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spectral/notebooks/experiment_3_compact_representations.ipynb

@@ -2007,8 +2007,6 @@
     "        patches = x.unfold(2, ps, ps).unfold(3, ps, ps)\n",
     "        patches = patches.contiguous().reshape(B, C, self.n_patches, ps * ps)\n",
     "        # Project each patch onto basis: (B, C, n_patches, n_basis)\n",
-    "        coeffs = torch.einsum('bcnp,bp->bcn', patches, self.basis.T.contiguous())\n",
-    "        # Wait, wrong einsum. Let me fix:\n",
     "        # patches: (B, C, n_patches, ps*ps), basis: (n_basis, ps*ps)\n",
     "        coeffs = torch.einsum('bcnp,kp->bcnk', patches, self.basis)\n",
     "        return coeffs.reshape(B, -1)\n",

spectral/notebooks/experiment_5_matrix_decompositions.ipynb

@@ -1862,8 +1862,11 @@
     "        X = patches.permute(0, 2, 3, 1, 4, 5).reshape(B * n_p, C, ps * ps).permute(0, 2, 1)\n",
     "        # X^T X: (B*n_p, 3, 3)\n",
     "        XtX = torch.bmm(X.transpose(1, 2), X)\n",
-    "        # Add small diagonal for numerical stability\n",
-    "        XtX = XtX + 1e-6 * torch.eye(self.k, device=x.device, dtype=XtX.dtype).unsqueeze(0)\n",
+    "        # Regularize relative to matrix scale: eps * tr(XtX)/k * I\n",
+    "        # Constant-color patches have near-zero eigenvalues; 1e-6 isn't enough\n",
+    "        trace = XtX.diagonal(dim1=-2, dim2=-1).sum(-1, keepdim=True).unsqueeze(-1)  # (N,1,1)\n",
+    "        reg = (1e-4 * trace / self.k + 1e-6)  # scale-adaptive floor + absolute floor\n",
+    "        XtX = XtX + reg * torch.eye(self.k, device=x.device, dtype=XtX.dtype).unsqueeze(0)\n",
     "        # Cholesky: R^T R = X^T X \u2192 R is the upper Cholesky factor\n",
     "        R = torch.linalg.cholesky(XtX).transpose(1, 2)  # upper triangular (B*n_p, k, k)\n",
     "        k = self.k\n",