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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.09833 |
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| _version_ | 1866918493833658368 |
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| author | Nguyen, Nam Tavakoli, Hassan Vuong, An Nguyen, Thinh Bose, Bella |
| author_facet | Nguyen, Nam Tavakoli, Hassan Vuong, An Nguyen, Thinh Bose, Bella |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09833 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cross-Domain Lossy Compression via Constrained Minimum Entropy Coupling Nguyen, Nam Tavakoli, Hassan Vuong, An Nguyen, Thinh Bose, Bella Information Theory Machine Learning 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. |
| title | Cross-Domain Lossy Compression via Constrained Minimum Entropy Coupling |
| topic | Information Theory Machine Learning |
| url | https://arxiv.org/abs/2605.09833 |