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UserStep 0
Task: ml-dimensionality-reduction
Dimensionality Reduction: Nonlinear Embedding Method Design
Research Question
Design a novel nonlinear dimensionality reduction method that preserves data structure (both local neighborhoods and global relationships) better than existing methods when embedding high-dimensional data into 2D.
Background
Dimensionality reduction is fundamental to data analysis and visualization. PCA provides a fast linear baseline but cannot capture nonlinear manifold structure. Other methods trade off local and global structure preservation in different ways. This task evaluates dimensionality reduction methods by neighborhood preservation across diverse data types.
Task
Modify the CustomDimReduction class (lines 14-70) in custom_dimred.py to implement a novel nonlinear dimensionality reduction algorithm. Your implementation must:
- Accept high-dimensional data X of shape (n_samples, n_features) where n_samples <= 5000 and n_features ranges from 50 to 784.
- Return a 2D embedding of shape (n_samples, 2).
- Respect the
random_stateparameter for reproducibility. - Complete within a reasonable time (under 5 minutes per dataset on CPU).
You may use numpy, scipy, and scikit-learn utilities (already installed). The method is evaluated on three diverse datasets: MNIST (digit images), Fashion-MNIST (clothing images), and 20 Newsgroups (text, pre-processed to 50D via TF-IDF + SVD).
Interface
class CustomDimReduction:
def __init__(self, n_components: int = 2, random_state: int | None = None):
...
def fit_transform(self, X: NDArray[np.float64]) -> NDArray[np.float64]:
# X: (n_samples, n_features), returns: (n_samples, n_components)
...Evaluation
Three metrics are computed on each dataset (k=7 neighbors):
- kNN accuracy: Classification accuracy of a 7-NN classifier in the 2D space (higher is better). Measures how well class structure is preserved.
- Trustworthiness: Whether points that are neighbors in the embedding are also neighbors in the original space (higher is better, max 1.0).
- Continuity: Whether points that are neighbors in the original space remain neighbors in the embedding (higher is better, max 1.0).
Success means improving on existing methods across all three datasets and all three metrics.
scikit-learn/bench/custom_dimred.py [EDITABLE — lines 15–59 only]
1: """Custom dimensionality reduction benchmark -- agent-editable template.
2:
3: The agent modifies `CustomDimReduction` to implement a novel nonlinear
4: dimensionality reduction method. The evaluation harness embeds three
5: datasets into 2D, then measures kNN accuracy, trustworthiness, and
6: continuity in the reduced space.
7: """
8:
9: import numpy as np
10: from numpy.typing import NDArray
11:
12: # =====================================================================
13: # EDITABLE: implement AssistantStep 1edit
Tool Input
1{
2 "content": "class CustomDimReduction:\n \"\"\"Multi-Scale Affinity Embedding (MSAE) - Novel nonlinear dimensionality reduction.\n \n Combines multi-scale nearest-neighbor affinity construction with\n gradient-descent optimization using a heavy-tailed kernel.\n Preserves both local neighborhoods and global manifold structure.\n \"\"\"\n\n def __init__(self, n_components: int = 2, random_state: int | None = None):\n self.n_components = n_components\n self.random_state = random_state\n\n def _build_multiscale_affinity(self, X, k_list=[10, 30, 100]):\n \"\"\"Build multi-scale affinity matrix combining multiple neighbor sizes.\"\"\"\n n = X.shape[0]\n \n # Compute pairwise squared distances efficiently (chunked)\n # Using ||a-b||^2 = ||a||^2 + ||b||^2 - 2*a.b\n X_sq = np.sum(X ** 2, axis=1)\n \n # Process in chunks to manage memory\n W = np.zeros((n, n), dtype=np.float64)\n chunk_size = 500\n \n for i_start in range(0, n, chunk_size):\n i_end = min(i_start + chunk_size, n)\n # X[i_start:i_end] @ X.T gives dot products\n dot = X[i_start:i_end] @ X.T\n D2 = X_sq[i_start:i_end, None] + X_sq[None, :] - 2 * dot\n D2 = np.maximum(D2, 0) # numerical safety\n \n for k in k_list:\n # For each point, find k nearest neighbors and set affinity\n for i in range(i_start, i_end):\n row_idx = i - i_start\n indices = np.argpartition(D2[row_idx], k + 1)[:k + 1]\n indices = indices[indices != i]\n if len(indices) > k:\n indices = indices[:k]\n # Gaussian affinity with adaptive bandwidth\n dists = np.sqrt(D2[row_idx, indices])\n sigma = np.mean(dists) if len(dists) > 0 else 1.0\n if sigma < 1e-10:\n sigma = 1.0\n W[i, indices] += np.exp(-dists ** 2 / (2 * sigma ** 2))\n \n # Symmetrize\n W = (W + W.T) / 2.0\n np.fill_diagonal(W, 0)\n \n # Normalize\n total = W.sum()\n if total > 0:\n W /= total\n \n return W\n\n def _compute_embedding(self, W, n_samples, n_iter=400, init='pca'):\n \"\"\"Optimize 2D embedding using gradient descent with Cauchy kernel.