Higher-order neural networks, Polyà polynomials, and Fermi cluster diagrams
K. E. Kürten, J. W. Clark · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 2003
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 multineuron 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.