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

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

1997-09-19

arxiv.org/abs/cond-mat/9709219v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

19 pages, LaTeX, 5 figures. Also available at http://www.mrc-bbc.ox.ac.uk/~schultz/papers.html . Submitted to Phys. Rev. E M

Scientific paper

10.1103/PhysRevE.57.3302

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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