\"\"\"\n rng = np.random.RandomState(self.random_state)\n \n # Initialization\n if init == 'pca':\n from sklearn.decomposition import PCA\n Y = PCA(n_components=self.n_components, random_state=self.random_state).fit_transform(\n W @ (np.eye(n_samples) - np.eye(n_samples))\n )\n # Actually, let's use PCA on the original data - but we don't have it here\n # Use spectral initialization instead\n D = np.diag(W.sum(axis=1))\n L = D - W\n # Compute smallest eigenvectors\n from scipy.sparse.linalg import eigsh\n try:\n # Use dense eigendecomposition for small matrices\n eigenvalues, eigenvectors = np.linalg.eigh(L)\n idx = np.argsort(eigenvalues)[1:self.n_components + 1]\n Y = eigenvectors[:, idx]\n except:\n Y = rng.randn(n_samples, self.n_components) * 0.01\n else:\n Y = rng.randn(n_samples, self.n_components) * 0.01\n \n # Gradient descent optimization with Cauchy kernel\n # Cost: sum_ij W_ij * log(1 + ||y_i - y_j||^2)\n # which is equivalent to minimizing KL-like divergence with t-distribution\n \n eta = 1.0 # initial learning rate\n momentum = 0.8\n velocity = np.zeros_like(Y)\n \n # Precompute sum of W for normalization\n w_sum = W.sum()\n if w_sum == 0:\n w_sum = 1.0\n \n for iteration in range(n_iter):\n # Compute pairwise distances in embedding\n Y_sq = np.sum(Y ** 2, axis=1)\n DY = Y_sq[:, None] + Y_sq[None, :] - 2 * Y @ Y.T\n DY = np.maximum(DY, 0)\n \n # Q matrix: Cauchy kernel\n Q = 1.0 / (1.0 + DY)\n np.fill_diagonal(Q, 0)\n \n # Normalize Q\n q_sum = Q.sum()\n if q_sum > 0:\n Q /= q_sum\n \n # Gradient: dC/dY_i = 4 * sum_j (W_ij - Q_ij) * (y_i - y_j) / (1 + ||y_i-y_j||^2)\n # = 4 * [sum_j W_ij * (y_i - y_j) / (1 + DY_ij) - sum_j Q_ij * (y_i - y_j) / (1 + DY_ij)]\n \n # Compute affinity-weighted displacement\n QW = W - Q\n np.fill_diagonal(QW, 0)\n \n # Compute gradient efficiently\n # grad_i = 4 * sum_j QW_ij * (y_i - y_j) / (1 + DY_ij)\n # = 4 * [y_i * sum_j (QW_ij / (1 + DY_ij)) - sum_j (QW_ij * y_j / (1 + DY_ij))]\n \n denom = 1.0 + DY\n QW_norm = QW / denom\n \n grad = 4.0 * (Y * QW_norm.sum(axis=1, keepdims=True) - QW_norm @ Y)\n \n # Clip gradients\n grad_norm = np.linalg.norm(grad)\n if grad_norm > 10.0:\n grad = grad * 10.0 / grad_norm\n \n # Momentum update\n velocity = momentum * velocity - eta * grad\n Y = Y + velocity\n \n # Learning rate schedule: warmup then decay\n if iteration < 50:\n eta = 0.02 * (iteration + 1) / 50\n else:\n eta = 0.02 * (1 - (iteration - 50) / (n_iter - 50))\n eta = max(eta, 0.001)\n \n # Periodically recenter\n if iteration % 50 == 0:\n Y = Y - Y.mean(axis=0, keepdims=True)\n \n return Y\n\n def fit_transform(self, X: NDArray[np.float64]) -> NDArray[np.float64]:\n \"\"\"Reduce dimensionality of X.\n \n Parameters\n ----------\n X : ndarray of shape (n_samples, n_features)\n High-dimensional input data (standardized).\n \n Returns\n -------\n X_reduced : ndarray of shape (n_samples, n_components)\n Low-dimensional embedding.\n \"\"\"\n n_samples, n_features = X.shape\n rng = np.random.RandomState(self.random_state)\n \n # Step 1: PCA initialization for global structure\n from sklearn.decomposition import PCA\n Y_init = PCA(n_components=self.n_components, random_state=self.random_state).fit_transform(X)\n \n # Step 2: Build multi-scale affinity using multiple k values\n # Combines local (k=10), medium (k=30), and global (k=100) structure\n W = self._build_multiscale_affinity(X, k_list=[10, 30, 100])\n \n # Step 3: Optimize embedding with gradient descent\n # Start from PCA initialization for better convergence\n Y = self._compute_embedding_optimized(W, X, Y_init, n_iter=300)\n \n return Y\n\n def _compute_embedding_optimized(self, W, X, Y_init, n_iter=300):\n \"\"\"Optimize embedding with PCA initialization and momentum.\"\"\"\n n = X.shape[0]\n Y = Y_init.copy()\n \n # Scale initialization\n Y = Y - Y.mean(axis=0, keepdims=True)\n Y_std = Y.std()\n if Y_std > 0:\n Y = Y / Y_std * 0.1\n \n # Adam-like optimizer\n eta = 1.0\n beta1 = 0.9\n beta2 = 0.999\n eps = 1e-8\n m = np.zeros_like(Y)\n v = np.zeros_like(Y)\n \n for iteration in range(n_iter):\n # Compute pairwise distances\n Y_sq = np.sum(Y ** 2, axis=1)\n DY = Y_sq[:, None] + Y_sq[None, :] - 2 * Y @ Y.T\n DY = np.maximum(DY, 0)\n \n # Q: Cauchy kernel (Student's t with df=1)\n Q = 1.0 / (1.0 + DY)\n np.fill_diagonal(Q, 0)\n \n # Normalize Q\n q_sum = Q.sum()\n if q_sum > 0:\n Q /= q_sum\n \n # Symmetrized gradient: 4 * sum_j (W_ij - Q_ij) * (y_i - y_j) / (1 + ||y_i-y_j||^2)\n QW = W - Q\n \n # Efficient gradient computation\n denom = 1.0 + DY\n A = QW / denom\n np.fill_diagonal(A, 0)\n \n grad = 4.0 * (Y * A.sum(axis=1, keepdims=True) - A @ Y)\n \n # Gradient clipping\n grad_norm = np.linalg.norm(grad, 'fro')\n max_norm = 5.0\n if grad_norm > max_norm:\n grad = grad * max_norm / grad_norm\n \n # Adam update\n m = beta1 * m + (1 - beta1) * grad\n v = beta2 * v + (1 - beta2) * grad ** 2\n m_hat = m / (1 - beta1 ** (iteration + 1))\n v_hat = v / (1 - beta2 ** (iteration + 1))\n \n # Learning rate with warmup and decay\n if iteration < 30:\n lr = 1.0 * (iteration + 1) / 30\n else:\n progress = (iteration - 30) / (n_iter - 30)\n lr = 1.0 * (1 - 0.8 * progress)\n \n Y = Y - lr * m_hat / (np.sqrt(v_hat) + eps)\n \n # Recenter periodically\n if iteration % 25 == 0:\n Y = Y - Y.mean(axis=0, keepdims=True)\n \n return Y",
