2025-07-24 サセックス大学
＜関連情報＞
- https://www.sussex.ac.uk/research/full-news-list?id=68600
- https://www.nature.com/articles/s41467-025-61475-w
曲面統計多様体における高次相互作用による爆発的ニューラルネットワーク Explosive neural networks via higher-order interactions in curved statistical manifolds
Miguel Aguilera,Pablo A. Morales,Fernando E. Rosas & Hideaki Shimazaki
Nature Communications Published:24 July 2025
DOI:https://doi.org/10.1038/s41467-025-61475-w
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.
