A perspective of fault tolerance for XOR in neural network

Abstract

It is commonly assumed that neural networks have a built in fault tolerance property mainly due to their parallel structures. Recently the subject was again brought to discussion due to the possibility of using neural networks in nano-electronic systems where fault tolerance and graceful degradation properties would be very important. Neural networks that learn to compute Boolean functions is one of the first topics discussed in accounts of neural computing for fault tolerance. Of these functions, only two pose any difficulty: these are XOR and its complement. XORoccupies, therefore, a historic position and is considered as a bench mark problem for neural network It has long been recognized that simple networks often have trouble in learning the function, and as a result their behavior has been much discussed, and the ability and to learn to compute XOR has been used as a test of variants of the standard algorithms. This paper puts forward a framework for looking at the XOR problem, and, using that framework shows that the nature of the problem has often been misunderstood and also the fault tolerance capability of neural networks.