3 "end_line": 59,
4 "filename": "scikit-learn/bench/custom_dimred.py",
5 "start_line": 15
6}Tool ResultStep 1
ERROR: Invalid arguments for 'edit': WorkspaceTools.edit() missing 1 required positional argument: 'op'
AssistantStep 2edit
Tool Input
1{
2 "op": "replace",
3 "content": "class CustomDimReduction:\n \"\"\"Multi-Scale Affinity Embedding (MSAE) - Novel nonlinear dimensionality reduction.\n \n Combines multi-scale nearest-neighbor affinity construction with\n gradient-descent optimization using a heavy-tailed kernel.\n Preserves both local neighborhoods and global manifold structure.\n \"\"\"\n\n def __init__(self, n_components: int = 2, random_state: int | None = None):\n self.n_components = n_components\n self.random_state = random_state\n\n def fit_transform(self, X: NDArray[np.float64]) -> NDArray[np.float64]:\n \"\"\"Reduce dimensionality of X.\n\n Parameters\n ----------\n X : ndarray of shape (n_samples, n_features)\n High-dimensional input data (standardized).\n\n Returns\n -------\n X_reduced : ndarray of shape (n_samples, n_components)\n Low-dimensional embedding.\n \"\"\"\n n = X.shape[0]\n rng = np.random.RandomState(self.random_state)\n \n # Step 1: PCA initialization for global structure\n from sklearn.decomposition import PCA\n Y_pca = PCA(n_components=self.n_components, random_state=self.random_state).fit_transform(X)\n Y_pca = Y_pca - Y_pca.mean(axis=0, keepdims=True)\n \n # Step 2: Build multi-scale affinity matrix\n W = self._build_multiscale_affinity(X, k_list=[10, 30, 100])\n \n # Step 3: Optimize embedding with gradient descent\n Y = self._optimize_embedding(W, Y_pca, n_iter=300)\n \n return Y\n\n def _compute_distances(self, X):\n \"\"\"Compute pairwise squared Euclidean distances.\"\"\"\n X_sq = np.sum(X ** 2, axis=1)\n D2 = X_sq[:, None] + X_sq[None, :] - 2 * X @ X.T\n return np.maximum(D2, 0)\n\n def _build_multiscale_affinity(self, X, k_list=[10, 30, 100]):\n \"\"\"Build multi-scale affinity matrix combining multiple neighbor sizes.\"\"\"\n n = X.shape[0]\n D2 = self._compute_distances(X)\n \n W = np.zeros((n, n), dtype=np.float64)\n \n for k in k_list:\n # For each row, find k nearest neighbors\n for i in range(n):\n indices = np.argpartition(D2[i], k + 1)[:k + 1]\n indices = indices[indices != i]\n if len(indices) > k:\n indices = indices[:k]\n dists = np.sqrt(D2[i, indices])\n sigma = np.mean(dists) if len(dists) > 0 else 1.0\n if sigma < 1e-10:\n sigma = 1.0\n W[i, indices] += np.exp(-dists ** 2 / (2 * sigma ** 2))\n \n # Symmetrize\n W = (W + W.T) / 2.0\n np.fill_diagonal(W, 0)\n \n # Normalize\n total = W.sum()\n if total > 0:\n W /= total\n \n return W\n\n def _optimize_embedding(self, W, Y_init, n_iter=300):\n \"\"\"Optimize 2D embedding with Cauchy kernel and Adam optimizer.\"\"\"\n n = Y_init.shape[0]\n Y = Y_init.copy()\n \n # Scale initialization\n Y_std = Y.std()\n if Y_std > 0:\n Y = Y / Y_std * 0.1\n \n # Adam parameters\n beta1, beta2, eps = 0.9, 0.999, 1e-8\n m = np.zeros_like(Y)\n v = np.zeros_like(Y)\n \n for iteration in range(n_iter):\n # Pairwise squared distances in embedding\n Y_sq = np.sum(Y ** 2, axis=1)\n DY = Y_sq[:, None] + Y_sq[None, :] - 2 * Y @ Y.T\n DY = np.maximum(DY, 0)\n \n # Q: Cauchy kernel (Student's t with df=1)\n Q = 1.0 / (1.0 + DY)\n np.fill_diagonal(Q, 0)\n \n q_sum = Q.sum()\n if q_sum > 0:\n Q /= q_sum\n \n # Gradient computation\n QW = W - Q\n denom = 1.0 + DY\n A = QW / denom\n np.fill_diagonal(A, 0)\n \n grad = 4.0 * (Y * A.sum(axis=1, keepdims=True) - A @ Y)\n \n # Gradient clipping\n grad_norm = np.linalg.norm(grad, 'fro')\n max_norm = 5.0\n if grad_norm > max_norm:\n grad = grad * max_norm / grad_norm\n \n # Adam update\n m = beta1 * m + (1 - beta1) * grad\n v = beta2 * v + (1 - beta2) * grad ** 2\n m_hat = m / (1 - beta1 ** (iteration + 1))\n v_hat = v / (1 - beta2 ** (iteration + 1))\n \n # Learning rate schedule\n if iteration < 30:\n lr = 1.0 * (iteration + 1) / 30\n else:\n progress = (iteration - 30) / (n_iter - 30)\n lr = 1.0 * (1 - 0.8 * progress)\n \n Y = Y - lr * m_hat / (np.sqrt(v_hat) + eps)\n \n # Recenter periodically\n if iteration % 25 == 0:\n Y = Y - Y.mean(axis=0, keepdims=True)\n \n return Y",
4 "end_line": 59,
5 "filename": "scikit-learn/bench/custom_dimred.py",
6 "start_line": 15
7}Tool ResultStep 2
OK: Replaced lines 15..59 with 141 line(s) in scikit-learn/bench/custom_dimred.py. Editable range: 15–155.
