact-match verifier", "seed-replicated signs", "#3c6ea5", "#e7eef8", "#adc8e8", "#1d3f66", "robot.svg"), ] ROWS = [ ("Grounding = immigration", "fresh verified samples from a\nfixed external source enter the\ntraining mix every generation", ["immigration\u2013drift equilibrium:\n$g \\approx 0.05$ retains $\\geq$95% diversity;\nobservation floor $1-e^{-mp}$", "collapse & rescue in every\narchitecture; MNIST: dry 30$\\to$1 modes,\n10% grounding holds 30/30;\nestimator-bias learning kernel", "LIT:established at LLM scale in\nprior work (refs. 21, 30);\nnot re-run here"]), ("Recombination = sex", "a child inherits from several\nparents, reassembling variants\nthat arose in different lineages", ["blending conservation law\n(first-order cancellation);\nunion-operator gain; Fisher\u2013Muller", "merge rescues two forgetting\nspecialists ($\\approx$0.50 $\\to$ 0.955)", "merged specialists beat every parent\n(5 seeds at 0.5B; 7B); routing vs\naveraging: the headroom rule"]), ("Epistasis (entangled skills)", "a variant's fitness contribution\ndepends on the variants present\nat the other loci", ["NK landscapes: outbreeding\ndepression; directed sex restores\nthe gain; mate-pool breadth optimum", None, "bred-and-screened offspring beat\nthe blind blend in every seed\n(hard, unsaturated tasks)"]), ("The composed society", "selection, recombination,\ndiversity preservation and\ngrounding on one population", ["four-arm ablation: grounding, sex,\ndiversity each removed\n$\\to$ three distinct failures", None, "OPEN"]), ("Speciation", "reproductive isolation: diverged\nlineages no longer produce\nviable (mergeable) offspring", ["BDM incompatibility model:\nisolation cliff; quadratic snowball", "barrier decomposition under\npermutation+rescaling; conflict\nsweep 0.97$\\to$0.03; emergent null", "convention conflict $\\to$ hybrid\nbreakdown; duration null; pre-merge\npredictive test (13 cond. $\\times$ 3 seeds)"]), ] TAGS = [("Fig. 2A", "Fig. 2B", None), ("Fig. 4", "Table S2", "Fig. 3A\u2013B"), ("Fig. 5", None, "Table S2"), ("Fig. 6", None, None), ("Fig. 7A\u2013B", "Fig. 7C\u2013D", "Figs. 7E\u2013F, 3C\u2013D")] fig, ax = plt.subplots(figsize=(11.4, 5.3)) ax.set_axis_off() ax.set_xlim(0, 1) ax.set_ylim(0, 1) ax.text(0.0, 0.995, "A", fontsize=13, fontweight="bold", va="top") x0, gap, sep = 0.205, 0.008, 0.02 # sep: extra gutter between theory and the AI pair cw = (1.0 - x0 - sep) / 3 xs = [x0, x0 + cw + sep, x0 + 2 * cw + sep] row_h, row_top = 0.157, 0.805 for j2, (name, arch, guarantee, edge, face, headfill, textcol, icon) in enumerate(TIERS): x = xs[j2] xc = x + cw / 2 - 0.02 # text centred left of the icon slot ax.add_patch(FancyBboxPatch((x + gap, 0.825), cw - 2 * gap, 0.170, boxstyle="round,pad=0.004", fc=headfill, ec=edge, lw=1.6)) ax.text(xc, 0.988, name, ha="center", va="top", fontsize=9.5, fontweight="bold", color=textcol) ax.text(x + cw / 2 - 0.030, 0.938, arch, ha="center", va="top", fontsize=6.6, linespacing=1.3, color=textcol) ax.text(x + cw / 2 - 0.030, 0.831, guarantee, ha="center", va="bottom", fontsize=6.4, style="italic", color=textcol, alpha=0.85) # Reason: imshow + interpolation="none" embeds the icon unsampled in the PDF (an # OffsetImage is always