Law Discovery Using Neural Networks

Abstract

This paper proposes a new connectionist approach to numeric law discovery; i.e., neural networks (law-candidates) are trained by using a newly invented second-order learning algorithm based on a quasi-Newton method, called BPQ, and the MDL criterion selects the most suitable from law-candidates. The main advantage of our method over previous work of symbolic or connectionist approach is that it can efficiently discover numeric laws whose power values are not restricted to integers. Experiments showed that the proposed method works well in discovering such laws even from data containing irrelevant variables or a small amount of noise. 1.