[Current file: scikit-learn/bench/custom_dimred.py | editable: 15–155 | total: 389 lines]
15 class CustomDimReduction:
16 """Multi-Scale Affinity Embedding (MSAE) - Novel nonlinear dimensionality reduction.
17
... (135 more lines) ...
153 Y = Y - Y.mean(axis=0, keepdims=True)
154
155 return YAssistantStep 3edit
Tool Input
1{
2 "end_line": 100,
3 "filename": "scikit-learn/bench/custom_dimred.py",
4 "op": "replace",
5 "start_line": 15,
6 "content": "class CustomDimReduction:\n \"\"\"Multi-Scale Affinity Embedding (MSAE) - Novel nonlinear dimensionality reduction.\n\n Combines multi-scale nearest-neighbor affinity with an adaptive\n Cauchy-kernel embedding optimized via Adam. Preserves both local\n neighborhoods and global manifold structure.\n \"\"\"\n\n def __init__(self, n_components: int = 2, random_state: int | None = None):\n self.n_components = n_components\n self.random_state = random_state\n\n def fit_transform(self, X: NDArray[np.float64]) -> NDArray[np.float64]:\n \"\"\"Reduce dimensionality of X.\n\n Parameters\n ----------\n X : ndarray of shape (n_samples, n_features)\n High-dimensional input data (standardized).\n\n Returns\n -------\n X_reduced : ndarray of shape (n_samples, n_components)\n Low-dimensional embedding.\n \"\"\"\n from sklearn.decomposition import PCA\n rng = np.random.RandomState(self.random_state)\n\n # Step 1: PCA initialization for global structure\n Y_pca = PCA(n_components=self.n_components, random_state=self.random_state).fit_transform(X)\n\n # Step 2: Build multi-scale affinity matrix\n W = self._build_multiscale_affinity(X, k_list=[10, 30, 100])\n\n # Step 3: Optimize embedding with gradient descent\n Y = self._optimize_embedding(W, Y_pca, n_iter=300)\n\n return Y\n\n def _compute_distances(self, X):\n \"\"\"Compute pairwise squared Euclidean distances.\"\"\"\n X_sq = np.sum(X ** 2, axis=1)\n D2 = X_sq[:, None] + X_sq[None, :] - 2.0 * (X @ X.T)\n return np.maximum(D2, 0.0)\n\n def _build_multiscale_affinity(self, X, k_list=(10, 30, 100)):\n \"\"\"Build multi-scale affinity matrix using multiple neighbor scales.\"\"\"\n n = X.shape[0]\n D2 = self._compute_distances(X)\n\n W_total = np.zeros((n, n), dtype=np.float64)\n\n for k in k_list:\n # Vectorized: find k nearest neighbors for all points at once\n k_eff = min(k, n - 1)\n # argpartition to get k+1 nearest (excluding self)\n idx = np.argpartition(D2, k_eff + 1, axis=1)[:, :k_eff + 1]\n\n # Mask out self (diagonal)\n rows = np.arange(n)[:, None]\n mask_self = (idx == rows)\n # Replace self-index with last column if needed\n last_col = idx[:, k_eff:k_eff + 1]\n idx[mask_self] = last_col[mask_self.sum(axis=1, keepdims=True) > 0][:, 0]\n\n # Gather distances\n D_nn = np.take_along_axis(np.sqrt(np.maximum(D2, 1e-30)), idx, axis=1)\n\n # Per-point bandwidth: mean distance to k neighbors\n sigma = D_nn.mean(axis=1, keepdims=True)\n sigma = np.maximum(sigma, 1e-10)\n\n # Compute Gaussian affinities\n W_k = np.exp(-D_nn ** 2 / (2.0 * sigma ** 2))\n # Zero out diagonal (self-affinity)\n np.fill_diagonal(W_k, 0.0)\n\n # Scatter back to full matrix\n W_partial = np.zeros((n, n), dtype=np.float64)\n for j in range(k_eff + 1):\n W_partial[rows.ravel(), idx[:, j]] = W_k[:, j]\n\n W_total += W_partial\n\n # Symmetrize and normalize\n W_total = (W_total + W_total.T) * 0.5\n np.fill_diagonal(W_total, 0.0)\n total = W_total.sum()\n if total > 0:\n W_total /= total\n\n return W_total\n\n def _optimize_embedding(self, W, Y_init, n_iter=300):\n \"\"\"Optimize 2D embedding with Cauchy kernel and Adam optimizer.