Log-Likelihood Loss for Semantic Compression
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917219394387968 |
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| author | Yadav, Anuj Kumar Song, Dan Shkel, Yanina Özgür, Ayfer |
| author_facet | Yadav, Anuj Kumar Song, Dan Shkel, Yanina Özgür, Ayfer |
| contents | We study lossy source coding under a distortion measure defined by the negative log-likelihood induced by a prescribed conditional distribution $P_{X|U}$. This \emph{log-likelihood distortion} models compression settings in which the reconstruction is a semantic representation from which the source can be probabilistically generated, rather than a pointwise approximation. We formulate the corresponding rate-distortion problem and characterize fundamental properties of the resulting rate-distortion function, including its connections to lossy compression under log-loss, classical rate-distortion problems with arbitrary distortion measures, and rate-distortion with perfect perception. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16461 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Log-Likelihood Loss for Semantic Compression Yadav, Anuj Kumar Song, Dan Shkel, Yanina Özgür, Ayfer Information Theory We study lossy source coding under a distortion measure defined by the negative log-likelihood induced by a prescribed conditional distribution $P_{X|U}$. This \emph{log-likelihood distortion} models compression settings in which the reconstruction is a semantic representation from which the source can be probabilistically generated, rather than a pointwise approximation. We formulate the corresponding rate-distortion problem and characterize fundamental properties of the resulting rate-distortion function, including its connections to lossy compression under log-loss, classical rate-distortion problems with arbitrary distortion measures, and rate-distortion with perfect perception. |
| title | Log-Likelihood Loss for Semantic Compression |
| topic | Information Theory |
| url | https://arxiv.org/abs/2601.16461 |