Learning and Controlling Multiscale Dynamics in Spiking Neural Networks Using Recursive Least Square Modifications
本文融合现代控制理论与脉冲神经网络，提出一种处理多尺度离散信号的方法，通过最优控制和递归最小二乘更新权重，实现从尖峰神经元到运动轨迹的建模，适用于脑机接口信号分析。
Invasive brain-computer interfaces (BCIs) have the capability to simultaneously record discrete signals across multiple scales, but how to effectively process and analyze these potentially related signals remains an open challenge. This article introduces an innovative approach that merges modern control theory with spiking neural networks (SNNs) to bridge the gap among multiscale discrete information. Specifically, the macroscopic point-to-point trajectory is formulated as an optimal control problem with fixed terminal time and state, and it is iteratively solved using the direct dynamic programming (DDP) algorithm. Additionally, SNN is utilized to simulate microscale neural activities in the premotor cortex, employing the product of the weighted adjacency matrix and the mesoscale firing rate to approximate the macroscopic trajectory. The error between actual macroscale behavior and the preceding approximation is then used to update the weighted adjacency matrix through the recursive least square (RLS) method. Analysis and simulation of various tasks, including low-dimensional point-to-point tasks, high-dimensional complex Lorenz systems, and center-out-and-back tasks, verify the feasibility and interpretability of our method in processing multiscale signals ranging from spiking neurons to motion trajectory through the integration of SNN and control theory.