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| Format: | Preprint |
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2023
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| Online-Zugang: | https://arxiv.org/abs/2310.16555 |
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| _version_ | 1866912054435119104 |
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| author | Charvin, Hippolyte Volpi, Nicola Catenacci Polani, Daniel |
| author_facet | Charvin, Hippolyte Volpi, Nicola Catenacci Polani, Daniel |
| contents | The presence of symmetries imposes a stringent set of constraints on a system. This constrained structure allows intelligent agents interacting with such a system to drastically improve the efficiency of learning and generalization, through the internalisation of the system's symmetries into their information-processing. In parallel, principled models of complexity-constrained learning and behaviour make increasing use of information-theoretic methods. Here, we wish to marry these two perspectives and understand whether and in which form the information-theoretic lens can "see" the effect of symmetries of a system. For this purpose, we propose a novel variant of the Information Bottleneck principle, which has served as a productive basis for many principled studies of learning and information-constrained adaptive behaviour. We show (in the discrete case and under a specific technical assumption) that our approach formalises a certain duality between symmetry and information parsimony: namely, channel equivariances can be characterised by the optimal mutual information-preserving joint compression of the channel's input and output. This information-theoretic treatment furthermore suggests a principled notion of "soft" equivariance, whose "coarseness" is measured by the amount of input-output mutual information preserved by the corresponding optimal compression. This new notion offers a bridge between the field of bounded rationality and the study of symmetries in neural representations. The framework may also allow (exact and soft) equivariances to be automatically discovered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_16555 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Towards Information Theory-Based Discovery of Equivariances Charvin, Hippolyte Volpi, Nicola Catenacci Polani, Daniel Information Theory Neural and Evolutionary Computing Group Theory The presence of symmetries imposes a stringent set of constraints on a system. This constrained structure allows intelligent agents interacting with such a system to drastically improve the efficiency of learning and generalization, through the internalisation of the system's symmetries into their information-processing. In parallel, principled models of complexity-constrained learning and behaviour make increasing use of information-theoretic methods. Here, we wish to marry these two perspectives and understand whether and in which form the information-theoretic lens can "see" the effect of symmetries of a system. For this purpose, we propose a novel variant of the Information Bottleneck principle, which has served as a productive basis for many principled studies of learning and information-constrained adaptive behaviour. We show (in the discrete case and under a specific technical assumption) that our approach formalises a certain duality between symmetry and information parsimony: namely, channel equivariances can be characterised by the optimal mutual information-preserving joint compression of the channel's input and output. This information-theoretic treatment furthermore suggests a principled notion of "soft" equivariance, whose "coarseness" is measured by the amount of input-output mutual information preserved by the corresponding optimal compression. This new notion offers a bridge between the field of bounded rationality and the study of symmetries in neural representations. The framework may also allow (exact and soft) equivariances to be automatically discovered. |
| title | Towards Information Theory-Based Discovery of Equivariances |
| topic | Information Theory Neural and Evolutionary Computing Group Theory |
| url | https://arxiv.org/abs/2310.16555 |