Agent Conversation: openai/gpt-5.4
Model: openai/gpt-5.4
Total steps: 7
Messages: 16
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 "op": "replace",
3 "filename": "scikit-learn/bench/custom_dimred.py",
4 "content": "class CustomDimReduction:\n \"\"\"Multiscale fusion + anchored LLE refinement.\"\"\"\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 from scipy.linalg import orthogonal_procrustes\n from scipy.sparse import csr_matrix, eye\n from scipy.sparse.linalg import spsolve\n from sklearn.decomposition import PCA\n from sklearn.neighbors import NearestNeighbors\n import pacmap, umap\n\n n, d = X.shape\n p = min(50, d, max(8, 8 * self.n_components))\n Z = PCA(n_components=p, random_state=self.random_state).fit_transform(X)\n k = min(max(12, int(np.sqrt(n) / 2)), 40, n - 1)\n\n Y_local = umap.UMAP(\n n_components=self.n_components, n_neighbors=max(10, k), min_dist=0.03,\n init=\"spectral\", metric=\"euclidean\", random_state=self.random_state,\n ).fit_transform(Z)\n Y_global = pacmap.PaCMAP(\n n_components=self.n_components, n_neighbors=max(10, k // 2),\n MN_ratio=0.5, FP_ratio=2.0, random_state=self.random_state,\n ).fit_transform(Z)\n\n def _norm(Y):\n Y = Y - Y.mean(0, keepdims=True)\n return Y / (np.sqrt((Y * Y).mean()) + 1e-9)\n\n Y_local, Y_global = _norm(Y_local), _norm(Y_global)\n R, _ = orthogonal_procrustes(Y_global, Y_local)\n Y0 = 0.65 * Y_local + 0.35 * (Y_global @ R)\n\n dist, ind = NearestNeighbors(n_neighbors=k + 1).fit(Z).kneighbors(Z)\n ind = ind[:, 1:]\n rows, cols, vals = [], [], []\n for i in range(n):\n G = (Z[ind[i]] - Z[i]) @ (Z[ind[i]] - Z[i]).T\n reg = 1e-3 * np.trace(G) + 1e-6\n G.flat[:: k + 1] += reg\n w = np.linalg.solve(G, np.ones(k))\n w /= w.sum()\n rows.extend([i] * k); cols.extend(ind[i]); vals.extend(w)\n\n W = csr_matrix((vals, (rows, cols)), shape=(n, n))\n I = eye(n, format=\"csr\")\n mu = 0.2\n A = (I - W).T @ (I - W) + mu * I\n Y = np.column_stack([spsolve(A, mu * Y0[:, j]) for j in range(self.n_components)])\n return _norm(Y)",
5 "after_line": 14,
6 "start_line": 15,
7 "end_line": 59
8}Tool ResultStep 1
OK: Replaced lines 15..59 with 54 line(s) in scikit-learn/bench/custom_dimred.py. Editable range: 15–68.
[Current file: scikit-learn/bench/custom_dimred.py | editable: 15–68 | total: 302 lines]
15 class CustomDimReduction:
16 """Multiscale fusion + anchored LLE refinement."""
17
... (48 more lines) ...
66 A = (I - W).T @ (I - W) + mu * I
67 Y = np.column_stack([spsolve(A, mu * Y0[:, j]) for j in range(self.n_components)])
68 return _norm(Y)AssistantStep 2test
Tool ResultStep 2
[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/openai_gpt-5.4_20260414_110948/scikit-learn/bench/custom_dimred.py", line 302, in <module>
main()
File "/srv/home/bohanlyu/MLS-Bench/vendor/workspace/ml-dimensionality-reduction/openai_gpt-5.4_20260414_110948/scikit-learn/bench/custom_dimred.py", line 298, in main
evaluate(args.dataset, seed=args.seed, n_neighbors=args.n_neighbors)
File "/srv/home/bohanlyu/MLS-Bench/vendor/workspace/ml-dimensionality-reduction/openai_gpt-5.4_20260414_110948/scikit-learn/bench/custom_dimred.py", line 256, in evaluate
X_reduced = reducer.fit_transform(X)
^^^^^^^^^^^^^^^^^^^^^^^^
File "/srv/home/bohanlyu/MLS
AssistantStep 3edit
Tool Input
1{
2 "op": "replace",
3 "filename": "scikit-learn/bench/custom_dimred.py",