\"\"\"\n n = Y_init.shape[0]\n Y = Y_init.copy()\n Y = Y - Y.mean(axis=0, keepdims=True)\n\n # Scale initialization to small random\n Y_std = Y.std()\n if Y_std > 0:\n Y = Y / Y_std * 0.01\n\n # Adam parameters\n beta1, beta2, eps = 0.9, 0.999, 1e-8\n m = np.zeros_like(Y)\n v = np.zeros_like(Y)\n\n for iteration in range(n_iter):\n # Pairwise squared distances in embedding\n Y_sq = np.sum(Y ** 2, axis=1)\n DY = Y_sq[:, None] + Y_sq[None, :] - 2.0 * (Y @ Y.T)\n DY = np.maximum(DY, 0.0)\n\n # Q: Cauchy kernel (Student's t with df=1)\n Q = 1.0 / (1.0 + DY)\n np.fill_diagonal(Q, 0.0)\n q_sum = Q.sum()\n if q_sum > 0:\n Q /= q_sum\n\n # Gradient: dC/dY_i = 4 * sum_j (W_ij - Q_ij) * (y_i - y_j) / (1 + ||y_i-y_j||^2)\n QW = W - Q\n denom = 1.0 + DY\n A = QW / denom\n np.fill_diagonal(A, 0.0)\n\n grad = 4.0 * (Y * A.sum(axis=1, keepdims=True) - A @ Y)\n\n # Gradient clipping\n grad_norm = np.linalg.norm(grad, 'fro')\n max_norm = 5.0\n if grad_norm > max_norm:\n grad = grad * max_norm / grad_norm\n\n # Adam update\n m = beta1 * m + (1 - beta1) * grad\n v = beta2 * v + (1 - beta2) * grad ** 2\n m_hat = m / (1 - beta1 ** (iteration + 1))\n v_hat = v / (1 - beta2 ** (iteration + 1))\n\n # Learning rate schedule: warmup then decay\n if iteration < 30:\n lr = 1.0 * (iteration + 1) / 30\n else:\n progress = (iteration - 30) / (n_iter - 30)\n lr = 1.0 * (1 - 0.8 * progress)\n\n Y = Y - lr * m_hat / (np.sqrt(v_hat) + eps)\n\n # Recenter periodically\n if iteration % 25 == 0:\n Y = Y - Y.mean(axis=0, keepdims=True)\n\n return Y"
7}Tool ResultStep 3
OK: Replaced lines 15..100 with 156 line(s) in scikit-learn/bench/custom_dimred.py. Editable range: 15–225.
[Current file: scikit-learn/bench/custom_dimred.py | editable: 15–225 | total: 459 lines]
15 class CustomDimReduction:
16 """Multi-Scale Affinity Embedding (MSAE) - Novel nonlinear dimensionality reduction.
17
... (205 more lines) ...
223 Y = Y - Y.mean(axis=0, keepdims=True)
224
225 return YAssistantStep 4edit
Tool Input
1{
2 "end_line": 225,
3 "filename": "scikit-learn/bench/custom_dimred.py",
4 "op": "replace",
5 "start_line": 15,
6 "content": "class CustomDimReduction:\n \"\"\"Multi-Scale Affinity Embedding (MSAE) - Novel nonlinear dimensionality reduction.\n\n Combines multi-scale nearest-neighbor affinity construction with an\n adaptive Cauchy-kernel embedding optimized via Adam. Key ideas:\n 1. Multi-scale affinity: multiple k values capture local AND global structure\n 2. Adaptive bandwidth: per-point sigma normalizes for varying density\n 3. Cauchy kernel: heavier tails preserve global relationships better\n 4. PCA init + Adam: robust optimization from a meaningful starting point\n \"\"\"\n\n def __init__(self, n_components: int = 2, random_state: int | None = None):\n self.n_components = n_components\n self.random_state = random_state\n\n def fit_transform(self, X: NDArray[np.float64]) -> NDArray[np.float64]:\n \"\"\"Reduce dimensionality of X.\n\n Parameters\n ----------\n X : ndarray of shape (n_samples, n_features)\n High-dimensional input data (standardized).\n\n Returns\n -------\n X_reduced : ndarray of shape (n_samples, n_components)\n Low-dimensional embedding.\n \"\"\"\n from sklearn.decomposition import PCA\n from sklearn.neighbors import NearestNeighbors\n\n # Step 1: PCA initialization for global structure\n Y_pca = PCA(n_components=self.n_components, random_state=self.random_state).fit_transform(X)\n\n # Step 2: Build multi-scale affinity matrix using sklearn NN (faster)\n W = self._build_multiscale_affinity_sklearn(X)\n\n # Step 3: Optimize embedding with gradient descent\n Y = self._optimize_embedding(W, Y_pca, n_iter=300)\n\n return Y\n\n def _build_multiscale_affinity_sklearn(self, X, k_list=(10, 30, 100)):\n \"\"\"Build multi-scale affinity matrix using sklearn NearestNeighbors.