Free-space real-time training of a single-layer optical neural network on a phase light modulator with quantized...

We demonstrate a single-layer, feed-forward free-space optical neural network (ONN) for image classification using a mass-producible micro electromechanical system (MEMS)-based phase light modulator (PLM) to achieve an unprecedented reduction in in-situ model-free training time. Compared to liquid-crystal-based spatial light modulators (LC-SLMs), PLMs have much higher switching speed at lower costs, which is preferable for practical applications. However, the naturally low phase resolution and non-uniform phase quantization of a PLM present challenges in ONN optimization. We demonstrate with an evolutionary strategy that utilizing a discrete distribution offers many benefits over a continuous distribution, which is often used in systems based on LC-SLMs. Compared to a policy with a normal distribution, perturbation with a categorical distribution is less susceptible to the impact of phase quantization, and it follows the behavior of the natural gradient for better convergence as its exploration can be shaped to more efficiently traverse the action-space. Thus, despite the non-uniformity of phase quantization intrinsic to the PLM, our testbed achieved comparable performance to the reported ONN based on LC-SLMs of the same dataset size, but with approximately 10-fold reduction of in-situ training time. This increased speed is critically important for many practical applications, especially for systems in uncontrolled environments. We systemically investigated the impact of phase quantization levels on ONN performance. We show that the exploration of discrete categorical policy is less affected by the number of phase levels, maintaining good performance under coarse quantization. In contrast, the ONN performance of a continuous normal policy can be severely penalized with the reduction of quantization levels because of the reduced exploration and slower convergence.