Research Seminar - December 11, 1998

Abstract

An artificial neural network is a function: given an input, it produces a unique output. In this talk, we restrict ourselves to the Boolean function implemented by a network. In particular, the inputs to the network are restricted to Boolean values, and the network's output is thresholded to produce a Boolean value.

The information contained in a neural network is distributed over its internal components, primarily its weights, transfer functions, and network topology. It is difficult to manipulate this information using symbolic techniques. Furthermore, it is difficult to compare the symbolic information contained in two networks, or even the Boolean functions implemented by a single network during training.

Part I of this two-part series presented an algorithm that efficiently extracts a Boolean function from a single neuron. This talk, part II, presents an algorithm that approximates the Boolean function implemented by a three-layer network. Some early experiments are also presented, in which the Boolean function implemented by a network is extracted at regular intervals during training, and then compared to the Boolean function implemented by the network at the final training epoch. Although the training set only uses 8 of the 1024 possible input combinations, the experiments indicate that in most cases, the total Boolean function implemented by a network (not just the training set) converges during training.