Towards high-performance spatially parallel optical reservoir computing

We present numerical results on a spatially parallel photonic reservoir computer. In this computing paradigm, an input signal couples to a randomly interconnected reservoir of state variables (neurons). The reservoirs output is constructed by combining the neural responses with different weights, and is used to perform useful computation. Reservoir computers are easy to train as only these output weights are optimize while keeping internal connections fixed. We are currently building a bulk optics high bandwidth reservoir computer where neurons are encoded using the spatial degree of freedom of light. We use a linear Fabry-Prot resonator as reservoir and implement a nonlinear readout layer. New input samples are injected every 2ns. The neurons are encoded as a grid of 9 by 9 spots in the 2-dimensional transverse spatial extent of the cavity input coupler. We place a lens in the middle of the resonator with focal length half the resonator length, so that the conjugate plane of the neuron grid is on the resonator back plane. At this end, a phase-only spatial light modulator acts as a programmable diffraction grating, mixing the spatial modes in the resonator. We have simulated the optical reservoir and an electronic nonlinear output layer. These simulations were performed in discrete time, and take into account photodetector noise. We study the effect of the diffractive coupling scheme and its symmetry on the simulated reservoir computing performance on a standard benchmark test. We find that symmetry improve noise robustness at the expense of diversity in the neural responses.