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 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 n

SUBMITTER: Aguilera M 

PROVIDER: S-EPMC12290047 | biostudies-literature | 2025 Jul

REPOSITORIES: biostudies-literature