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Paper · 2501.18901 · ICML · 2025

Lightspeed Geometric Dataset Distance via Sliced Optimal Transport

Nhat Ho, Khai Nguyen, Hai Nguyen, Tuan Pham

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 3 functions out of this paper's own repositories and ran 2 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
hainn2803/s-otdd canonical 2 of 3
FunctionStatusWhere it lives
Embeddings_sOTDD Ran hainn2803/s-otdd/otdd/pytorch/sotdd.py
code served (permissive licence) · get_code("4f2f6872ffb1eea3")
generate_reference Ran hainn2803/s-otdd/correlation_mnist_experiment.py
code served (permissive licence) · get_code("5b0a1096ff34a995")
compute_pairwise_distance Not yet run hainn2803/s-otdd/otdd/pytorch/sotdd.py
code served (permissive licence) · get_code("a8a074c26dbfa82c")

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Abstract

We introduce sliced optimal transport dataset distance (s-OTDD), a model-agnostic, embeddingagnostic approach for dataset comparison that requires no training, is robust to variations in the number of classes, and can handle disjoint label sets. The core innovation is Moment Transform Projection (MTP), which maps a label, represented as a distribution over features, to a real number. Using MTP, we derive a data point projection that transforms datasets into onedimensional distributions. The s-OTDD is defined as the expected Wasserstein distance between the projected distributions, with respect to random projection parameters. Leveraging the closed form solution of one-dimensional optimal transport, s-OTDD achieves (near-)linear computational complexity in the number of data points and feature dimensions and is independent of the number of classes. With its geometrically meaningful projection, s-OTDD strongly correlates with the optimal transport dataset distance while being more efficient than existing dataset discrepancy measures. Moreover, it correlates well with the performance gap in transfer learning and classification accuracy in data augmentation.

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