This report presents a formalism that enables the dynamics of a broad class of neural networks to be understood. A number of previous works have analyzed the Lyapunov stability of neural network models. This type of analysis shows that the excursion of the solutions from a stable point is bounded. The purpose of this work is to present a model of the dynamics that also describes the phase space behavior as well as the structural stability of the system. This is achieved by writing the general equations of the neural network dynamics as the sum of gradient-like and Hamiltonian-like systems. In this paper some important properties of both gradient-like and Hamiltonian-like systems are developed and then it is demonstrated that a broad class of neural network models are expressible in this form.
The University of New Mexico
Abdallah, Chaouki T.; James W. Howse; and Gregory L. Heileman. "General Neural Networks Dynamics are a Superposition of Gradient-like and Hamiltonian-like Systems." (2012). http://digitalrepository.unm.edu/ece_fsp/56