refactor: 将子模块转为普通目录，移除外部 git 依赖

- 移除 JEPA/lejepa-identifiability 子模块 gitlink
- 移除 research/multiply/MultiPLY 子模块 gitlink
- 删除 .gitmodules（不再有外部 URL 依赖）
- 两个目录内容作为普通文件纳入主仓库追踪
- 删除各自内部 .git 目录，消除嵌套 git 仓库

JEPA/lejepa-identifiability/experiments/analysis/plot_scaling.py

@@ -0,0 +1,73 @@
+"""
+Scaling plots: R² and orthogonality vs latent dimension N.
+
+Usage:
+    python analysis/plot_scaling.py --results_dir results/scaling/ --out figures/
+"""
+
+import argparse, os, glob, json
+import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+
+
+def load_results(results_dir):
+    rows = []
+    for path in sorted(glob.glob(os.path.join(results_dir, "*.json"))):
+        with open(path) as f:
+            r = json.load(f)
+        rows.append({k: r.get(k) for k in [
+            "N", "seed", "r2_zx", "r2_xz", "r2_zh", "r2_hz",
+            "orth_err", "orth_err_normalized", "final_loss",
+            "final_align", "final_sigreg", "final_whiten",
+            "epsilon", "delta", "approx_bound", "procrustes_mse",
+        ]})
+    return pd.DataFrame(rows)
+
+
+def main():
+    p = argparse.ArgumentParser()
+    p.add_argument("--results_dir", default="results/scaling/")
+    p.add_argument("--out", default="figures/")
+    args = p.parse_args()
+    os.makedirs(args.out, exist_ok=True)
+
+    df = load_results(args.results_dir)
+    if len(df) == 0:
+        print("No results."); return
+
+    summary = df.groupby("N").agg(
+        r2_xz_mean=("r2_xz", "mean"), r2_xz_std=("r2_xz", "std"),
+        r2_hz_mean=("r2_hz", "mean"), r2_hz_std=("r2_hz", "std"),
+        orth_mean=("orth_err_normalized", "mean"), orth_std=("orth_err_normalized", "std"),
+    ).reset_index()
+    dims = summary["N"].values
+
+    fig, axes = plt.subplots(1, 2, figsize=(8, 3.5))
+
+    ax = axes[0]
+    ax.errorbar(dims, summary["r2_xz_mean"], yerr=summary["r2_xz_std"],
+                fmt="o-", capsize=3, color="gray", label=r"Probe: $g(z) \to z$")
+    ax.errorbar(dims, summary["r2_hz_mean"], yerr=summary["r2_hz_std"],
+                fmt="s-", capsize=3, label=r"Probe: $f \circ g(z) \to z$")
+    ax.set_xscale("log", base=2)
+    ax.set_xlabel("Latent dimension $N$"); ax.set_ylabel(r"Linearity [$R^2$]")
+    ax.set_title("Latent Recovery"); ax.set_ylim(-0.05, 1.05)
+    ax.set_xticks(dims); ax.legend(); ax.grid(alpha=0.3)
+
+    ax = axes[1]
+    ax.errorbar(dims, summary["orth_mean"], yerr=summary["orth_std"],
+                fmt="D-", capsize=3, color="tab:green")
+    ax.set_xscale("log", base=2)
+    ax.set_xlabel("Latent dimension $N$")
+    ax.set_ylabel(r"$\|A^\top A - I\|_F / \sqrt{N}$")
+    ax.set_title("Orthogonality Error"); ax.set_xticks(dims); ax.grid(alpha=0.3)
+
+    fig.tight_layout()
+    fig.savefig(os.path.join(args.out, "fig_scaling.pdf"), bbox_inches="tight")
+    print("Saved fig_scaling.pdf")
+    plt.close()
+
+
+if __name__ == "__main__":
+    main()