On the equivalence of two-layered perceptrons with binary neurons.
We consider two-layered perceptions consisting of N binary input units, K binary hidden units and one binary output unit, in the limit N >> K > or = 1. We prove that the weights of a regular irreducible network are uniquely determined by its input-output map up to some obvious global symmetries. A network is regular if its K weight vectors from the input layer to the K hidden units are linearly independent. A (single layered) perceptron is said to be irreducible if its output depends on every one of its input units; and a two-layered perceptron is irreducible if the K + 1 perceptrons that constitute such network are irreducible. By global symmetries we mean, for instance, permuting the labels of the hidden units. Hence, two irreducible regular two-layered perceptrons that implement the same Boolean function must have the same number of hidden units, and must be composed of equivalent perceptrons.
Blatt
M
M
Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, Israel.
Domany
E
E
Kanter
I
I
D003198:Computer Simulation; D005246:Feedback; D008433:Mathematics; D008959:Models, Neurological; D016571:Neural Networks, Computer