Performance Optimization Of A Reservoir Computing System Based On A Solitary Semiconductor Laser Under Electrical-message Injection

Reservoir computing(RC)is a biologically inspired paradigm recently introduced in the machine learning field.It overcomes the problems of large energy consumption and slow computation speed of traditional computers,and can solve complex tasks such as speech recognition,face recognition and chaotic time series forecasting.One of the key advantages of RC is that the training algorithms are efficient and rapidly converge to reach the global optimum since it only need to train the output connection weights without optimizing the internal connections of the network.This concept makes the hardware implementation of RC possible.There are two hardware implementation schemes of RC:one is the spatial RC composed of a large number of nonlinear nodes distributed in space;the other is the delay-based RC system composed of a nonlinear time-delay system.In particular,RC composed of a single node based on the latter has the advantages of easy hardware implementation and low cost,thus attracting people's interest dramatically.Semiconductor laser(SL)has a rich and controllable nonlinear dynamic state under external interference(such as light injection and current modulation),fast response speed,small size,low energy consumption and easy integration,so it is an ideal device for RC construction.Therefore,related researches on RC system based on a semiconductor laser(named as SL-RC)have received extensive attention.Considering that the performance of the delay-based SL-RC system is drastically changed with the fluctuation of feedback phase,while the fluctuation of the feedback phase is difficult to eliminate in this system.In this work,the SL-RC system under electrical message injection has the unique advantage of simple structure.We proposed an RC system based on a solitary SL under electrical-message injection,and the performances of the RC are numerically investigated.Considering the lack of memory capacity(MC)in such a system,some auxiliary methods are introduced to enhance the MC and optimize the performances for processing complex tasks.In the pre-existing method,the input information is the current input data combined with some past input data in a weighted sum in the input layer(named as M-input).Another auxiliary method(named as M-output)is proposed to introduce the output layer.The final state for training and testing can be expressed as the weighted sum of the past virtual node state and the current virtual node state.After adopting three auxiliary methods of M-input,M-output and M-both(the M-input integrated with the M-output),the MC of the RC system are numerically analyzed.The simulated results demonstrate that the MC of the system can be improved after adopting the three auxiliary methods and can be increased about an order of magnitude under adopting M-both.After adopting these auxiliary methods,the performances for processing the Santa Fe time series prediction task and the nonlinear channel equalization(NCE)task can be enhanced.Since different tasks have different requirements for the nonlinearity and the MC of RC,the three auxiliary methods have different effects on the two task.In this paper,the impact of the number of summed past data(named as Q_inor Q_out)introduced in the input layer or output layer on the performance of the RC is investigated.The simulated results show that the M-input is more suitable than others for the prediction task,and the lowest prediction error can be decreased from 0.027 to0.0034 for Q_in=7.For an NCE task,the M-both is relatively better,and the lowest symbol error rate(SER)can be decreased from 0.05 to 1.1×10^-3 under Q_in=25 and Q_out=3.