scripts/make_poster_figs.py

"""Render poster PNGs (3200x2000, aspect 1.6) from the reproduction CSVs."""

from __future__ import annotations

import math
import os

import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

from analyze import linfit

RES, OUT = "results", "images"
os.makedirs(OUT, exist_ok=True)

ACC = "#1f4e79"
ACC2 = "#c2410c"
GOLD = "#b45309"
GREY = "#6b7280"
CMAP = plt.get_cmap("plasma")

plt.rcParams.update({
    "font.size": 26, "axes.labelsize": 30, "axes.titlesize": 32,
    "legend.fontsize": 24, "xtick.labelsize": 25, "ytick.labelsize": 25,
    "axes.linewidth": 2.2, "lines.linewidth": 4.0, "grid.alpha": 0.28,
    "figure.dpi": 200, "savefig.bbox": "tight", "savefig.pad_inches": 0.25,
})
FS = (16, 10)
FS_WIDE = (17.6, 8.0)


def _dcolors(dims):
    return {d: CMAP(0.06 + 0.82 * i / max(len(dims) - 1, 1)) for i, d in enumerate(dims)}


def fig_overlap(act, title, fname, annotate=None):
    a = pd.read_csv(f"{RES}/agg_{act}.csv")
    dims = sorted(a["d"].unique())
    cols = _dcolors(dims)
    fig, ax = plt.subplots(figsize=FS)
    for d in dims:
        s = a[a["d"] == d].sort_values("delta")
        ax.plot(s["delta"], s["mean"], "-o", ms=8, color=cols[d], label=f"d={d}")
    ax.set_xlabel(r"$\delta = n/d$")
    ax.set_ylabel(r"squared overlap $\langle\theta^\star,\hat\theta\rangle^2$")
    ax.set_title(title, pad=14)
    ax.grid(True, ls=":")
    ax.legend(ncol=2, frameon=False, loc="lower right")
    if annotate:
        ax.annotate(annotate, xy=(0.03, 0.95), xycoords="axes fraction", va="top",
                    fontsize=26, color=ACC2, weight="bold")
    fig.savefig(f"{OUT}/{fname}", dpi=200)
    plt.close(fig)


def fig_separation():
    t = pd.read_csv(f"{RES}/thresholds.csv")
    fig, ax = plt.subplots(figsize=(16, 10.6))
    combos = [("one-pass-sgd", "trunc", "one-pass SGD, truncated", ACC2, "o"),
              ("full-batch", "quad", "full-batch GD, quadratic", GOLD, "s"),
              ("full-batch", "trunc", "full-batch GD, truncated", ACC, "D")]
    for meth, act, lab, col, mk in combos:
        s = t[(t["method"] == meth) & (t["act"] == act) & (t["target"] == 0.3)].sort_values("logd")
        s = s[np.isfinite(s["value"])]
        f = linfit(s["logd"], s["value"])
        ax.plot(s["logd"], s["value"], mk, ms=16, color=col,
                label=f"{lab} — slope {f['slope']:.2f}")
        xs = np.linspace(s["logd"].min(), s["logd"].max(), 10)
        ax.plot(xs, f["intercept"] + f["slope"] * xs, "-", color=col, lw=3.5, alpha=0.8)
    ax.set_xlabel(r"$\log d$")
    ax.set_ylabel(r"threshold $\delta = n/d$ for overlap$^2 = 0.3$")
    ax.set_title("Sample complexity: full-batch removes the $\\log d$ factor", pad=14)
    ax.grid(True, ls=":")
    ax.legend(frameon=False, loc="upper left")
    fig.savefig(f"{OUT}/pf_separation.png", dpi=200)
    plt.close(fig)


def fig_strong():
    a = pd.read_csv(f"{RES}/agg_gd_trunc_r2.csv")
    dims = sorted(a["d"].unique())
    cols = _dcolors(dims)
    fig, ax = plt.subplots(figsize=FS_WIDE)
    for d in dims:
        s = a[a["d"] == d].sort_values("step")
        ax.semilogy(s["step"], np.maximum(s["dist2"], 1e-13), color=cols[d], label=f"d={d}")
    ax.set_xlabel("GD step $t$")
    ax.set_ylabel(r"$\|\theta_t-\theta^\star\|^2$")
    ax.set_title(r"Strong recovery: geometric convergence after the search phase", pad=14)
    ax.grid(True, ls=":", which="both")
    ax.legend(ncol=2, frameon=False, loc="upper right")
    fig.savefig(f"{OUT}/pf_strong.png", dpi=200)
    plt.close(fig)