composited at figure dpi, i.e. ~39 px, whatever the source). img = _icon(icon) iw = 56.0 / 1140.0 # 56 display px on an 11.4in/100dpi fig ih = iw * 11.4 / 5.3 icx, icy = x + cw - gap - 0.030, 0.906 ax.imshow(img, extent=(icx - iw / 2, icx + iw / 2, icy - ih / 2, icy + ih / 2), interpolation="none", aspect="auto", zorder=5) ax.set_xlim(0, 1) ax.set_ylim(0, 1) for i2, (label, definition, cells) in enumerate(ROWS): tags = TAGS[i2] y1 = row_top - i2 * row_h y0 = y1 - row_h + 2 * gap yc = (y0 + y1) / 2 ax.text(0.0, y1 - 0.014, label, ha="left", va="top", fontsize=8, fontweight="bold") ax.text(0.0, y1 - 0.054, definition, ha="left", va="top", fontsize=6.2, style="italic", color="#555", linespacing=1.35) for j2, cell in enumerate(cells): x = xs[j2] edge = TIERS[j2][3] face = TIERS[j2][4] if cell is None: ax.add_patch(FancyBboxPatch((x + gap, y0), cw - 2 * gap, y1 - y0, boxstyle="round,pad=0.004", fc="white", ec="#bbbbbb", lw=0.8, ls=(0, (3, 2)))) ax.text(x + cw / 2, yc, "adds no discriminating test\nat this tier", ha="center", va="center", fontsize=6.4, style="italic", color="#999", linespacing=1.35) elif cell.startswith("LIT:"): ax.add_patch(FancyBboxPatch((x + gap, y0), cw - 2 * gap, y1 - y0, boxstyle="round,pad=0.004", fc="white", ec="#bbbbbb", lw=0.8, ls=(0, (3, 2)))) ax.text(x + cw / 2, yc, cell[4:], ha="center", va="center", fontsize=6.4, style="italic", color="#777", linespacing=1.35) elif cell == "OPEN": ax.add_patch(FancyBboxPatch((x + gap, y0), cw - 2 * gap, y1 - y0, boxstyle="round,pad=0.004", fc="white", ec=edge, lw=0.8, ls=(0, (3, 2)))) ax.text(x + cw / 2, yc, "open \u2014 the stated gap", ha="center", va="center", fontsize=6.6, style="italic", color=edge) else: ax.add_patch(FancyBboxPatch((x + gap, y0), cw - 2 * gap, y1 - y0, boxstyle="round,pad=0.004", fc=face, ec=edge, lw=0.9)) ax.text(x + cw / 2, yc + 0.008, cell, ha="center", va="center", fontsize=6.4, linespacing=1.35) if tags[j2]: # where the result lives (the ToC role) ax.text(x + cw - gap - 0.005, y0 + 0.006, tags[j2], ha="right", va="bottom", fontsize=5.6, style="italic", color=edge) save(fig, "fig1a") # ------------------------------------------------------- fig 1B: society in space -> in time BLUE, GREEN, GOLD = "#4292c6", "#41ab5d", "#d4a017" def _robot(ax, x, y, fc="#e8eef5", dots=(), lost=(), w=0.52, h=0.52): """A friendly robot head with capability dots beneath (gold = the rare skill).""" from matplotlib.patches import Arc, Circle, FancyBboxPatch ax.add_patch(FancyBboxPatch((x - w / 2, y - h / 2), w, h, boxstyle="round,pad=0.03", fc=fc, ec="#445", lw=1.1)) for dx in (-w / 4.5, w / 4.5): ax.add_patch(Circle((x + dx, y + h / 7), w / 9, fc="white", ec="#445", lw=0.7)) ax.add_patch(Circle((x + dx, y + h / 7), w / 24, fc="#334", ec="none")) ax.add_patch(Arc((x, y - h / 7), w / 2.4, h / 3.2, theta1=195, theta2=345, ec="#445", lw=1.0)) ax.plot([x, x], [y + h / 2 + 0.03, y + h / 2 + 0.10], color="#445", lw=1.1) ax.add_patch(Circle((x, y + h / 2 + 0.135), 0.04, fc="#445", ec="none")) marks = [(c, False) for c in dots] + [(c, True) for c in lost] n = len(marks) for i, (c, is_lost) in enumerate(marks): cx = x + (i - (n - 1) / 2) * 0.19 cy = y - h / 2 - 0.17 if is_lost: ax.add_patch(Circle((cx, cy), 