Research Seminar - May 20, 1998

Abstract

The function implemented by an artificial neural network is determined by its weights and transfer functions. However, the description of the function in terms of weights and transfer functions is not particularly suited to human understanding or symbolic computation. This is true even for a function implemented by a single neuron.

This talk presents an algorithm for extracting a Boolean expression from a trained neuron. The expression is produced in a normal form (called BNF) that takes advantage of the neuron's boolean incompleteness. BNF has been demonstrated in experiments to be more compact than the optimised disjunctive normal form (where expressions of the form aX v (not a)X are reduced to X).

The length of expressions in BNF varies with the order in which the variables are considered. The shortest BNF expression is produced when the weights are all positive, and the variables are considered in decreasing order of their associated weights.

All neurons can be transformed such that their weights are all positive, so we can always extract a minimal BNF expression from a trained neuron.