Convexity, internal representations and the statistical mechanics of neural networks

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Abstract
We present an approach to the statistical mechanics of feedforward neural networks which is based on counting realizable internal representations by utilizing convexity properties of the weight space. For a toy model, our method yields storage capacities based on an annealed approximation, which are in close agreement to one step replica symmetry breaking results obtained from a standard approach. For a single layer perceptron, a combinatorial result for the number of realizable output combinations is recovered and generalized to fixed stabilities.