# Cross-Domain Lossy Compression via Constrained Minimum Entropy Coupling

arXiv: https://arxiv.org/abs/2605.09833 · HTML: https://mlsanity.com/paper/2605.09833/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 34 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 17 of 17)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Autoencoding beyond pixels using a learned similarity metric](https://mlsanity.com/paper/1512.09300/) (2015)
- [Generative Adversarial Networks for Extreme Learned Image Compression](https://mlsanity.com/paper/1804.02958/) (2018)
- [Rethinking Lossy Compression: The Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/1901.07821/) (2019)
- [A unifying mutual information view of metric learning: cross-entropy vs. pairwise losses](https://mlsanity.com/paper/2003.08983/) (2020)
- [Deep Generative Models for Distribution-Preserving Lossy Compression](https://mlsanity.com/paper/1805.11057/) (2018)
- [On the advantages of stochastic encoders](https://mlsanity.com/paper/2102.09270/) (2021)
- [Entropic Causal Inference](https://mlsanity.com/paper/1611.04035/) (2016)
- [On The Classification-Distortion-Perception Tradeoff](https://mlsanity.com/paper/1904.08816/) (2019)
- [Minimum--Entropy Couplings and their Applications](https://mlsanity.com/paper/1901.07530/) (2019)
- [Minimum-Entropy Coupling Approximation Guarantees Beyond the Majorization Barrier](https://mlsanity.com/paper/2302.11838/) (2023)
- [Entropic Causality and Greedy Minimum Entropy Coupling](https://mlsanity.com/paper/1701.08254/) (2017)
- [Minimum Entropy Coupling with Bottleneck](https://mlsanity.com/paper/2410.21666/) (2024)
- [A Rate-Distortion-Classification Approach for Lossy Image Compression](https://mlsanity.com/paper/2405.03500/) (2024)

## Abstract (arXiv)

This paper studies cross-domain lossy compression through the lens of minimum entropy coupling (MEC) with rate and classification constraints. In this setting, an encoder observes samples from a degraded source domain, while the decoder is required to generate outputs following a prescribed target distribution and to preserve information relevant to a downstream classification task. Motivated by logarithmic-loss distortion, we adopt an information-based objective that maximizes the coupling strength between the source and reconstruction, rather than minimizing a sample-wise distortion. Under common randomness, we formulate a rate-constrained MEC problem (MEC-B) and show that the intermediate representation can be removed without loss of optimality, yielding an equivalent deterministic coupling formulation. For Bernoulli sources, closed-form expressions are derived with and without classification constraints. In addition, we implement a neural restoration framework using quantization, entropy modeling, distribution matching, and classification regularization. Experiments on MNIST super-resolution and SVHN denoising show that increasing the available rate improves classification accuracy and yields more informative reconstructions.