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/mixing.py

@@ -0,0 +1,56 @@
+"""Nonlinear mixing functions."""
+
+import torch
+
+
+# ── 2D mixing functions ──────────────────────────────────────────────────────
+
+def mix_spiral(z):
+    """g(z) = R(π‖z‖) z — measure-preserving spiral diffeomorphism."""
+    norms = z.norm(dim=-1) * torch.pi
+    c, s = norms.cos(), norms.sin()
+    R = torch.stack([torch.stack([c, -s], dim=-1),
+                     torch.stack([s,  c], dim=-1)], dim=-2)
+    return (R @ z.unsqueeze(-1)).squeeze(-1)
+
+
+def mix_banana(z):
+    """Banana: x0 = z0, x1 = z1 + z0²."""
+    return torch.stack([z[..., 0], z[..., 1] + z[..., 0] ** 2], dim=-1)
+
+
+def mix_sinusoid(z):
+    """Sinusoidal shear: x0 = z0 + sin(1.5 z1), x1 = z1."""
+    return torch.stack([z[..., 0] + torch.sin(1.5 * z[..., 1]), z[..., 1]], dim=-1)
+
+
+MIXINGS_2D = {
+    "spiral": mix_spiral,
+    "banana": mix_banana,
+    "sinusoid": mix_sinusoid,
+    # "nvp" handled via make_coupling_mixing(N=2, n_layers=...)
+}
+
+
+# ── Coupling-layer mixing (any dimension) ────────────────────────────────────
+
+def make_coupling_mixing(N, n_layers=4, seed=1337, device="cuda"):
+    """RealNVP-style coupling layers. Works for any even N (including N=2)."""
+    half = N // 2
+    torch.manual_seed(seed)
+    Ws = []
+    for _ in range(n_layers):
+        W, _ = torch.linalg.qr(torch.randn(half, half, device=device))
+        Ws.append(W * 2.0)
+
+    def mix(z):
+        for i, W in enumerate(Ws):
+            z1, z2 = z[..., :half], z[..., half:]
+            if i % 2 == 0:
+                z2 = z2 + torch.tanh(z1 @ W)
+            else:
+                z1 = z1 + torch.tanh(z2 @ W)
+            z = torch.cat([z1, z2], dim=-1)
+        return z
+
+    return mix