XOR HAS NO LOCAL MINIMA - A CASE-STUDY IN NEURAL-NETWORK ERROR SURFACE-ANALYSIS

This paper presents a case study of the analysis of local minima in fe edforward neural networks, Firstly, a new methodology for analysis is presented, based upon consideration of trajectories through weight spa ce by which a training algorithm might escape a hypothesized local min imum. This analysis method is then applied to the well known XOR (excl usive-or) problem, which has previously been considered to exhibit loc al minima, The analysis proves the absence of local minima, eliciting significant aspects of the structure of the error surface. The present work is important for the study of the existence of local minima in f eedforward neural networks, and also for the development of training a lgorithms which avoid or escape entrapment in local minima. (C) 1998 E lsevier Science Ltd. All rights reserved.