def fig_two_phase():
    a = pd.read_csv(f"{RES}/agg_gd_trunc_r2.csv")
    ph = pd.read_csv(f"{RES}/gd_phases.csv").groupby("d").median(numeric_only=True)
    d = 1024 if 1024 in set(a["d"]) else sorted(a["d"])[-1]
    s = a[a["d"] == d].sort_values("step")
    tb = float(ph.loc[d, "tbar"])
    fig, ax = plt.subplots(figsize=FS_WIDE)
    ax.plot(s["step"], s["norm"], color=ACC, label=r"$\|\theta_t\|$")
    ax.plot(s["step"], s["sq_overlap"], color=ACC2, label=r"overlap$^2$")
    ax.axvline(tb, color="#374151", ls="--", lw=3)
    ax.axvspan(0, tb, color=GOLD, alpha=0.09)
    ax.text(tb * 0.5, 0.55, "Phase 1\nangle ↓, norm ↑", ha="center", fontsize=26, color=GOLD)
    ax.text(tb * 1.35, 0.30, "Phase 2\ngeometric", ha="left", fontsize=26, color=ACC)
    ax2 = ax.twinx()
    ax2.semilogy(s["step"], np.maximum(s["dist2"], 1e-13), color=GREY, ls=":", lw=3.5,
                 label=r"$\|\theta_t-\theta^\star\|^2$")
    ax2.set_ylabel(r"$\|\theta_t-\theta^\star\|^2$", color=GREY)
    ax.set_xlim(0, min(float(s["step"].max()), tb * 2.6))
    ax.set_xlabel("GD step $t$")
    ax.set_ylabel(r"$\|\theta_t\|$  /  overlap$^2$")
    ax.set_title(f"Two-phase trajectory (d={d}, $\\bar t\\approx${tb:.0f})", pad=14)
    ax.grid(True, ls=":")
    ax.legend(frameon=False, loc="center right")
    fig.savefig(f"{OUT}/pf_two_phase.png", dpi=200)
    plt.close(fig)


def fig_time():
    t = pd.read_csv(f"{RES}/gd_time_thresholds.csv")
    ph = pd.read_csv(f"{RES}/gd_phases.csv").groupby("d").median(numeric_only=True).reset_index()
    fig, ax = plt.subplots(figsize=FS)
    tg = sorted(t["target"].unique())
    for i, g in enumerate(tg):
        s = t[t["target"] == g].sort_values("logd")
        f = linfit(s["logd"], s["value"])
        c = CMAP(0.08 + 0.75 * i / max(len(tg) - 1, 1))
        ax.plot(s["logd"], s["value"], "o", ms=14, color=c,
                label=f"overlap$^2$={g} ($R^2$={f['r2']:.2f})")
        xs = np.linspace(s["logd"].min(), s["logd"].max(), 10)
        ax.plot(xs, f["intercept"] + f["slope"] * xs, "-", color=c, lw=3, alpha=0.85)
    f = linfit(np.log(ph["d"]), ph["tbar"])
    ax.plot(np.log(ph["d"]), ph["tbar"], "k^--", ms=15, lw=3,
            label=f"$\\bar t$ (phase 1 end), $R^2$={f['r2']:.2f}")
    ax.set_xlabel(r"$\log d$")
    ax.set_ylabel("GD steps")
    ax.set_title(r"Iteration complexity grows like $\log d$", pad=14)
    ax.grid(True, ls=":")
    ax.legend(frameon=False, loc="upper left", ncol=2)
    fig.savefig(f"{OUT}/pf_time.png", dpi=200)
    plt.close(fig)


