# Lightspeed Geometric Dataset Distance via Sliced Optimal Transport

arXiv: https://arxiv.org/abs/2501.18901 · HTML: https://mlsanity.com/paper/2501.18901/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 51 references that are in the map.
- First posted on arXiv 31 Jan 2025.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Task2Vec: Task Embedding for Meta-Learning](https://mlsanity.com/paper/1902.03545/) (2019)
- [Adaptive Gradient-Based Meta-Learning Methods](https://mlsanity.com/paper/1906.02717/) (2019)
- [Geometric Dataset Distances via Optimal Transport](https://mlsanity.com/paper/2002.02923/) (2020)
- [Transferability and Hardness of Supervised Classification Tasks](https://mlsanity.com/paper/1908.08142/) (2019)
- [Continual Learning in the Teacher-Student Setup: Impact of Task Similarity](https://mlsanity.com/paper/2107.04384/) (2021)
- [Statistical and Topological Properties of Sliced Probability Divergences](https://mlsanity.com/paper/2003.05783/) (2020)
- [Continual Learning of a Mixed Sequence of Similar and Dissimilar Tasks](https://mlsanity.com/paper/2112.10017/) (2021)
- [OTCE: A Transferability Metric for Cross-Domain Cross-Task Representations](https://mlsanity.com/paper/2103.13843/) (2021)
- [Wasserstein Embedding for Graph Learning](https://mlsanity.com/paper/2006.09430/) (2020)
- [Hierarchical Optimal Transport for Document Representation](https://mlsanity.com/paper/1906.10827/) (2019)
- [Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distances](https://mlsanity.com/paper/2210.09160/) (2022)
- [Sliced-Wasserstein Distances and Flows on Cartan-Hadamard Manifolds](https://mlsanity.com/paper/2403.06560/) (2024)
- [The Joint Effect of Task Similarity and Overparameterization on Catastrophic Forgetting -- An Analytical Model](https://mlsanity.com/paper/2401.12617/) (2024)
- [Revisiting Sliced Wasserstein on Images: From Vectorization to Convolution](https://mlsanity.com/paper/2204.01188/) (2022)
- [Wasserstein Task Embedding for Measuring Task Similarities](https://mlsanity.com/paper/2208.11726/) (2022)
- [Minimax Confidence Intervals for the Sliced Wasserstein Distance](https://mlsanity.com/paper/1909.07862/) (2019)
- [Quasi-Monte Carlo for 3D Sliced Wasserstein](https://mlsanity.com/paper/2309.11713/) (2023)
- [Dataset Dynamics via Gradient Flows in Probability Space](https://mlsanity.com/paper/2010.12760/) (2020)
- [Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projections](https://mlsanity.com/paper/2211.10066/) (2022)
- [An Information-Geometric Distance on the Space of Tasks](https://mlsanity.com/paper/2011.00613/) (2020)
- [Stereographic Spherical Sliced Wasserstein Distances](https://mlsanity.com/paper/2402.02345/) (2024)
- [Parallelly Sliced Optimal Transport on Spheres and on the Rotation Group](https://mlsanity.com/paper/2401.16896/) (2024)
- [Sharp bounds for max-sliced Wasserstein distances](https://mlsanity.com/paper/2403.00666/) (2024)
- [Hilbert Curve Projection Distance for Distribution Comparison](https://mlsanity.com/paper/2205.15059/) (2022)
- [Validating Climate Models with Spherical Convolutional Wasserstein Distance](https://mlsanity.com/paper/2401.14657/) (2024)
- [Sliced-Wasserstein Estimation with Spherical Harmonics as Control Variates](https://mlsanity.com/paper/2402.01493/) (2024)

## Built on by (most cited first, 10 of 10)

- [Slicing the Gaussian Mixture Wasserstein Distance](https://mlsanity.com/paper/2504.08544/) (2025)
- [Slicing Wasserstein Over Wasserstein Via Functional Optimal Transport](https://mlsanity.com/paper/2509.22138/) (2025)
- [Optimizing Distributional Geometry Alignment with Optimal Transport for Generative Dataset Distillation](https://mlsanity.com/paper/2512.00308/) (2025)
- [Generalized Wasserstein Flow Matching: Transport Plans, Everywhere, All at Once](https://mlsanity.com/paper/2605.08424/) (2026)
- [Busemann Functions in the Wasserstein Space: Existence, Closed-Forms, and Applications to Slicing](https://mlsanity.com/paper/2510.04579/) (2025)
- [Geometry-Aware Dataset Condensation for Diffusion Model Training](https://mlsanity.com/paper/2606.05883/) (2026)
- [Rethinking Transfer in Continual Learning: A Replay-Based Realisation](https://mlsanity.com/paper/2607.15587/) (2026)
- [HOT-POT: Optimal Transport for Sparse Stereo Matching](https://mlsanity.com/paper/2601.12423/) (2026)
- [RADAR: Relative Angular Divergence Across Representations](https://mlsanity.com/paper/2605.23028/) (2026)
- [Towards Truly Unsupervised Evaluation of Feature Selection -- Extended Version](https://mlsanity.com/paper/2608.12057/) (2026)

## Abstract (arXiv)

We introduce sliced optimal transport dataset distance (s-OTDD), a model-agnostic, embedding-agnostic 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 one-dimensional 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.