title: Training multilayer perceptrons via minimization of sum of ridge functions
abstract: Motivated by the problem of training multilayer perceptrons in neural networks, we consider the problem of minimizing E(x)= Sigma /sub i=1//sup n/ f/sub i/( xi /sub i/.x), where xi /sub i/ in R/sup S/, 1<or=i<or=n, and each f/sub i/( xi /sub i/.x) is a ridge function. We show that when n is small the problem of minimizing E can be treated as one of minimizing univariate functions, and we use the gradient algorithms for minimizing E when n is moderately large. For a large n, we present the online gradient algorithms and especially show the monotonicity and weak convergence of the algorithms
keyphrases: multilayer perceptrons minimization ridge functions neural networks univariate functions gradient algorithms online gradient algorithms monotonicity weak convergence