Backpropagation based on the logarithmic error function and elimination of local minima

Abstract

It is has previously been pointed out that, in backpropagation learning of neural networks, using a logarithmic error function instead of the familiar quadratic error function yields remarkable reductions in learning times. In the present work, it is shown theoretically and experimentally that learning based on the logarithmic error function has the effect of reducing the density of local minima. It is proved mathematically that, in a particular sense, the logarithmic error function provides a lower (at most equal) density of local minima in any network. the logarithmic error function also alleviates the problem of getting stuck in local minima.<>