The mechanism between the specific modular structure and dynamic economic optimisation in a neural network with heterogeneity based on accurate mean-field derivation

The process of biological evolution has driven the brain to strike a balance between improving computational efficiency and reducing costs, thereby forming a neural network architecture with optimal performance. The network topology structure, especially modularisation, is one of the key features that affect its information processing capacity and cost. The critical avalanche phenomenon is regarded as a sign of efficient information processing in the network, and thus, its relationship with the network topology has attracted much attention. The latest research focuses on a neural network constructed from one-dimensional leakage-integrate-and-fire (LIF) neurons and its semi-analytical mean-field, revealing the universal mechanism underlying cost-effective modular organisation and critical dynamics. However, experimental research shows that an appropriate level of modularity is conducive to achieving low-cost, high-efficiency network activity. In this paper, a modular neural network composed of Izhikevich neurons with neural heterogeneity is considered. Using the accurate mean-field model to predict the critical avalanches of a single module, thereby deriving the connection probability within the module. Further, it analyses the modularisation degree of the network from the perspective of global avalanche criticality. The results support the experimental conclusion that a moderate modular configuration allows heterogeneous neural networks to achieve a balance between lower cost and higher efficiency. This study provides a certain theoretical foundation for further understanding the structure-dynamics-economic relationship in the nervous system.