CONVEXITY, INTERNAL REPRESENTATIONS AND THE STATISTICAL-MECHANICS OF NEURAL NETWORKS

We present an approach to the statistical mechanics of feedforward neu ral networks which is based on counting realizable internal representa tions by utilizing convexity properties of the weight space. For a toy model, our method yields storage capacities based on an annealed appr oximation, which are in close agreement with one-step replica symmetry -breaking results obtained from a standard approach. For a single-laye r perceptron, a combinatorial result for the number of realizable outp ut combinations is recovered and generalized to fixed stabilities.