File size: 3,664 Bytes
7d41a21 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 | """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)
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