A signal processing neural network resembling the simple cells of the visual cortex

A single-layer neural network that mimics the quadratic phase relationship between the adjacent simple cells in the visual cortex is described. The input nodes of the network use neurons that have multiple output synapses. The resulting system, called the orthonormal neural network, can approximate any L₂ mapping function between the input and output vectors without using hidden layers or the backpropagation rule. It is also free from the problems of local minima. Because the transfer functions of the input nodes are the terms of the Fourier series, the synaptic link values between the input and output layers represent the frequency spectrum of the signals of the output nodes. As a result by auto-associatively training the network with all the synaptic links and testing it with certain selected ones, it is quite easy to build a nonlinear bandpass filter. Several systems built with this new network are discussed