4 "content": "class CustomDimReduction:\n \"\"\"Perplexity-curriculum t-SNE with anchored LLE refinement.\"\"\"\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 from scipy.sparse import csr_matrix, eye\n from scipy.sparse.linalg import spsolve\n from sklearn.decomposition import PCA\n from sklearn.manifold import TSNE\n from sklearn.neighbors import NearestNeighbors\n\n n, d = X.shape\n p = min(50, d, max(8, 8 * self.n_components))\n Z = PCA(n_components=p, random_state=self.random_state).fit_transform(X)\n k = min(max(12, int(np.sqrt(n) / 2)), 40, n - 1)\n p1 = min(20.0, max(7.0, np.sqrt(n) / 4.0))\n p2 = min(80.0, max(35.0, np.sqrt(n)))\n\n Y_local = TSNE(\n n_components=self.n_components, perplexity=p1, init=\"pca\",\n learning_rate=\"auto\", early_exaggeration=14.0, n_iter=700,\n random_state=self.random_state,\n ).fit_transform(Z)\n Y_global = TSNE(\n n_components=self.n_components, perplexity=p2, init=Y_local,\n learning_rate=\"auto\", early_exaggeration=4.0, n_iter=400,\n random_state=self.random_state,\n ).fit_transform(Z)\n\n def _norm(Y):\n Y = Y - Y.mean(0, keepdims=True)\n return Y / (np.sqrt((Y * Y).mean()) + 1e-9)\n\n Y0 = _norm(0.7 * _norm(Y_local) + 0.3 * _norm(Y_global))\n ind = NearestNeighbors(n_neighbors=k + 1).fit(Z).kneighbors(Z, return_distance=False)[:, 1:]\n rows, cols, vals = [], [], []\n for i in range(n):\n G = (Z[ind[i]] - Z[i]) @ (Z[ind[i]] - Z[i]).T\n G.flat[:: k + 1] += 1e-3 * np.trace(G) + 1e-6\n w = np.linalg.solve(G, np.ones(k))\n w /= w.sum()\n rows.extend([i] * k); cols.extend(ind[i]); vals.extend(w)\n\n W = csr_matrix((vals, (rows, cols)), shape=(n, n))\n I = eye(n, format=\"csr\")\n A = (I - W).T @ (I - W) + 0.25 * I\n Y = np.column_stack([spsolve(A, 0.25 * Y0[:, j]) for j in range(self.n_components)])\n return _norm(Y)",
5 "after_line": 14,
6 "start_line": 15,
7 "end_line": 68
8}Tool ResultStep 3
OK: Replaced lines 15..68 with 51 line(s) in scikit-learn/bench/custom_dimred.py. Editable range: 15–65.
[Current file: scikit-learn/bench/custom_dimred.py | editable: 15–65 | total: 299 lines]
15 class CustomDimReduction:
16 """Perplexity-curriculum t-SNE with anchored LLE refinement."""
17
... (45 more lines) ...
63 A = (I - W).T @ (I - W) + 0.25 * I
64 Y = np.column_stack([spsolve(A, 0.25 * Y0[:, j]) for j in range(self.n_components)])
65 return _norm(Y)AssistantStep 4test
Tool ResultStep 4
[Test #2] (1 test remaining; call submit(n=N) to choose which test result to submit as final)
### mnist (scripts/mnist.sh)
Reduction timing (mnist):
TRAIN_METRICS dataset=mnist elapsed=22.99s
Results (mnist):
kNN accuracy=0.750000
Trustworthiness=0.798613
Continuity=0.957146
Time=22.99s
### fashion_mnist (scripts/fashion_mnist.sh)
Reduction timing (fashion_mnist):
TRAIN_METRICS dataset=fashion_mnist elapsed=14.36s
Results (fashion_mnist):
kNN accuracy=0.699333
Trustworthiness=0.940169
Continuity=0.982765
Time=14.36s
[Leaderboard] Results saved: {'knn_acc_mnist': 0.75, 'trustworthiness_mnist': 0.798613, 'continuity_mnist': 0.957146, 'elapsed_mnist': 51, 'knn_acc_fashion_mnist': 0.699333, 'trustworthiness_fashion_mnist': 0.940169, 'continuity_fashion_mnist': 0.982765, 'elapsed_fashion_mnist': 51, 'knn_acc_newsgroups': 0.577088, 'trustworthiness_newsgroups': 0.659047, 'continuity_newsgroups': 0.876174, 'elapsed_newsgroups': 51}AssistantStep 5edit
Tool Input
1{
2 "op": "replace",
3 "filename": "scikit-learn/bench/custom_dimred.py",
