Fixed points of Hopfield type neural networks

1999/01/23 by Leonid B. Litinskii, Litinskii, Leonid B.
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Biological sciences #FOS: Physical sciences #Quantitative Biology (q-bio) #cond-mat.dis-nn #q-bio

paper · pdf · doi:10.48550/arxiv.cond-mat/9901251

5 pages, Revtex, 1 Postscript-file

arxiv created 1999/01/23 · arxiv updated 2009/11/30

Abstract

The set of the fixed points of the Hopfield type network is under investigation. The connection matrix of the network is constructed according the Hebb rule from the set of memorized patterns which are treated as distorted copies of the standard-vector. It is found that the dependence of the set of the fixed points on the value of the distortion parameter can be described analytically. The obtained results are interpreted in the terms of neural networks and the Ising model at T=0.

Related

• Some Exact Results of Hopfield Neural Networks and Applications
• Highly Symmetric Neural Networks of Hopfield Type (exact results)
• Hopfield model with quasi-diagonal connection matrix
• Energy Functional and Fixed Points of a Neural Networks
• Some rigorous results for the Hopfield Model