Incorporation of liquid-crystal light valve nonlinearities in optical multilayer neural networks

Sigmoidlike activation functions, as available in analog hardware, differ in various ways from the standard sigmoidal function because they are usually asymmetric, truncated, and have a nonstandard gain. We present an adaptation of the backpropagation learning rule to compensate for these nonstandard sigmoids. This method is applied to multilayer neural networks with all-optical forward propagation and liquid-crystal light valves (LCLV) as optical thresholding devices. The results of simulations of a backpropagation neural network with five different LCLV response curves as activation functions are presented. Although LCLV's perform poorly with the standard backpropagation algorithm, it is shown that our adapted learning rule performs well with these LCLV curves.