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/lejepa_id/metrics.py

@@ -0,0 +1,65 @@
+"""Evaluation metrics — standardized across all experiments."""
+
+import torch
+
+def bidirectional_r2(a, b):
+    """R²(a->b) and R²(b->a) via torch lstsq on GPU. a, b are tensors."""
+    def _r2(x, y):
+        x1 = torch.cat([x, torch.ones(len(x), 1, device=x.device)], dim=1)
+        W = torch.linalg.lstsq(x1, y).solution
+        ss_res = ((y - x1 @ W) ** 2).sum()
+        ss_tot = ((y - y.mean(0)) ** 2).sum()
+        return (1 - ss_res / ss_tot).item()
+    return _r2(a, b), _r2(b, a)
+
+
+def compute_all_metrics(z, x, h, h_prime, rho, N):
+    """All metrics on GPU. z, x, h, h_prime are torch tensors."""
+    r2_zx, r2_xz = bidirectional_r2(z, x)
+    r2_zh, r2_hz = bidirectional_r2(z, h)
+
+    # Orthogonality
+    z1 = torch.cat([z, torch.ones(len(z), 1, device=z.device)], dim=1)
+    W = torch.linalg.lstsq(z1, h).solution
+    A = W[:N].T
+    orth_err = torch.linalg.norm(A.T @ A - torch.eye(N, device=A.device), 'fro').item()
+    orth_err_normalized = orth_err / (N ** 0.5)
+
+    # Bound quantities
+    cov_h = torch.cov(h.T)
+    epsilon = torch.linalg.norm(cov_h - torch.eye(N, device=h.device), 'fro').item()
+    trace_cov = torch.trace(cov_h).item()
+    L_h = ((h_prime - h) ** 2).sum(dim=1).mean().item()
+    delta = max(L_h - 2 * (1 - rho) * trace_cov, 0.0)
+    spectral_gap = 2 * rho * (1 - rho)
+    D_bound = delta / spectral_gap if spectral_gap > 0 else float("inf")
+    approx_bound = D_bound + (epsilon + D_bound) ** 2
+
+    # Procrustes
+    M = (h.T @ z) / len(z)
+    U, S, Vt = torch.linalg.svd(M)
+    Q = U @ Vt
+    procrustes_mse = ((h - z @ Q.T) ** 2).sum(dim=1).mean().item()
+
+    return {
+        "r2_zx": r2_zx, "r2_xz": r2_xz,
+        "r2_zh": r2_zh, "r2_hz": r2_hz,
+        "orth_err": orth_err, "orth_err_normalized": orth_err_normalized,
+        "epsilon": epsilon, "delta": delta, "D_bound": D_bound,
+        "approx_bound": approx_bound, "procrustes_mse": procrustes_mse,
+        "L_h": L_h, "trace_cov": trace_cov,
+    }
+
+
+def compute_recovery_metrics(z, h, N, suffix=""):
+    """R² in both directions + orthogonality. Suffix appended to keys."""
+    r2_zh, r2_hz = bidirectional_r2(z, h)
+    z1 = torch.cat([z, torch.ones(len(z), 1, device=z.device)], dim=1)
+    W = torch.linalg.lstsq(z1, h).solution
+    A = W[:N].T
+    orth_err = torch.linalg.norm(A.T @ A - torch.eye(N, device=A.device), 'fro').item()
+    return {
+        f"r2_zh{suffix}": r2_zh, f"r2_hz{suffix}": r2_hz,
+        f"orth_err{suffix}": orth_err,
+        f"orth_err_normalized{suffix}": orth_err / (N ** 0.5),
+    }