Extracting Propositions from Trained Neural Networks

Abstract

This paper presents an algorithm for extracting propositions from trained neural networks. The algorithm is a decompositional approach which can be applied to any neural network whose output function is monotone such as sigmoid function. Therefore, the algorithm can be applied to multi-layer neural networks, recurrent neural networks and so on. The algorithm does not depend on training methods. The algorithm is polynomial in computational complexity. The basic idea is that the units of neural networks are approximated by Boolean functions. But the computational complexity of the approximation is exponential, so a polynomial algorithm is presented. The authors have applied the algorithm to several problems to extract understandable and accurate propositions. This paper shows the results for votes data and mushroom data. The algorithm is extended to the continuous domain, where extracted propositions are continuous Boolean functions. Roughly speaking, the representation by continuous Boolean functions means the representation using conjunction, disjunction, direct proportion and reverse proportion. This paper shows the results for iris data.