Explosive neural networks via higher-order interactions in curved statistical manifolds - Aguilera, Miguel; Morales, Pablo A.; Rosas, Fernando E.; Shimazaki, Hideaki (Nature communications, 2025)
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.