Theory of the backpropagation neural network

Abstract

The author presents a survey of the basic theory of the backpropagation neural network architecture covering architectural design, performance measurement, function approximation capability, and learning. The survey includes previously known material, as well as some new results, namely, a formulation of the backpropagation neural network architecture to make it a valid neural network (past formulations violated the locality of processing restriction) and a proof that the backpropagation mean-squared-error function exists and is differentiable. Also included is a theorem showing that any L/sub 2/ function from (0, 1)/sup n/ to R/sup m/ can be implemented to any desired degree of accuracy with a three-layer backpropagation neural network. The author presents a speculative neurophysiological model illustrating how the backpropagation neural network architecture might plausibly be implemented in the mammalian brain for corticocortical learning between nearby regions of the cerebral cortex.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>