def fig_spectrum():
    a = pd.read_csv(f"{RES}/audit_spectrum.csv")
    fig, ax = plt.subplots(figsize=FS)
    q = a[(a["act"] == "quad")].groupby(["d", "delta"])[["lam1", "lam2"]].mean().reset_index()
    tr = a[(a["act"] == "trunc") & (a["M"] == 8.0)].groupby(["d", "delta"])[["lam1", "lam2"]] \
          .mean().reset_index()
    dims = sorted(set(q["d"]) & set(tr["d"]))
    cols = _dcolors(dims)
    for d in dims:
        s = q[q["d"] == d].sort_values("delta")
        ax.plot(s["delta"], s["lam1"], "--o", ms=9, color=cols[d], alpha=0.85)
        s = tr[tr["d"] == d].sort_values("delta")
        ax.plot(s["delta"], s["lam1"], "-D", ms=9, color=cols[d])
    ax.axhline(6, color="#111", ls=":", lw=3)
    ax.text(a["delta"].max() * 0.55, 6.4, r"population $\lambda_1=6$", fontsize=25)
    ax.set_xscale("log")
    ax.set_yscale("log")
    ax.set_xlabel(r"$\delta = n/d$")
    ax.set_ylabel(r"$\lambda_1(A^\star)$")
    ax.set_title(r"BBP spike survives only under truncation (solid) — quadratic (dashed) diverges",
                 pad=14, fontsize=27)
    ax.grid(True, ls=":", which="both")
    hd = [plt.Line2D([], [], color="k", ls="-", marker="D", label="truncated $\\sigma$"),
          plt.Line2D([], [], color="k", ls="--", marker="o", label="quadratic $\\sigma$")]
    hd += [plt.Line2D([], [], color=cols[d], lw=5, label=f"d={d}") for d in dims]
    ax.legend(handles=hd, frameon=False, ncol=2, loc="upper right")
    fig.savefig(f"{OUT}/pf_spectrum.png", dpi=200)
    plt.close(fig)


def fig_scorecard():
    rows = [
        ("1", "Quadratic σ: no full-batch gain (Thm 3.1)", "SUPPORTED",
         "δ* ∝ log d, slope 0.65–0.95, R² 0.97–0.99"),
        ("2", "Truncated σ: weak recovery at n ≳ d (Thm 3.2)", "SUPPORTED",
         "curves collapse: spread 0.020 vs 0.126"),
        ("3", "Strong recovery, T ≳ log d (Thm 4.1)", "SUPPORTED",
         "‖θ_T−θ*‖² → 1e-13 at r₀ = d⁻¹⁵"),
        ("4", "Two-phase trajectory (Sec. 4)", "SUPPORTED",
         "t̄ ∝ log d (R² 0.97) and ∝ 1/η; α ≈ 2.7"),
        ("5", "Matches the n ≳ d lower bound (Thm 3.2)", "SUPPORTED",
         "slope 0.04 vs 1.52 for one-pass SGD"),
    ]
    fig, ax = plt.subplots(figsize=FS)
    ax.axis("off")
    ax.set_xlim(0, 1)
    ax.set_ylim(0, 1)
    y = 0.90
    ax.text(0.02, 0.985, "Verdict by claim", fontsize=34, weight="bold", color=ACC, va="top")
    for num, name, verdict, ev in rows:
        ax.add_patch(plt.Rectangle((0.015, y - 0.145), 0.97, 0.14, facecolor="#f6f7f9",
                                   edgecolor="#d7dbe0", lw=2))
        ax.add_patch(plt.Rectangle((0.015, y - 0.145), 0.012, 0.14, facecolor=ACC, lw=0))
        ax.text(0.045, y - 0.035, f"Claim {num} · {name}", fontsize=27, weight="bold", va="top")
        ax.text(0.045, y - 0.098, ev, fontsize=24, color="#334155", va="top")
        ax.text(0.965, y - 0.062, verdict, fontsize=26, weight="bold", color="#166534",
                ha="right", va="center")
        y -= 0.165
    ax.text(0.02, 0.055, "5/5 claims reproduced · 2× RTX 4000 Ada · ~5.6 GPU-hours · $0 cloud spend",
            fontsize=25, color=GREY, va="center")
    fig.savefig(f"{OUT}/pf_scorecard.png", dpi=200)
    plt.close(fig)


if __name__ == "__main__":
    fig_overlap("quad", r"Quadratic $\sigma(z)=z^2$: threshold drifts right with $d$",
                "pf_quad.png")
    fig_overlap("trunc", r"Truncated $\sigma(z)=\min(z^2,8)$: curves collapse",
                "pf_trunc.png")
    fig_separation()
    fig_strong()
    fig_two_phase()
    fig_time()
    try:
        fig_spectrum()
    except FileNotFoundError:
        print("skip spectrum (audit not finished)")
    fig_scorecard()
    print("wrote", sorted(os.listdir(OUT)))