2025-07-29 京都大学
曲がったニューラルネットで遊ぶ子どもたちで爆発的記憶想起を表現したイメージ図 (Illust. Robin Hoshino)
<関連情報>
- https://www.kyoto-u.ac.jp/ja/research-news/2025-07-29-0
- https://www.kyoto-u.ac.jp/sites/default/files/2025-07/web_2507_Shimazaki_relj-a9949506e0363b509ae2dcec2b159761.pdf
- 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を介した爆発的神経ネットワーク 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.
