Information Capacity of a Hierarchical Neural Network

Abstract

The information conveyed by a hierarchical attractor neural network is examined. The network learns sets of correlated patterns (the examples) in the lowest level of the hierarchical tree and can categorize them at the upper levels. A way to measure the non-extensive information content of the examples is formulated. Curves showing the transition from a large retrieval information to a large categorization information behavior, when the number of examples increase, are displayed. The conditions for the maximal information are given as functions of the correlation between examples and the load of concepts. Numerical simulations support the analytical results.