Convexity, internal representations and the statistical mechanics of neural networks
Institut für Theoretische Physik III, Universität Würzburg Am Hubland, D-97074 Würzburg
Accepted: 15 November 1996
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 with 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.
PACS: 87.10.+e – General, theoretical, and mathematical biophysics (including logic of biosystems, quantum biology, and relevant aspects of thermodynamics, information theory, cybernetics, and bionics) / 05.90.+m – Other topics in statistical physics and thermodynamics
© EDP Sciences, 1997