Complex Systems

Energy Functions in Neural Networks with Continuous Local Functions Download PDF

F. Fogelman Soulié
C. Mejia
Laboratoire de Recherche en Informatique, bat. 490,
Université de Paris Sud, 91405 Orsay Cedex, France

Eric Goles
S. Martinez
Departamento de Matemáticas, Escuela de Ingeniería,
Universidad de Chile, Casilla 170, Correo 3, Santiago, Chile


Neural networks with continuous local transition functions have been recently used for a variety of applications, especially in learning tasks. Previous works have shown that Lyapunov --- or "energy'' --- functions could be derived for networks of binary elements, thus allowing a rather complete characterization of their dynamics. We show here that it is possible to write down Lyapunov functions for continuous networks as well. We then use these functions to provide some results for the dynamical behavior of such networks. We discuss the link with the binary case and illustrate our results with some simulations.