# Optimal Transport PAC-Bayes Bounds

arXiv: https://arxiv.org/abs/2610.16560 · HTML: https://mlsanity.com/paper/2610.16560/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 32 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Builds on (most cited first, 10 of 10)

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Stronger generalization bounds for deep nets via a compression approach](https://mlsanity.com/paper/1802.05296/) (2018)
- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [Non-Vacuous Generalization Bounds at the ImageNet Scale: A PAC-Bayesian Compression Approach](https://mlsanity.com/paper/1804.05862/) (2018)
- [Simpler PAC-Bayesian Bounds for Hostile Data](https://mlsanity.com/paper/1610.07193/) (2016)
- [Measuring Generalization with Optimal Transport](https://mlsanity.com/paper/2106.03314/) (2021)
- [Learning via Wasserstein-Based High Probability Generalisation Bounds](https://mlsanity.com/paper/2306.04375/) (2023)
- [An Optimal Transport View on Generalization](https://mlsanity.com/paper/1811.03270/) (2018)
- [Separating Geometry from Probability in the Analysis of Generalization](https://mlsanity.com/paper/2604.19560/) (2026)

## Abstract (arXiv)

PAC-Bayesian generalization bounds are among the strongest distribution-dependent guarantees in statistical learning and are typically expressed in terms of the Kullback-Leibler (KL) divergence between a prior and posterior distribution. While analytically convenient, the KL divergence requires the posterior to be absolutely continuous w.r.t. the prior, imposing support constraints that can substantially restrict the choice of posterior. Moreover, the KL divergence does not account for the underlying geometry of the probability space. In this work, we derive new PAC-Bayesian bounds replacing the KL divergence with general optimal transport (OT) distances, including the total variation and Wasserstein-p distances.