Research map / Learning theory and algorithms / Optimal transport
Lightspeed Geometric Dataset Distance via Sliced Optimal Transport
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Proposes s-OTDD, a training-free sliced optimal transport dataset distance that projects labeled data points to 1D via Moment Transform Projection, achieving near-linear cost independent of class count.
Problem
Comparing labeled datasets with optimal transport is computationally prohibitive (cubic/quadratic in sample size and class count), and existing OT dataset distances (OTDD, WTE, CHSW) scale poorly, especially with many classes or high resolution.
Approach
Map each label (a class-conditional feature distribution) to a scalar via Moment Transform Projection (scaled moments of a random 1D feature projection), combine with a random feature projection into a 1D data-point projection, and define s-OTDD as the expected 1D Wasserstein distance between projected datasets.
Key results
- On MNIST/CIFAR10 subset pairs, s-OTDD (10,000 projections) correlates significantly with OTDD (Exact), comparable to OTDD (Gaussian) and WTE while being faster.
- On NIST transfer learning, s-OTDD achieves Spearman rho = 0.42 with performance gap, identical to OTDD (Exact) (final version of appendix).
- On data augmentation (augmented Tiny-ImageNet to CIFAR10), s-OTDD obtains Spearman -0.74 vs -0.70 for OTDD (Exact), and runs in about 53x10^3 s vs over 74x10^3 s for OTDD (Exact) despite using 10x more data.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use s-OTDD instead of OTDD (Exact) | Dataset distance for NIST transfer learning · NIST datasets | Spearman correlation with performance gap: 0.40 vs 0.40; appendix: 0.42 vs 0.42 | No clear effect |
| Use s-OTDD instead of OTDD (Exact) | Dataset distance for text transfer learning · Text datasets | Pearson correlation with performance gap: r = 0.48 for both | No clear effect |
| Use s-OTDD instead of OTDD (Exact) | Distance-driven data augmentation · Tiny-ImageNet augmented to CIFAR10 | Spearman correlation with test accuracy: -0.70 to -0.74 | Helped |
| Use s-OTDD instead of OTDD (Exact) | Distance-driven data augmentation · Tiny-ImageNet augmented to CIFAR10 | processing time: over $74 \times10^3$ seconds to about $53 \times10^3$ seconds | Helped |
| Increase the number of s-OTDD projections (ablation) | s-OTDD · MNIST and CIFAR10 distance correlation with OTDD (Exact) | correlation | Helped |
Surprising findings
- CHSW's correlation with OTDD does not consistently improve as the number of projections increases, unlike s-OTDD.
Limitations
- Pearson and Spearman correlations on text and NIST transfer tasks are modest (e.g., rho about 0.4), and OTDD (Exact) is slightly better on Spearman for text.
- Requires moment existence assumptions and injectivity conditions; higher moments can overflow numerically, limiting the number of moments k.
- Correlation results with OTDD depend on the number of projections; Monte Carlo error decays only at O(L^-1/2).
Experimental setup
Datasets: MNIST CIFAR10 NIST datasets AG News DBPedia Yelp Reviews Amazon Reviews Yahoo Answers Tiny-ImageNet
Benchmarks: MNIST CIFAR10 NIST datasets AG News DBPedia Yelp Reviews Amazon Reviews Yahoo Answers Split Tiny-ImageNet
Metrics: Spearman correlation Pearson correlation runtime
Baselines: OTDD (Exact) OTDD (Gaussian approximation) WTE CHSW
Builds on: OTDD Sliced Wasserstein distance Cartan-Hadamard Sliced-Wasserstein Wasserstein Task Embedding hierarchical hybrid projection
Closest papers by meaning
- Differentiable Generalized Sliced Wasserstein Plans (NeurIPS 2025 · similarity 0.86)
- Geometry-Aware Optimal Transport: Fast Intrinsic Dimension and Wasserstein Distance Estimation (NeurIPS 2026 · similarity 0.85)
- Integrating Efficient Optimal Transport and Functional Maps For Unsupervised Shape Correspondence Learning (CVPR 2024 · similarity 0.85)
- Distance-Based Tree-Sliced Wasserstein Distance (ICLR 2025 · similarity 0.85)
- Tree-Sliced Wasserstein Distance with Nonlinear Projection (ICML 2025 · similarity 0.85)
- Wasserstein Wormhole: Scalable Optimal Transport Distance with Transformer (ICML 2024 · similarity 0.84)
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