\"\"\"\n n = X.shape[0]\n W_total = np.zeros((n, n), dtype=np.float64)\n\n for k in k_list:\n k_eff = min(k, n - 1)\n nn = NearestNeighbors(n_neighbors=k_eff, metric='euclidean').fit(X)\n distances, indices = nn.kneighbors(X)\n\n # distances has shape (n, k_eff), including self at index 0\n # Remove self (first column, dist=0)\n dists = distances[:, 1:] # (n, k_eff-1)\n idx = indices[:, 1:] # (n, k_eff-1)\n\n # Per-point bandwidth\n sigma = dists.mean(axis=1, keepdims=True)\n sigma = np.maximum(sigma, 1e-10)\n\n # Gaussian affinities\n W_k = np.exp(-dists ** 2 / (2.0 * sigma ** 2))\n\n # Vectorized scatter using advanced indexing\n rows = np.arange(n)[:, None]\n W_total[rows, idx] += W_k\n\n # Symmetrize\n W_total = (W_total + W_total.T) * 0.5\n np.fill_diagonal(W_total, 0.0)\n\n # Normalize\n total = W_total.sum()\n if total > 0:\n W_total /= total\n\n return W_total\n\n def _optimize_embedding(self, W, Y_init, n_iter=300):\n \"\"\"Optimize 2D embedding with Cauchy kernel and Adam optimizer.\"\"\"\n Y = Y_init.copy()\n Y = Y - Y.mean(axis=0, keepdims=True)\n\n # Scale initialization small\n Y_std = Y.std()\n if Y_std > 0:\n Y = Y / Y_std * 0.01\n\n # Adam parameters\n beta1, beta2, eps = 0.9, 0.999, 1e-8\n m = np.zeros_like(Y)\n v = np.zeros_like(Y)\n\n for iteration in range(n_iter):\n # Pairwise squared distances in embedding\n Y_sq = np.sum(Y ** 2, axis=1)\n DY = Y_sq[:, None] + Y_sq[None, :] - 2.0 * (Y @ Y.T)\n DY = np.maximum(DY, 0.0)\n\n # Q: Cauchy kernel (Student's t with df=1)\n Q = 1.0 / (1.0 + DY)\n np.fill_diagonal(Q, 0.0)\n q_sum = Q.sum()\n if q_sum > 0:\n Q /= q_sum\n\n # Gradient: dC/dY_i = 4 * sum_j (W_ij - Q_ij) * (y_i - y_j) / (1 + ||y_i-y_j||^2)\n QW = W - Q\n denom = 1.0 + DY\n A = QW / denom\n np.fill_diagonal(A, 0.0)\n\n grad = 4.0 * (Y * A.sum(axis=1, keepdims=True) - A @ Y)\n\n # Gradient clipping\n grad_norm = np.linalg.norm(grad, 'fro')\n max_norm = 5.0\n if grad_norm > max_norm:\n grad = grad * max_norm / grad_norm\n\n # Adam update\n m = beta1 * m + (1 - beta1) * grad\n v = beta2 * v + (1 - beta2) * grad ** 2\n m_hat = m / (1 - beta1 ** (iteration + 1))\n v_hat = v / (1 - beta2 ** (iteration + 1))\n\n # Learning rate schedule\n if iteration < 30:\n lr = 1.0 * (iteration + 1) / 30\n else:\n progress = (iteration - 30) / (n_iter - 30)\n lr = 1.0 * (1 - 0.8 * progress)\n\n Y = Y - lr * m_hat / (np.sqrt(v_hat) + eps)\n\n # Recenter periodically\n if iteration % 25 == 0:\n Y = Y - Y.mean(axis=0, keepdims=True)\n\n return Y"
7}Tool ResultStep 4
OK: Replaced lines 15..225 with 141 line(s) in scikit-learn/bench/custom_dimred.py. Editable range: 15–155.
[Current file: scikit-learn/bench/custom_dimred.py | editable: 15–155 | total: 389 lines]
15 class CustomDimReduction:
16 """Multi-Scale Affinity Embedding (MSAE) - Novel nonlinear dimensionality reduction.
17
... (135 more lines) ...
153 Y = Y - Y.mean(axis=0, keepdims=True)
154
155 return YAssistantStep 5edit
Tool Input
1{
2 "end_line": 155,
3 "filename": "scikit-learn/bench/custom_dimred.py",
4 "op": "replace",
5 "start_line": 15,
6 "content": "class CustomDimReduction:\n \"\"\"Multi-Scale Affinity Embedding (MSAE) - Novel nonlinear dimensionality reduction.\n\n Combines multi-scale nearest-neighbor affinity construction with an\n adaptive Cauchy-kernel embedding optimized via Adam. Key ideas:\n 1. Multi-scale affinity: multiple k values capture local AND global structure\n 2. Adaptive bandwidth: per-point sigma normalizes for varying density\n 3. Cauchy kernel: heavier tails preserve global relationships better\n 4. PCA init + Adam: robust optimization from a meaningful starting point\n \"\"\"\n\n def __init__(self, n_components: int = 2, random_state: int | None = None):\n self.n_components = n_components\n self.random_state = random_state\n\n def fit_transform(self, X: NDArray[np.float64]) -> NDArray[np.float64]:\n \"\"\"Reduce dimensionality of X.\n\n Parameters\n ----------\n X : ndarray of shape (n_samples, n_features)\n High-dimensional input data (standardized).\n\n Returns\n -------\n X_reduced : ndarray of shape (n_samples, n_components)\n Low-dimensional embedding.