Explosive neural networks via higher-order interactions in curved statistical manifolds
Abstract 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...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-07-01
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| Series: | Nature Communications |
| Online Access: | https://doi.org/10.1038/s41467-025-61475-w |
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| _version_ | 1849342729812705280 |
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| author | Miguel Aguilera Pablo A. Morales Fernando E. Rosas Hideaki Shimazaki |
| author_facet | Miguel Aguilera Pablo A. Morales Fernando E. Rosas Hideaki Shimazaki |
| author_sort | Miguel Aguilera |
| collection | DOAJ |
| description | Abstract 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 | Article |
| id | doaj-art-ff94f5df904246db8ba284ee53a9adf2 |
| institution | Kabale University |
| issn | 2041-1723 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Nature Communications |
| spelling | doaj-art-ff94f5df904246db8ba284ee53a9adf22025-08-20T03:43:16ZengNature PortfolioNature Communications2041-17232025-07-0116111010.1038/s41467-025-61475-wExplosive neural networks via higher-order interactions in curved statistical manifoldsMiguel Aguilera0Pablo A. Morales1Fernando E. Rosas2Hideaki Shimazaki3BCAM – Basque Center for Applied MathematicsResearch Division, Araya Inc.Sussex AI and Sussex Centre for Consciousness Science, Department of Informatics, University of SussexGraduate School of Informatics, Kyoto UniversityAbstract 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.https://doi.org/10.1038/s41467-025-61475-w |
| spellingShingle | Miguel Aguilera Pablo A. Morales Fernando E. Rosas Hideaki Shimazaki Explosive neural networks via higher-order interactions in curved statistical manifolds Nature Communications |
| title | Explosive neural networks via higher-order interactions in curved statistical manifolds |
| title_full | Explosive neural networks via higher-order interactions in curved statistical manifolds |
| title_fullStr | Explosive neural networks via higher-order interactions in curved statistical manifolds |
| title_full_unstemmed | Explosive neural networks via higher-order interactions in curved statistical manifolds |
| title_short | Explosive neural networks via higher-order interactions in curved statistical manifolds |
| title_sort | explosive neural networks via higher order interactions in curved statistical manifolds |
| url | https://doi.org/10.1038/s41467-025-61475-w |
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