Optical higher-order neural networks for invariant pattern recognition

Higher-order neural networks 1 have several desirable computational characteristics such as significantly decreased convergence times, increased storage capacity over first-order layered networks (which respond only to weighted sums of the inputs ∑ W i x i ), and an ability to encode a priori knowledge in the network. Simulation results for the problem of learning to classify clusters in a binary string showed that a second-order network (which also includes weighted sums of products ∑ W i j x i x j ) generalized correctly 90% of the time after training on only 10% of the training set.