Information flow in multilayer perceptrons: an in-depth analysis

Abstract: Analysing how information flows along the layers of a multilayer perceptron is a topic of paramount importance in the field of artificial neural networks. After framing the problem from the point of view of information theory, in this position article a specific investigation is conducted on the way information is processed, with particular reference to the requirements imposed by supervised learning. To this end, the concept of information matrix is devised and then used as formal framework for understanding the aetiology of optimisation strategies and for studying the information flow. The underlying research for this article has also produced several key outcomes: i) the definition of a parametric optimisation strategy, ii) the finding that the optimisation strategy proposed in the information bottleneck framework shares strong similarities with the one derived from the information matrix, and iii) the insight that a multilayer perceptron serves as a kind of "adaptor", meant to process the input according to the given objective.