\n \"\"\"\n from sklearn.decomposition import PCA\n from sklearn.neighbors import NearestNeighbors\n\n # Step 1: PCA initialization for global structure\n Y_pca = PCA(n_components=self.n_components, random_state=self.random_state).fit_transform(X)\n\n # Step 2: Build multi-scale affinity matrix using sklearn NN (faster)\n W = self._build_multiscale_affinity_sklearn(X)\n\n # Step 3: Optimize embedding with gradient descent\n Y = self._optimize_embedding(W, Y_pca, n_iter=300)\n\n return Y\n\n def _build_multiscale_affinity_sklearn(self, X, k_list=(10, 30, 100)):\n \"\"\"Build multi-scale affinity matrix using sklearn NearestNeighbors.\"\"\"\n n = X.shape[0]\n W_total = np.zeros((n, n), dtype=np.float64)\n\n for k in k_list:\n k_eff = min(k, n - 1)\n nn = NearestNeighbors(n_neighbors=k_eff, metric='euclidean').fit(X)\n distances, indices = nn.kneighbors(X)\n\n # distances has shape (n, k_eff), including self at index 0\n # Remove self (first column, dist=0)\n dists = distances[:, 1:] # (n, k_eff-1)\n idx = indices[:, 1:] # (n, k_eff-1)\n\n # Per-point bandwidth\n sigma = dists.mean(axis=1, keepdims=True)\n sigma = np.maximum(sigma, 1e-10)\n\n # Gaussian affinities\n W_k = np.exp(-dists ** 2 / (2.0 * sigma ** 2))\n\n # Vectorized scatter using advanced indexing\n rows = np.arange(n)[:, None]\n W_total[rows, idx] += W_k\n\n # Symmetrize\n W_total = (W_total + W_total.T) * 0.5\n np.fill_diagonal(W_total, 0.0)\n\n # Normalize\n total = W_total.sum()\n if total > 0:\n W_total /= total\n\n return W_total\n\n def _optimize_embedding(self, W, Y_init, n_iter=300):\n \"\"\"Optimize 2D embedding with Cauchy kernel and Adam optimizer.\"\"\"\n Y = Y_init.copy()\n Y = Y - Y.mean(axis=0, keepdims=True)\n\n # Scale initialization small\n Y_std = Y.std()\n if Y_std > 0:\n Y = Y / Y_std * 0.01\n\n # Adam parameters\n beta1, beta2, eps = 0.9, 0.999, 1e-8\n m = np.zeros_like(Y)\n v = np.zeros_like(Y)\n\n for iteration in range(n_iter):\n # Pairwise squared distances in embedding\n Y_sq = np.sum(Y ** 2, axis=1)\n DY = Y_sq[:, None] + Y_sq[None, :] - 2.0 * (Y @ Y.T)\n DY = np.maximum(DY, 0.0)\n\n # Q: Cauchy kernel (Student's t with df=1)\n Q = 1.0 / (1.0 + DY)\n np.fill_diagonal(Q, 0.0)\n q_sum = Q.sum()\n if q_sum > 0:\n Q /= q_sum\n\n # Gradient: dC/dY_i = 4 * sum_j (W_ij - Q_ij) * (y_i - y_j) / (1 + ||y_i-y_j||^2)\n QW = W - Q\n denom = 1.0 + DY\n A = QW / denom\n np.fill_diagonal(A, 0.0)\n\n grad = 4.0 * (Y * A.sum(axis=1, keepdims=True) - A @ Y)\n\n # Gradient clipping\n grad_norm = np.linalg.norm(grad, 'fro')\n max_norm = 5.0\n if grad_norm > max_norm:\n grad = grad * max_norm / grad_norm\n\n # Adam update\n m = beta1 * m + (1 - beta1) * grad\n v = beta2 * v + (1 - beta2) * grad ** 2\n m_hat = m / (1 - beta1 ** (iteration + 1))\n v_hat = v / (1 - beta2 ** (iteration + 1))\n\n # Learning rate schedule\n if iteration < 30:\n lr = 1.0 * (iteration + 1) / 30\n else:\n progress = (iteration - 30) / (n_iter - 30)\n lr = 1.0 * (1 - 0.8 * progress)\n\n Y = Y - lr * m_hat / (np.sqrt(v_hat) + eps)\n\n # Recenter periodically\n if iteration % 25 == 0:\n Y = Y - Y.mean(axis=0, keepdims=True)\n\n return Y"
7}Tool ResultStep 5
OK: Replaced lines 15..155 with 141 line(s) in scikit-learn/bench/custom_dimred.py. Editable range: 15–155.
[Current file: scikit-learn/bench/custom_dimred.py | editable: 15–155 | total: 389 lines]
15 class CustomDimReduction:
16 """Multi-Scale Affinity Embedding (MSAE) - Novel nonlinear dimensionality reduction.
17
... (135 more lines) ...
153 Y = Y - Y.mean(axis=0, keepdims=True)
154
155 return YAssistantStep 6test
Tool ResultStep 6
[Test #1] (2 tests remaining; call submit(n=N) to choose which test result to submit as final)
### mnist (scripts/mnist.sh)
[COMMAND FAILED exit=1]
Loading dataset: mnist ...
Shape: (5000, 784), classes: 10
Running custom dimensionality reduction ...
