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Higher-Order Neutral Networks, Polya Polynomials, and Fermi Cluster Diagrams

K. E. Kurten·J. W. Clark
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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 Polyà's combinatoric group-theoretical approach or equivalently by exploiting a precise formal analogy with fermion diagrammatics.

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K. E. Kurten, J. W. Clark. 2001-09-04. Higher-Order Neutral Networks, Polya Polynomials, and Fermi Cluster Diagrams. https://arxiv.org/abs/cond-mat/0109053

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