0.07, fc="white", ec=c, lw=0.9, ls=(0, (2, 2)))) ax.text(cx, cy - 0.005, "\u00d7", ha="center", va="center", fontsize=6, color=c) else: ax.add_patch(Circle((cx, cy), 0.07, fc=c, ec="none")) def fig1b(): from matplotlib.patches import Circle, FancyArrowPatch W, H = 11.4, 4.75 fig, ax = plt.subplots(figsize=(W, H)) ax.set_xlim(0, W) ax.set_ylim(0, H) ax.set_aspect("equal") ax.set_axis_off() ax.text(0.05, H - 0.05, "B", fontsize=13, fontweight="bold", va="top") def arrow(p, q, color="#666", lw=1.2, style="-|>", shrink=2.0, ls="-"): ax.add_patch(FancyArrowPatch(p, q, arrowstyle=style, mutation_scale=10, color=color, lw=lw, linestyle=ls, shrinkA=shrink, shrinkB=shrink)) # ---------------- left: a society in space (contemporaries exchanging messages) cx, cy, r = 2.45, 2.95, 0.95 dotsets = [(BLUE, GOLD), (GREEN,), (BLUE, GREEN), (GOLD, GREEN), (BLUE,)] pos = [] for i, ds in enumerate(dotsets): a = np.pi / 2 + i * 2 * np.pi / 5 x, y = cx + r * np.cos(a) * 1.4, cy + r * np.sin(a) * 0.95 pos.append((x, y)) _robot(ax, x, y, dots=ds) for i, j2 in [(0, 2), (1, 3), (2, 4), (0, 3), (1, 4)]: arrow(pos[i], pos[j2], color="#99a", lw=0.9, style="<|-|>", shrink=26, ls=(0, (4, 2))) ax.text(pos[0][0] + 0.72, pos[0][1] + 0.38, "hi!", fontsize=8, ha="center", bbox=dict(boxstyle="round,pad=0.25", fc="white", ec="#99a", lw=0.8)) clk = (0.55, 4.33) ax.add_patch(Circle(clk, 0.21, fc="white", ec="#445", lw=1.1)) ax.plot([clk[0], clk[0]], [clk[1], clk[1] + 0.13], color="#445", lw=1.0) 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", ha="center", fontsize=7.2, style="italic", color="#555") # ---------------- 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) # ---------------- right: a society in time (a pedigree) axx = 6.8 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) _robot(ax, *p1, dots=(BLUE, GOLD)) _robot(ax, *p2, dots=(GREEN, BLUE)) _robot(ax, *c1, dots=(BLUE,), lost=(GOLD,)) _robot(ax, *c2, dots=(BLUE, GREEN, GOLD)) _robot(ax, *g2, 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") 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, 3.5), gridspec_kw={"width_ratios": [1, 1.35]}) ax = axes[0] 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") 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 equilibrium") ax.axhline(H_star, ls=":", color="gray", lw=1, label="source diversity $H^*$") 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"95%-retention threshold $g\\approx{r['g_star']:.3f}$") ax.set(xlabel="grounding fraction $g = m/(n+m)$", ylabel="stationary diversity $H$") ax.legend() letter(ax, "A") ax = axes[1] 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() letter(ax, "B", x=-0.02) save(fig, "fig2") # ---------------------------------------------------------------- fig 4: blending vs union + Fisher–Muller def fig4(): fig, axes = plt.subplots(1, 2, figsize=(10.6, 3.5)) df, _ = load_bundle("results/E4") r0 = df[(df["g"] == 0.0) & (df["rho"] == 0.0)] mx = r0.groupby("K_T")["surviving_max"].agg(["mean", "sem"]) mn = r0.groupby("K_T")["surviving_mean"].agg(["mean", "sem"]) ax = axes[0] ax.errorbar(mx.index, mx["mean"], yerr=1.96 * mx["sem"], fmt="-o", color="#1f77b4", capsize=2, label="union operator (strongest source)") ax.errorbar(mn.index, mn["mean"], yerr=1.96 * mn["sem"], fmt="--s", color="#d62728", capsize=2, label="output-mean (blending)") ax.set(xlabel="number of parents", ylabel="rare capabilities surviving in the child", xticks=sorted(r0["K_T"].unique())) ax.legend() letter(ax, "A") df8, cfg8 = load_bundle("results/E8") L = cfg8["society"]["L"] d0 = df8[df8["rho"] == 0.0] ax = axes[1] for col, c, lab in [("best_parent", "#7f7f7f", "best single parent"), ("average", "#1f77b4", "blended average"), ("sexual", "#d62728", "recombined offspring")]: k, m, ci = mean_ci(d0, "K_T", col) ax.errorbar(k, m, yerr=ci, fmt="-o", color=c, capsize=2, label=lab) ax.axhline(L, ls=":", color="green", lw=1, label="optimum") ax.set(xlabel="number of parents", ylabel="offspring capability") ax.legend() letter(ax, "B") save(fig, "fig4") # ---------------------------------------------------------------- fig 5: rugged landscapes def fig5(): fig, axes = plt.subplots(2, 2, figsize=(10.6, 6.8)) df9, _ = load_bundle("results/E9") Ks = sorted(df9["K"].unique()) colors = plt.cm.viridis(np.linspace(0, 0.85, len(Ks))) bp = df9.groupby("K")["best_parent"].mean() ax = axes[0, 0] for K, c in zip(Ks, colors): s = df9[df9["K"] == K].groupby("rate")["mean_offspring"].mean() - bp[K] ax.plot(s.index, s.values, "-o", color=c, label=f"$K$={K}") ax.axhline(0, ls=":", color="gray", lw=1) ax.set(xlabel="recombination rate", ylabel="mean offspring − best parent") ax.legend(title="ruggedness", ncol=2) letter(ax, "A") df10, _ = load_bundle("results/E10") ax = axes[0, 1] for col, c, lab in [("global_opt", "green", "global optimum"), ("directed_sex", "#d62728", "screened recombination (directed)"), ("best_parent", "#7f7f7f", "best single parent"), ("random_sex", "#1f77b4", "blind recombination")]: k, m, ci = mean_ci(df10, "K", col) if col == "global_opt": ax.plot(k, m, ":", color=c, label=lab) else: ax.errorbar(k, m, yerr=ci, fmt="-o", color=c, capsize=2, label=lab) ax.set(xlabel="landscape ruggedness $K$", ylabel="offspring capability") ax.legend() letter(ax, "B") df14, _ = load_bundle("results/E14") last = df14[df14["generation"] == df14["generation"].max()].copy() last["best_n"] = last["best_fitness"] / last["global_opt"] K14 = sorted(last["K"].unique()) cmap = plt.get_cmap("viridis") c14 = {K: cmap(i / max(1, len(K14) - 1)) for i, K in enumerate(K14)} for ax, col, ylab, L in [(axes[1, 0], "best_n", "best fitness / optimum", "C"), (axes[1, 1], "diversity", "population diversity", "D")]: for K in K14: g = last[last["K"] == K].groupby("breadth")[col].agg(["mean", "sem"]).reset_index() ax.errorbar(g["breadth"], g["mean"], yerr=1.96 * g["sem"].fillna(0), fmt="-o", color=c14[K], capsize=2, label=f"$K$={K}") ax.set_xscale("log") ax.set(xlabel="mate-pool breadth (monogamous → panmictic)", ylabel=ylab) ax.legend(title="ruggedness") letter(ax, L) save(fig, "fig5") # ---------------------------------------------------------------- fig 6: the society def fig6(): 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, axes = plt.subplots(1, 3, figsize=(11.4, 3.2)) panels = [("best_fitness", "best real fitness", "A"), ("diversity", "population diversity", "B"), ("conformity_true_gap", "conformity − true fitness", "C")] for ax, (col, ylab, L) in