Extracting Propositions from Trained Neural Networks

This paper presents an algorithm for extract­ ing 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 sig­ moid function. Therefore, the algorithm can be applied to multi-layer neural networks, re­ current 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 poly­ nomial 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 representa­ tion by continuous Boolean functions means the representation using conjunction, disjunc­ tion, direct proportion and reverse proportion. This paper shows the results for iris data. 1 Introduction Extracting rules or propositions from trained neural net­ works is important[1], [6], Although several algorithms have been proposed by Shavlik, Ishikawa and others [2],[3], every algorithm is subject to problems in that it is applicable only to certain types of networks or to certain training methods. 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, although some other methods[2], [3] do. The algorithm does not modify the training re­ sults, although some other methods [2] do. Extracted propositions are Boolean functions. The algorithm is polynomial in computational complexity. The basic idea is that the units of neural networks are approximated by Boolean functions. But the computa­ tional complexity of the approximation is exponential, so a polynomial algorithm is presented. The basic idea of reducing the computational complexity to a polynomial is that only low order terms are generated, that is, high order terms are neglected. Because high order terms are not informative, the approximation by low order terms is accurate[4]. In order to obtain accurate propositions, when the hidden units of neural networks are approximated to Boolean functions, …