Equilibrium Stability Analysis in Neural Networks
Xuecheng Zhao, Fei Wang, Zhiqiang Huang, Feng Lin · 2024
In this paper, the stability of equilibrium in neural networks is investigated. In a non-hierarchical neural network, the outputs of neurons are not explicit functions of the outputs of preceding neurons. The solution to these implicit functions are the equilibrium of the neural network. It is important to know whether the equilibrium is stable or not. The stability of equilibrium can be determined by first linearizing the neural net-work around the equilibrium and then checking the eigenvalues of the linearized neural network. The stability of the equilibrium is characterized by the largest absolute value of eigenvalues. This stability measure allows us to determine the stability of equilibrium, and enables us to investigate the impacts of various parameters on the stability. Simulations are used to numerically analyze the impacts of several parameters on the stability. We also discuss biological implications of our findings and biologically plausible learning using the Brandt-Lin algorithm.