Flow of Information in Hopfield Neural Networks

Abstract

Deep learning and neural networks have been used in various machine learning applications in the past decades. Developing a precise understanding of the underling behavior of neural networks is crucial for their efficient deployment. In this paper, we use an information theoretic approach to study the flow of information in a discrete Hopfield neural network. While discrete Hopfield networks, are used as associative memories, study of their dynamic behavior is important in general, as they represent the family of recurrent neural networks. We determine lower and upper bounds for the entropy and the conditional entropy. We also study the mutual information between the input patterns and the final output of the network. Experimental results support the theoretical conclusions of the paper.