The Role of Higher-Order Self-Dynamics in Neural Dynamical Networks: Preserving Memory Capacity and Enhancing Retrieval Basin
Weichen Fu, Zhuchun Li, Wei Lin, Xiaoxue Zhao · SIAM Journal on Applied Mathematics · 2025
Abstract. Networks of coupled Kuramoto-type oscillators have been proposed as models of associative memory. In this paper, we design a model for neural dynamical networks by incorporating higher-order self-dynamics. This system is not invariant under global phase translation, which makes it more direct to link phases and patterns. We present a unified approach for error-free retrieval in the pattern retrieval problem with an arbitrary set of standard patterns. We find that this model preserves the memory capacity, simultaneously enhancing the basin for error-free retrieval. More practically, we propose a strategy for the retrieval problems with grayscale and even colorful images.