zip(axes, panels): for name, c, lab in arms: sub = df[df["arm"] == name] g, m, ci = mean_ci(sub, "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="global optimum") ax.legend() ax.set(xlabel="generation", ylabel=ylab) letter(ax, L) save(fig, "fig6") # ---------------------------------------------------------------- fig 7: speciation, three tiers def fig7(): fig, axes = plt.subplots(2, 3, figsize=(11.4, 6.6)) 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[0, 0] 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") ax.legend() letter(ax, "A") ax = axes[0, 1] 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="P(hybrid inviable)", ylim=(-0.02, 1.02)) ax.legend(title="incompatibility density") letter(ax, "B") 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, 2] x = np.arange(len(order)); w = 0.38 ax.bar(x - w / 2, g["naive"], w, color="#9ecae1", label="before alignment") ax.bar(x + w / 2, g["res"], w, color="#d62728", label="after alignment (residual)") ax.set_xticks(x) ax.set_xticklabels(["same task,\nshared start", "same task,\ndifferent start", "conflicting\ntasks"]) ax.set(ylabel="merge error barrier") ax.legend() letter(ax, "C") 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[1, 0] ax.plot(cg["conflict_frac"], cg["res"], "-o", color="#d62728", label="residual barrier") ax2 = ax.twinx() ax2.plot(cg["conflict_frac"], cg["hyb"], "-s", color="#2c7fb8", label="merged-model accuracy") ax2.set_ylabel("merged accuracy", color="#2c7fb8") ax2.tick_params(axis="y", labelcolor="#2c7fb8") ax2.spines["right"].set_visible(True) ax.set(xlabel="fraction of classes in conflict", ylabel="residual barrier") l1, la1 = ax.get_legend_handles_labels(); l2, la2 = ax2.get_legend_handles_labels() ax.legend(l1 + l2, la1 + la2, loc="center left") letter(ax, "D") rep, _ = load_bundle("results/llm_speciation") def series(df, mode, model, metric): sub = df[(df["mode"] == mode) & (df["model"] == model) & (df["metric"] == metric)] g = sub.groupby("x")["accuracy"].mean().reset_index() return g["x"], g["accuracy"] ax = axes[1, 1] x_, y_ = series(rep, "conflict", "parent_a", "ambig_asc") ax.plot(x_, y_, "--o", color="#9ecae1", label="parent A, own convention") x_, y_ = series(rep, "conflict", "parent_b", "ambig_desc") ax.plot(x_, y_, "--o", color="#a1d99b", label="parent B, own convention") x_, y_ = series(rep, "conflict", "merge_soup", "coherence") ax.plot(x_, y_, "-s", color="#d62728", label="merge, best convention") ax.set(xlabel="fraction of training in conflict", ylabel="accuracy, shared prompts") ax.legend() letter(ax, "E") ax = axes[1, 2] x_, y_ = series(rep, "duration", "merge_soup", "mean_private") ax.plot(x_, y_, "-o", color="#d62728", label="merged model") x_, y_ = series(rep, "duration", "parent_a", "strings") ax.plot(x_, y_, "--o", color="#9ecae1", label="parent A, own task") x_, y_ = series(rep, "duration", "parent_b", "arith") ax.plot(x_, y_, "--o", color="#a1d99b", label="parent B, own task") ax.set(xlabel="specialist training (epochs)", ylabel="accuracy", ylim=(0, 1.02)) ax.legend() letter(ax, "F") save(fig, "fig7") # ---------------------------------------------------------------- fig 3: the language-model tier def fig3(): import pandas as pd