Traceback (most recent call last):
File "/srv/home/bohanlyu/MLS-Bench/vendor/workspace/ml-dimensionality-reduction/qwen_qwen3.6-plus_20260414_110948/scikit-learn/bench/custom_dimred.py", line 389, in <module>
main()
File "/srv/home/bohanlyu/MLS-Bench/vendor/workspace/ml-dimensionality-reduction/qwen_qwen3.6-plus_20260414_110948/scikit-learn/bench/custom_dimred.py", line 385, in main
evaluate(args.dataset, seed=args.seed, n_neighbors=args.n_neighbors)
File "/srv/home/bohanlyu/MLS-Bench/vendor/workspace/ml-dimensionality-reduction/qwen_qwen3.6-plus_20260414_110948/scikit-learn/bench/custom_dimred.py", line 343, in evaluate
X_reduced = reducer.fit_transform(X)
^^^^^^^^^^^^^^^^^^^^^^^^
File "/srv/home/boh
AssistantStep 7edit
Tool Input
1{
2 "end_line": 63,
3 "filename": "scikit-learn/bench/custom_dimred.py",
4 "op": "replace",
5 "start_line": 15,
6 "content": "class CustomDimReduction:\n \"\"\"Multi-Scale Affinity Embedding (MSAE) - Novel nonlinear dimensionality reduction.\n\n Combines multi-scale nearest-neighbor affinity construction with an\n adaptive Cauchy-kernel embedding optimized via Adam. Key ideas:\n 1. Multi-scale affinity: multiple k values capture local AND global structure\n 2. Adaptive bandwidth: per-point sigma normalizes for varying density\n 3. Cauchy kernel: heavier tails preserve global relationships better\n 4. PCA init + Adam: robust optimization from a meaningful starting point\n \"\"\"\n\n def __init__(self, n_components: int = 2, random_state: int | None = None):\n self.n_components = n_components\n self.random_state = random_state\n\n def fit_transform(self, X: NDArray[np.float64]) -> NDArray[np.float64]:\n \"\"\"Reduce dimensionality of X.\"\"\"\n from sklearn.decomposition import PCA\n from sklearn.neighbors import NearestNeighbors\n\n # Step 1: PCA initialization for global structure\n Y_pca = PCA(n_components=self.n_components, random_state=self.random_state).fit_transform(X)\n\n # Step 2: Build multi-scale affinity matrix\n W = self._build_multiscale_affinity(X)\n\n # Step 3: Optimize embedding with gradient descent\n Y = self._optimize_embedding(W, Y_pca, n_iter=300)\n\n return Y\n\n def _build_multiscale_affinity(self, X, k_list=(10, 30, 100)):\n \"\"\"Build multi-scale affinity matrix using sklearn NearestNeighbors.\"\"\"\n from sklearn.neighbors import NearestNeighbors\n\n n = X.shape[0]\n W_total = np.zeros((n, n), dtype=np.float64)\n\n for k in k_list:\n k_eff = min(k, n - 1)\n nn = NearestNeighbors(n_neighbors=k_eff, metric='euclidean').fit(X)\n distances, indices = nn.kneighbors(X)\n\n # distances has shape (n, k_eff), including self at index 0\n # Remove self (first column, dist=0)\n dists = distances[:, 1:] # (n, k_eff-1)\n idx = indices[:, 1:] # (n, k_eff-1)\n\n # Per-point bandwidth\n sigma = dists.mean(axis=1, keepdims=True)\n sigma = np.maximum(sigma, 1e-10)\n\n # Gaussian affinities\n W_k = np.exp(-dists ** 2 / (2.0 * sigma ** 2))\n\n # Vectorized scatter using advanced indexing\n rows = np.arange(n)[:, None]\n W_total[rows, idx] += W_k\n\n # Symmetrize\n W_total = (W_total + W_total.T) * 0.5\n np.fill_diagonal(W_total, 0.0)\n\n # Normalize\n total = W_total.sum()\n if total > 0:\n W_total /= total\n\n return W_total"
7}Tool ResultStep 7
OK: Replaced lines 15..63 with 69 line(s) in scikit-learn/bench/custom_dimred.py. Editable range: 15–175.
[Current file: scikit-learn/bench/custom_dimred.py | editable: 15–175 | total: 409 lines]
15 class CustomDimReduction:
16 """Multi-Scale Affinity Embedding (MSAE) - Novel nonlinear dimensionality reduction.
17
... (155 more lines) ...
173 Y = Y - Y.mean(axis=0, keepdims=True)
174
175 return YAssistantStep 8test
Tool ResultStep 8
[Test #2] (1 test remaining; call submit(n=N) to choose which test result to submit as final)
### mnist (scripts/mnist.sh)
[COMMAND FAILED exit=1]
File "/srv/home/bohanlyu/MLS-Bench/vendor/workspace/ml-dimensionality-reduction/qwen_qwen3.6-plus_20260414_110948/scikit-learn/bench/custom_dimred.py", line 84
nn = NearestNeighbors(n_neighbors=k_eff, metric='euclidean').fit(X)
IndentationError: unexpected indent
ERROR conda.cli.main_run:execute(142): `conda run bash /srv/home/bohanlyu/MLS-Bench/vendor/workspace/ml-dimensionality-reduction/qwen_qwen3.6-plus_20260414_110948/.local_scripts/scripts/mnist.sh` failed. (See above for error)
### fashion_mnist (scripts/fashion_mnist.sh)
[COMMAND FAILED exit=1]
File "/srv/home/bohanlyu/MLS-Bench/vendor/workspace/ml-dimensionality-reduction/qwen_qwen3.6-plus_20260414_110948/scikit-learn/bench/custom_dimred.py", line 84
nn = NearestNeighbors(n_neighbors=k_eff, metric='euclidean').fit(X)
IndentationError: unexpected indent
ERROR conda.cli
AssistantStep 9test
Tool ResultStep 9
[Test #3] (0 tests remaining; call submit(n=N) to choose which test result to submit as final)
[NOTE] This was your last test. You MUST now call submit(n=X) to choose which test result to submit as your final answer.
### mnist (scripts/mnist.sh)
[COMMAND FAILED exit=1]
File "/srv/home/bohanlyu/MLS-Bench/vendor/workspace/ml-dimensionality-reduction/qwen_qwen3.6-plus_20260414_110948/scikit-learn/bench/custom_dimred.py", line 84
nn = NearestNeighbors(n_neighbors=k_eff, metric='euclidean').fit(X)
IndentationError: unexpected indent
ERROR conda.cli.main_run:execute(142): `conda run bash /srv/home/bohanlyu/MLS-Bench/vendor/workspace/ml-dimensionality-reduction/qwen_qwen3.6-plus_20260414_110948/.local_scripts/scripts/mnist.sh` failed. (See above for error)
### fashion_mnist (scripts/fashion_mnist.sh)
[COMMAND FAILED exit=1]
File "/srv/home/bohanlyu/MLS-Bench/vendor/workspace/ml-dimensionality-reduction/qwen_qwen3.6-plus_20260414_110948/scikit-learn/bench/custom_dimred.py", line 84