language: en

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

Simon Schultzy and Alessandro Trevesz
Department of Experimental Psychology,
South Parks Rd.,
University of Oxford,
Oxford OX1 3UD, U.K.
Programme in Neuroscience, International School for Advanced Studies,
via Beirut 2-4, 34013 Trieste, Italy
(November 7, 1997)

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.

84.35.+i,89.70.+c,87.10.+e

[Typeset using REVT E X]