Equilibrium Stability Analysis in Neural Networks

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.

I. Introduction

AI has significantly impacted engineering systems, partic-ularly in the realm of cyber-physical systems(CPS). Among the various methods of AI, neural networks and deep learning stand out as crucial technologies that have received substantial attention and development within the research community [1]–[4]. This paper delves into a critical aspect of neural networks, namely, the analysing of the stability of equilibrium in neural networks. We embark on an exploration of the stability of equilibrium in neural networks, a fundamental concept within neural networks, shedding light on its intricate dynamics and implications.