Qualitative approach to gradient based learning algorithms

Abstract

This work is concerned with the establishment of a relation between the fields of qualitative reasoning (QR) and neural networks. We explore how well-known backpropagation learning algorithm can be studied from the point of view of QR. Qualitative models are based on the discretization of their parameters and the use of closed operators on the sets induced by the discretization. Henceforth, a qualitative version of backpropagation is an algorithm in which the variables involved in it belong to one of the finite classes defined. We analyse the algorithms resulting from this transformation and test their performance with a set of four problems. The results are encouraging and provide an empirical basis for a deeper, theoretical study, which can be very useful to realize physical implementations of the algorithm or as a starting point for the development of reinforcement learning algorithms.