Optics is a promising platform in which to help realise the next generation of fast, parallel and energy-efficient computation. We demonstrate a reconfigurable free-space optical multiplier that is capable of over 3000 computations in parallel, using
spatial light modulators with a pixel resolution of only 340x340. This enables vector-matrix multiplication and parallel vector-vector multiplication with vector size of up to 56. Our design is the first to simultaneously support optical implementation of reconfigurable, large-size and real-valued linear algebraic operations. Such an optical multiplier can serve as a building block of special-purpose optical processors such as optical neural networks and optical Ising machines.
Backpropagation through nonlinear neurons is an outstanding challenge to the field of optical neural networks and the major conceptual barrier to all-optical training schemes. Each neuron is required to exhibit a directionally dependent response to p
ropagating optical signals, with the backwards response conditioned on the forward signal, which is highly non-trivial to implement optically. We propose a practical and surprisingly simple solution that uses saturable absorption to provide the network nonlinearity. We find that the backward propagating gradients required to train the network can be approximated in a pump-probe scheme that requires only passive optical elements. Simulations show that, with readily obtainable optical depths, our approach can achieve equivalent performance to state-of-the-art computational networks on image classification benchmarks, even in deep networks with multiple sequential gradient approximations. This scheme is compatible with leading optical neural network proposals and therefore provides a feasible path towards end-to-end optical training.
