# Understanding Learning with Sliced-Wasserstein Requires Rethinking Informative Slices

arXiv: https://arxiv.org/abs/2411.10651 · HTML: https://mlsanity.com/paper/2411.10651/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 47 references that are in the map.
- First posted on arXiv 16 Nov 2024.

## Builds on (most cited first, 11 of 11)

- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [Distributional Sliced-Wasserstein and Applications to Generative Modeling](https://mlsanity.com/paper/2002.07367/) (2020)
- [Spherical Sliced-Wasserstein](https://mlsanity.com/paper/2206.08780/) (2022)
- [Sliced-Wasserstein Distances and Flows on Cartan-Hadamard Manifolds](https://mlsanity.com/paper/2403.06560/) (2024)
- [Quasi-Monte Carlo for 3D Sliced Wasserstein](https://mlsanity.com/paper/2309.11713/) (2023)
- [Efficient Gradient Flows in Sliced-Wasserstein Space](https://mlsanity.com/paper/2110.10972/) (2021)
- [Light Schr"odinger Bridge](https://mlsanity.com/paper/2310.01174/) (2023)
- [Sliced Wasserstein Estimation with Control Variates](https://mlsanity.com/paper/2305.00402/) (2023)
- [Sliced Wasserstein with Random-Path Projecting Directions](https://mlsanity.com/paper/2401.15889/) (2024)
- [Augmented Sliced Wasserstein Distances](https://mlsanity.com/paper/2006.08812/) (2020)
- [LCOT: Linear circular optimal transport](https://mlsanity.com/paper/2310.06002/) (2023)

## Built on by (most cited first, 2 of 2)

- [Constrained Sliced Wasserstein Embedding](https://mlsanity.com/paper/2506.02203/) (2025)
- [Adjusted Wasserstein distances for bridging empirical and true distributions with applications to MDS](https://mlsanity.com/paper/2606.29665/) (2026)

## Abstract (arXiv)

The practical applications of Wasserstein distances (WDs) are constrained by their sample and computational complexities. Sliced-Wasserstein distances (SWDs) provide a workaround by projecting distributions onto one-dimensional subspaces, leveraging the more efficient, closed-form WDs for one-dimensional distributions. However, in high dimensions, most random projections become uninformative due to the concentration of measure phenomenon. Although several SWD variants have been proposed to focus on textitinformative slices, they often introduce additional complexity, numerical instability, and compromise desirable theoretical (metric) properties of SWD. Amidst the growing literature that focuses on directly modifying the slicing distribution, which often face challenges, we revisit the classical Sliced-Wasserstein and propose instead to rescale the 1D Wasserstein to make all slices equally informative. Importantly, we show that with an appropriate data assumption and notion of textitslice informativeness, rescaling for all individual slices simplifies to a single global scaling factor on the SWD. This, in turn, translates to the standard learning rate search for gradient-based learning in common machine learning workflows. We perform extensive experiments across various machine learning tasks showing that the classical SWD, when properly configured, can often match or surpass the performance of more complex variants. We then answer the following question: "Is Sliced-Wasserstein all you need for common learning tasks?"