title: Dynamical and complexity results for high order neural networks.
abstract: We present dynamical results concerning neural networks with high order arguments. More precisely, we study the family of block-sequential iteration of neural networks with polynomial arguments. In this context, we prove that, under a symmetric hypothesis, the sequential iteration is the only one of this family to converge to fixed points. The other iteration modes present a highly complex dynamical behavior: non-bounded cycles and simulation of arbitrary non-symmetric linear neural network. We also study a high order memory iteration scheme which accepts an energy functional and bounded cycles in the size of the memory steps.
authors.affiliation: Universidad de Chile, Facultad de Ciencias Físicas y Matématicas, Departamento de Ingeniería Matéatica, Santiago.
authors.forename: E
authors.initials: E
authors.lastname: Goles
authors.forename: M
authors.initials: M
authors.lastname: Matamala
mesh_terms: D003198:Computer Simulation; D016571:Neural Networks, Computer