from scipy.stats import spearmanr fig, axes = plt.subplots(2, 2, figsize=(10.6, 6.6)) dfm, _ = load_bundle("results/llm_merge_seeds") specs = sorted(m for m in dfm["model"].unique() if m.startswith("spec_")) rows = [] for s, sub in dfm.groupby("seed"): ov = {m: sub[(sub["model"] == m) & (sub["metric"] == "overall")]["accuracy"].mean() for m in specs} b = sub[sub["model"] == max(ov, key=ov.get)].copy(); b["model"] = "best_specialist" rows.append(b) dfm = pd.concat([dfm] + rows, ignore_index=True) models = ["base", "best_specialist", "merge_soup", "merge_ties"] labels = ["base", "best\nspecialist", "merged\n(average)", "merged\n(interference-aware)"] ax = axes[0, 0] x = np.arange(len(models)) for off, metric, c, lab in ((-0.19, "overall", "#2c7fb8", "overall"), (0.19, "worst_family", "#d62728", "worst task family")): vals, errs = [], [] for m in models: v = dfm[(dfm["model"] == m) & (dfm["metric"] == metric)].groupby("seed")["accuracy"].mean() vals.append(v.mean()); errs.append(1.96 * v.std(ddof=1) / max(1, np.sqrt(len(v)))) ax.bar(x + off, vals, 0.36, yerr=errs, capsize=2, color=c, label=lab) ax.set_xticks(x); ax.set_xticklabels(labels, fontsize=7) ax.set(ylabel="verifier accuracy") ax.legend() letter(ax, "A") df7, _ = load_bundle("results/llm_moe_hard_hpc") def acc7(model, metric): r = df7[(df7["model"] == model) & (df7["metric"] == metric)]["accuracy"] return float(r.iloc[0]) if len(r) else np.nan specs7 = sorted(m for m in df7["model"].unique() if m.startswith("spec_")) best7 = max(specs7, key=lambda m: acc7(m, "overall")) models7 = [best7, "merge_soup", "merge_ties", "moe_oracle"] labels7 = ["best\nspecialist", "merged\n(average)", "merged\n(interference-aware)", "routed\n(kept separate)"] ax = axes[0, 1] x = np.arange(len(models7)) for off, metric, c, lab in ((-0.19, "overall", "#2c7fb8", "overall"), (0.19, "worst_family", "#d62728", "worst task family")): ax.bar(x + off, [acc7(m, metric) for m in models7], 0.36, color=c, label=lab) ax.set_xticks(x); ax.set_xticklabels(labels7, fontsize=7) ax.set(ylabel="verifier accuracy") ax.legend() letter(ax, "B") 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 = axes[1, 0] for mode, c, mk, lab in (("conflict", "#d62728", "o", "conflicting conventions"), ("duration", "#2c7fb8", "s", "divergence only"), ("compat", "#41ab5d", "^", "overlap, 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="pre-merge functional conflict (confidence-weighted)", ylabel="merge penalty") ax.legend() letter(ax, "C") preds = [("dis_raw", "raw\ndisagreement"), ("epi_conf", "conf-weighted\nconflict"), ("grad_cos", "gradient\nalignment"), ("delta_cos", "weight\ncosine"), ("delta_l2", "weight\ndistance"), ("cross_perf", "cross-task\naccuracy")] ax = axes[1, 1] rhos_ = [abs(spearmanr(dfe[c], dfe["merge_penalty"])[0]) for c, _ in preds] cols = ["#fc9272", "#d62728", "#9ecae1", "#9ecae1", "#9ecae1", "#9ecae1"] ax.bar(np.arange(len(preds)), rhos_, 0.6, color=cols) ax.set_xticks(np.arange(len(preds))) ax.set_xticklabels([l for _, l in preds], fontsize=6.5) ax.set(ylabel="|Spearman ρ| vs merge penalty", ylim=(0, 0.8)) letter(ax, "D") save(fig, "fig3") if __name__ == "__main__": for f in (fig1a, fig1b, fig2, fig3, fig4, fig5, fig6, fig7): f()