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Stability of the replica symmetric solution for the information conveyed by by a neural network

Simon Schultz·Alessandro Treves
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Abstract

The information that a pattern of firing in the output layer of a feedforward network of threshold-linear neurons conveys about the network's inputs is considered. A replica-symmetric solution is found to be stable for all but small amounts of noise. The region of instability depends on the contribution of the threshold and the sparseness: for distributed pattern distributions, the unstable region extends to higher noise variances than for very sparse distributions, for which it is almost nonexistant.

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Simon Schultz, Alessandro Treves. 1997-11-09. Stability of the replica symmetric solution for the information conveyed by by a neural network. https://doi.org/10.1103/physreve.57.3302

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