4 "content": "class CustomDimReduction:\n \"\"\"Density-calibrated perplexity-curriculum t-SNE.\"\"\"\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 from sklearn.decomposition import PCA\n from sklearn.manifold import TSNE\n from sklearn.neighbors import NearestNeighbors\n\n n, d = X.shape\n p = min(50, d, max(8, 8 * self.n_components))\n Z = PCA(n_components=p, random_state=self.random_state).fit_transform(X)\n p1 = min(30.0, max(12.0, np.sqrt(n) / 2.5))\n p2 = min(90.0, max(45.0, 1.2 * np.sqrt(n)))\n\n Y1 = TSNE(\n n_components=self.n_components, perplexity=p1, init=\"pca\",\n learning_rate=\"auto\", early_exaggeration=12.0, n_iter=900,\n random_state=self.random_state,\n ).fit_transform(Z)\n Y2 = TSNE(\n n_components=self.n_components, perplexity=p2, init=Y1,\n learning_rate=\"auto\", early_exaggeration=4.0, n_iter=350,\n random_state=self.random_state,\n ).fit_transform(Z)\n\n Y = 0.9 * Y1 + 0.1 * Y2\n Y -= Y.mean(0, keepdims=True)\n Y /= np.sqrt((Y * Y).mean()) + 1e-9\n\n k = min(12, n - 1)\n ind = NearestNeighbors(n_neighbors=k + 1).fit(Z).kneighbors(Z, return_distance=False)[:, 1:]\n Cz = Z[ind].mean(1)\n Cy = Y[ind].mean(1)\n dz = np.sqrt(((Z - Cz) ** 2).sum(1))\n dy = np.sqrt(((Y - Cy) ** 2).sum(1)) + 1e-9\n s = np.clip((dz / (np.median(dz) + 1e-9)) / (dy / np.median(dy)), 0.75, 1.25)[:, None]\n Y = Cy + 0.35 * s * (Y - Cy) + 0.65 * (Y - Cy)\n Y -= Y.mean(0, keepdims=True)\n return Y / (np.sqrt((Y * Y).mean()) + 1e-9)",
5 "after_line": 14,
6 "start_line": 15,
7 "end_line": 65
8}Tool ResultStep 5
OK: Replaced lines 15..65 with 43 line(s) in scikit-learn/bench/custom_dimred.py. Editable range: 15–57.
[Current file: scikit-learn/bench/custom_dimred.py | editable: 15–57 | total: 291 lines]
15 class CustomDimReduction:
16 """Density-calibrated perplexity-curriculum t-SNE."""
17
... (37 more lines) ...
55 Y = Cy + 0.35 * s * (Y - Cy) + 0.65 * (Y - Cy)
56 Y -= Y.mean(0, keepdims=True)
57 return Y / (np.sqrt((Y * Y).mean()) + 1e-9)AssistantStep 6test
Tool ResultStep 6
[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)
Reduction timing (mnist):
TRAIN_METRICS dataset=mnist elapsed=14.35s
Results (mnist):
kNN accuracy=0.875000
Trustworthiness=0.920733
Continuity=0.952903
Time=14.35s
### fashion_mnist (scripts/fashion_mnist.sh)
Reduction timing (fashion_mnist):
TRAIN_METRICS dataset=fashion_mnist elapsed=12.51s
Results (fashion_mnist):
kNN accuracy=0.755667
Trustworthiness=0.976455
Continuity=0.981007
Time=12.51s
### newsgroups (scripts/newsgroups.sh)
Reduction timing (newsgroups):
TRAIN_METRICS dataset=newsgroups elapsed=16.95s
Results (newsgroups):
kNN accuracy=0.650607
Trustworthiness=0.852212
Continuity=0.853485
Time=16.95s
[Leaderboard] Results saved: {'knn_acc_mnist': 0.875, 'trustworthiness_mnist': 0.920733, 'continuity_mnist'
AssistantStep 7submit
Tool Input
1{
2 "n": 3
3}Tool ResultStep 7
[submit] Submitting result from test #3 as final.
### mnist (scripts/mnist.sh)
Reduction timing (mnist):
TRAIN_METRICS dataset=mnist elapsed=14.35s
Results (mnist):
kNN accuracy=0.875000
Trustworthiness=0.920733
Continuity=0.952903
Time=14.35s
### fashion_mnist (scripts/fashion_mnist.sh)
Reduction timing (fashion_mnist):
TRAIN_METRICS dataset=fashion_mnist elapsed=12.51s
Results (fashion_mnist):
kNN accuracy=0.755667
Trustworthiness=0.976455
Continuity=0.981007
Time=12.51s
### newsgroups (scripts/newsgroups.sh)
Reduction timing (newsgroups):
TRAIN_METRICS dataset=newsgroups elapsed=16.95s
Results (newsgroups):
kNN accuracy=0.650607
Trustworthiness=0.852212
Continuity=0.853485
Time=16.95s
[submit] Finalized test #3 as final.
[Leaderboard] Results saved: {'knn_acc_mnist': 0.875, 'trustworthiness_mnist': 0.920733, 'continuity_mnist': 0.952903, 'elapsed_mnist': 45, 'knn_acc_fashion_mnist': 0.755667, 'trustworthiness_fashion_mnist': 0.976455, 'continuity_fashion