Phase Noise Robustness of a Coherent Spatially Parallel Optical Reservoir

Reservoir computing is a machine learning algorithm particularly adapted to process time-dependent signals. It can be easily implemented experimentally with good performance. However experimental implementations are subject to noise, which degrades performance. We develop strategies to mitigate the effects of noise. The specific system on which we illustrate our approaches-currently under development in our laboratory-is a coherent linear Fabry-Perot resonator in which neurons are encoded as a grid of spots on the input mirror plane. In this system, changes in the length of the resonator are the major source of noise and can be modeled as phase noise. This can in principle be partially solved by active stabilisation, but it is interesting to find other strategies to counter the effect of phase noise. We show that a completely unknown phase can be tolerated with only a small degradation of performance by using appropriate training and a readout layer architecture in which the output weights depend on the noisy parameter (the phase). Furthermore, the phase can be estimated by the reservoir itself, leading to an architecture in which the reservoir has two outputs, one of which (the phase estimation) is used to control the other. Our approach should find applications in many experimental implementations of reservoir computing.