Learning in Higher-Order "Artificial Dendritic Trees

The computational territory between the linearly summing McCulloch-Pitts neuron and the nonlinear differential equations of Hodgkin & Huxley is relatively sparsely populated. Connectionistsuse variants of the former and computational neuroscientists struggle with the exploding parameter spaces provided by the latter. However, evidence frombiophysical simulations suggests that the voltage transfer properties of synapses, spines and dendritic membranes involve many detailed nonlinear interactions, notjust a squashing function at the cell body. Real neurons may indeed be higher-order nets. For the computationally-minded, higher order interactions means, first of all, quadratic terms.