Abstract: Methods and apparatus for training a neural network are disclosed. In one arrangement, a method comprises performing forward propagation of information through the neural network. An error backpropagation is performed to update parameters defining the neural network. A mathematically linear stage of the forward propagation is performed optically.

Abstract: Systems and methods for optical multiplication are disclosed. In one arrangement, a first modulator comprising rows and columns of first modulator elements is configured to spatially modulate light received from a deflector. The first modulator encodes values of a first matrix. The first matrix defines a plurality of input vectors each corresponding to a respective row of the first matrix. A second modulator spatially modulates light received from the first modulator and encodes values of a second matrix in rows and columns of second modulator elements. A light-summing optical arrangement converges light output from each row of second modulator elements to encode a plurality of output vectors representing the results of vector-matrix multiplication between a respective plurality of the input vectors and the second matrix.