Method of selecting operating point of reservoir computing system based on semiconductor lasers

Abstract

Reservoir computing (RC) is an improved recurrent neural network with the simplified training process, therefore has broad application prospects. The RC can be implemented in hardware based on a nonlinear physical node and a delay feedback loop. Among the optical implementation schemes, the RC system based on semiconductor lasers can process information at high speed due to the inherently short time scales. However, the performance of the RC system, especially using the optical injection way of input signals, is affected by many factors, such as the virtual node interval, bias current, frequency detuning, feedback strength, injection strength, etc. The first three parameters can be reasonably set according to the existing studies. The feedback strength and injection strength are mostly determined through multiple attempts, and there is no method to follow, which brings great uncertainty to the RC. Although some researchers suggest that the optimal feedback strength is at the edge of consistency, the conclusion is only reached at some specific injection strengths, and nobody knows whether it is still valid when the injection strength and feedback strength change at the same time. Therefore, in this paper we investigate numerically the relationships between the optimal feedback strength and the consistency region under different injection strengths, based on the nonlinear auto regressive moving average of the 10th order (NARMA10) task. It is found that the optimal feedback strength is independent of the edge of consistency when the injection strength is large. Further research shows that the best performance of the RC system occurs at the edge of the injection locking states of the reservoir under the injection of continuous waveform light, different injection strengths and feedback strengths. Therefore this paper presents a method to select the optimal feedback strength and injection strength by using the edge of injection locking states of the reservoir under the injection of continuous waveform light. The method determines the edge of the injection locking states by searching the minimum injection strength for the injection locking states of the reservoir under one feedback strength and the injection of continuous waveform light. Then, along this edge, the optimal feedback strength and the matching injection strength are found by testing the system performance. Based on existing studies of other parameters, a method to select all parameters at the operating point is proposed. For the NARMA10 task, the normalized root mean square error at the operating point selected is as low as 0.3431 only by using 50 virtual nodes, showing that the proposed method of selecting operating point is feasible. From three properties of reservoirs, the reasons for the best performance of the system under these parameters are explained. The universality of this method for regression and classification task is tested by chaotic time series prediction task and handwritten digit recognition task. The results show that the two tasks can achieve good performance under the operating point selected by this proposed method, which verifies the universality of the method.