TY - JOUR

T1 - On the equivalence of two-layered perceptrons with binary neurons.

AU - Blatt, M.

AU - Domany, E.

AU - Kanter, I.

PY - 1995/9

Y1 - 1995/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0029366360&partnerID=8YFLogxK

U2 - 10.1142/S0129065795000160

DO - 10.1142/S0129065795000160

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C2 - 8589860

AN - SCOPUS:0029366360

SN - 0129-0657

VL - 6

SP - 225

EP - 231

JO - International Journal of Neural Systems

JF - International Journal of Neural Systems

IS - 3

ER -