Abstract

Higher-order neural networks allow a priori implementation of geometric invariances with the concomitant reduction in training complexity.¹ The symmetries inherent in a second-order translation-invariant classifier can be exploited in an elegant optical implementation.² An optical system based on a commercially available liquid crystal display, operating in transmission under external computer control, and with on-line learning capabilities has been constructed. The binary inputs are displayed as a series of black/white bars. A second pass through the same pattern arranged at right angles produces all the terms of the vector cross-product with itself. A third pass institutes the weight multiplication. The summed light totals are monitored with photodiodes. During the training phase the weight updates are determined by the measured light output at each iteration. Because of device limitations the learning rule must be adapted to produce a finite range of weighing values.

© 1991 Optical Society of America