Cross-Domain Lossy Compression via Constrained Minimum Entropy Coupling

• URL: http://arxiv.org/abs/2605.09833v1
• Date: Mon, 11 May 2026 00:19:11 GMT
• Title: Cross-Domain Lossy Compression via Constrained Minimum Entropy Coupling
• Abstract summary: We study cross-domain lossy compression through the lens of minimum entropy coupling (MEC) with rate and classification constraints.<n>Motivated by logarithmic-loss distortion, we adopt an information-based objective that maximizes the coupling strength between the source and reconstruction.<n> Experiments on MNIST super-resolution and SVHN denoising show that increasing the available rate improves classification accuracy and yields more informative reconstructions.
• Score: 5.404926467615337
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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