The Physical Effects of Learning
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909113807536128 |
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| author | Stern, Menachem Liu, Andrea J. Balasubramanian, Vijay |
| author_facet | Stern, Menachem Liu, Andrea J. Balasubramanian, Vijay |
| contents | Interacting many-body physical systems ranging from neural networks in the brain to folding proteins to self-modifying electrical circuits can learn to perform diverse tasks. This learning, both in nature and in engineered systems, can occur through evolutionary selection or through dynamical rules that drive active learning from experience. Here, we show that \added{learning in linear physical networks with weak input signals} leaves architectural imprints on the Hessian of a physical system. Compared to a generic organization of the system components, (a) the effective physical dimension of the response to inputs decreases, (b) the response of physical degrees of freedom to random perturbations (or system ``susceptibility'') increases, and (c) the low-eigenvalue eigenvectors of the Hessian align with the task. Overall, these effects embody the typical scenario for learning processes in physical systems in the weak input regime, suggesting ways of discovering whether a physical network may have been trained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_12928 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Physical Effects of Learning Stern, Menachem Liu, Andrea J. Balasubramanian, Vijay Disordered Systems and Neural Networks Soft Condensed Matter Statistical Mechanics Interacting many-body physical systems ranging from neural networks in the brain to folding proteins to self-modifying electrical circuits can learn to perform diverse tasks. This learning, both in nature and in engineered systems, can occur through evolutionary selection or through dynamical rules that drive active learning from experience. Here, we show that \added{learning in linear physical networks with weak input signals} leaves architectural imprints on the Hessian of a physical system. Compared to a generic organization of the system components, (a) the effective physical dimension of the response to inputs decreases, (b) the response of physical degrees of freedom to random perturbations (or system ``susceptibility'') increases, and (c) the low-eigenvalue eigenvectors of the Hessian align with the task. Overall, these effects embody the typical scenario for learning processes in physical systems in the weak input regime, suggesting ways of discovering whether a physical network may have been trained. |
| title | The Physical Effects of Learning |
| topic | Disordered Systems and Neural Networks Soft Condensed Matter Statistical Mechanics |
| url | https://arxiv.org/abs/2306.12928 |