Higher-Order Neutral Networks, Polya Polynomials, and Fermi Cluster Diagrams
Disordered Systems and Neural Networks
2007-05-23 v1 q-bio
Abstract
The problem of controlling higher-order interactions in neural networks is addressed with techniques commonly applied in the cluster analysis of quantum many-particle systems. For multi-neuron synaptic weights chosen according to a straightforward extension of the standard Hebbian learning rule, we show that higher-order contributions to the stimulus felt by a given neuron can be readily evaluated via Poly\`a's combinatoric group-theoretical approach or equivalently by exploiting a precise formal analogy with fermion diagrammatics.
Cite
@article{arxiv.cond-mat/0109053,
title = {Higher-Order Neutral Networks, Polya Polynomials, and Fermi Cluster Diagrams},
author = {K. E. Kurten and J. W. Clark},
journal= {arXiv preprint arXiv:cond-mat/0109053},
year = {2007}
}
Comments
11 pages, 1 figure