# Two-Sided Bounds for Entropic Optimal Transport via a Rate-Distortion Integral

arXiv: https://arxiv.org/abs/2604.14061 · HTML: https://mlsanity.com/paper/2604.14061/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 21 references that are in the map.
- First posted on arXiv 15 Apr 2026.

## Builds on (most cited first, 2 of 2)

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Information Constrained Optimal Transport: From Talagrand, to Marton, to Cover](https://mlsanity.com/paper/2008.10249/) (2020)

## Abstract (arXiv)

We show that the maximum expected inner product between a random vector and the standard normal vector over all couplings subject to a mutual information constraint or regularization is equivalent to a truncated integral involving the rate-distortion function, up to universal multiplicative constants. The proof is based on a lifting technique, which constructs a Gaussian process indexed by a random subset of the type class of the probability distribution involved in the information-theoretic inequality, and then applying a form of the majorizing measure theorem.