plot_cloverleaf.py

"""Plot the cloverleaf distribution of (w_1, w_2) from a trained 2-layer net.

Also shows: bias histogram, output-weight histogram, prediction surface."""
from __future__ import annotations

import argparse
from pathlib import Path

import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
import torch


def main(model_path: Path, out_dir: Path, tag: str = "cloverleaf"):
    ckpt = torch.load(model_path, map_location="cpu", weights_only=True)
    W = ckpt["W"].numpy()   # (N, 2)
    b = ckpt["b"].numpy()
    a = ckpt["a"].numpy()
    width = ckpt["width"]
    scale = ckpt["scale"]

    out_dir.mkdir(parents=True, exist_ok=True)
    sns.set_theme(style="white", context="paper")

    # ---- cloverleaf scatter ---------------------------------------------------
    df = pd.DataFrame({"w1": W[:, 0], "w2": W[:, 1], "a": a, "b": b})
    df["sign_a"] = np.where(df["a"] > 0, "+", "−")
    g = sns.JointGrid(data=df, x="w1", y="w2", hue="sign_a",
                      palette={"+": "#1f77b4", "−": "#d62728"}, height=6)
    g.plot_joint(sns.scatterplot, s=6, alpha=0.5, edgecolor=None)
    g.plot_marginals(sns.kdeplot, common_norm=False, fill=True, alpha=0.3)
    g.figure.suptitle(f"Hidden-layer (w₁, w₂) — width={width}, scale={scale}", y=1.02)
    g.savefig(out_dir / f"{tag}_scatter.pdf", bbox_inches="tight")
    plt.close("all")

    # ---- direction histogram (angle of incoming weight) -----------------------
    angle = np.arctan2(W[:, 1], W[:, 0])
    norm = np.linalg.norm(W, axis=1)
    df2 = pd.DataFrame({"angle_deg": np.degrees(angle), "norm": norm,
                        "sign_a": df["sign_a"]})
    fig, axes = plt.subplots(1, 2, figsize=(10, 4))
    sns.histplot(df2, x="angle_deg", hue="sign_a", bins=72, ax=axes[0],
                 palette={"+": "#1f77b4", "−": "#d62728"}, multiple="stack")
    axes[0].set_xlabel("angle of (w₁, w₂)  [deg]")
    axes[0].set_title("Incoming-weight direction histogram")
    # cloverleaf prediction: peaks at ±45° and ±135°
    for x0 in [-135, -45, 45, 135]:
        axes[0].axvline(x0, color="grey", lw=0.5, ls="--")
    sns.histplot(df2, x="norm", bins=60, ax=axes[1], color="grey")
    axes[1].set_xlabel("‖w‖₂")
    axes[1].set_title("Incoming-weight norms")
    fig.tight_layout()
    fig.savefig(out_dir / f"{tag}_angle_norm.pdf", bbox_inches="tight")
    plt.close(fig)

    # ---- prediction surface ---------------------------------------------------
    grid = np.linspace(-1, 1, 200)
    XX, YY = np.meshgrid(grid, grid)
    X = np.stack([XX.ravel(), YY.ravel()], axis=1)
    H = np.clip(X @ W.T + b, -1, 1)
    pred = H @ a
    if scale == "meanfield":
        pred = pred / width
    elif scale == "ntk":
        pred = pred / np.sqrt(width)
    pred = pred.reshape(XX.shape)
    target = np.sign(XX) * np.sign(YY)
    fig, axes = plt.subplots(1, 2, figsize=(10, 4))
    im0 = axes[0].imshow(pred, extent=[-1, 1, -1, 1], origin="lower",
                         cmap="RdBu_r", vmin=-1.2, vmax=1.2)
    axes[0].set_title("Network output")
    axes[1].imshow(target, extent=[-1, 1, -1, 1], origin="lower", cmap="RdBu_r")
    axes[1].set_title("Target (XOR)")
    plt.colorbar(im0, ax=axes, shrink=0.8)
    fig.savefig(out_dir / f"{tag}_pred_surface.pdf", bbox_inches="tight")
    plt.close(fig)

    print(f"Wrote plots under {out_dir}")


if __name__ == "__main__":
    p = argparse.ArgumentParser()
    p.add_argument("--model", type=Path, required=True)
    p.add_argument("--out", type=Path, required=True)
    p.add_argument("--tag", default="cloverleaf")
    args = p.parse_args()
    main(args.model, args.out, args.tag)