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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.02326 |
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| _version_ | 1866908700667543552 |
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| author | Aguilera, Miguel Morales, Pablo A. Rosas, Fernando E. Shimazaki, Hideaki |
| author_facet | Aguilera, Miguel Morales, Pablo A. Rosas, Fernando E. Shimazaki, Hideaki |
| contents | Higher-order interactions underlie complex phenomena in systems such as biological and artificial neural networks, but their study is challenging due to the scarcity of tractable models. By leveraging a generalisation of the maximum entropy principle, we introduce curved neural networks as a class of models with a limited number of parameters that are particularly well-suited for studying higher-order phenomena. Through exact mean-field descriptions, we show that these curved neural networks implement a self-regulating annealing process that can accelerate memory retrieval, leading to explosive order-disorder phase transitions with multi-stability and hysteresis effects. Moreover, by analytically exploring their memory-retrieval capacity using the replica trick, we demonstrate that these networks can enhance memory capacity and robustness of retrieval over classical associative-memory networks. Overall, the proposed framework provides parsimonious models amenable to analytical study, revealing higher-order phenomena in complex networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02326 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Explosive neural networks via higher-order interactions in curved statistical manifolds Aguilera, Miguel Morales, Pablo A. Rosas, Fernando E. Shimazaki, Hideaki Disordered Systems and Neural Networks Statistical Mechanics Information Theory Adaptation and Self-Organizing Systems Machine Learning Higher-order interactions underlie complex phenomena in systems such as biological and artificial neural networks, but their study is challenging due to the scarcity of tractable models. By leveraging a generalisation of the maximum entropy principle, we introduce curved neural networks as a class of models with a limited number of parameters that are particularly well-suited for studying higher-order phenomena. Through exact mean-field descriptions, we show that these curved neural networks implement a self-regulating annealing process that can accelerate memory retrieval, leading to explosive order-disorder phase transitions with multi-stability and hysteresis effects. Moreover, by analytically exploring their memory-retrieval capacity using the replica trick, we demonstrate that these networks can enhance memory capacity and robustness of retrieval over classical associative-memory networks. Overall, the proposed framework provides parsimonious models amenable to analytical study, revealing higher-order phenomena in complex networks. |
| title | Explosive neural networks via higher-order interactions in curved statistical manifolds |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Information Theory Adaptation and Self-Organizing Systems Machine Learning |
| url | https://arxiv.org/abs/2408.02326 |