Explosive neural networks via higher-order interactions in curved statistical manifolds

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 o...

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Vydáno v:Nature communications Ročník 16; číslo 1; s. 6511 - 10
Hlavní autoři: Aguilera, Miguel, Morales, Pablo A., Rosas, Fernando E., Shimazaki, Hideaki
Médium: Journal Article
Jazyk:angličtina
Vydáno: London Nature Publishing Group UK 24.07.2025
Nature Publishing Group
Nature Portfolio
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639/766/259
639/766/530/2795
639/766/530/2801
639/766/530/2804
Artificial neural networks
Associative memory
Energy
Entropy
Humanities and Social Sciences
Maximum entropy
multidisciplinary
Neural networks
Order disorder
Phase transitions
Retrieval
Science
Science (multidisciplinary)
Statistical physics
ISSN:2041-1723, 2041-1723
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Shrnutí: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. Higher-order interactions shape complex neural dynamics but are hard to model. Here, authors use a generalization of the maximum entropy principle to introduce a family of curved neural networks, revealing explosive phase transitions and enhanced memory via a self-regulating retrieval mechanism.
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ISSN:2041-1723
2041-1723
DOI:10.1038/s41467-025-61475-w