Higher-Order Neutral Networks, Polya Polynomials, and Fermi Cluster Diagrams
Abstract
Description
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 Polyà's combinatoric group-theoretical approach or equivalently by exploiting a precise formal analogy with fermion diagrammatics.
11 pages, 1 figure
11 pages, 1 figure