Fig. 5: The performance of reservoir computing based on the tri-layer ASI system.

a The concept of the ASI-based reservoir computing device. The device can be divided into three parts: the input, the reservoir, and the output. The input signals are encoded into the angle of the in-plane magnetic fields which applies globally on the ASI. The state evolution of ASI can be read out in situ via the transport measurement technique. Resistance matrix can be detected within each local segment as output, and fed into a following artificial neural network for further training and inference. b Structure for the ASI-based time-multiplexing RC. The original input data series is multiplexed to generate another data series where signal changes of higher frequencies are generated and linearly mapped to the range of the field angle. The resistance states between different pairs of electrodes are read out under the stimuli of the external magnetic field. The readout weight matrix is trained simply through ridge regression. c The nonlinear behavior of the ASI device used for the physical implementation of the RC system. We obtained the nonlinear curves of the input (angle of the in-plane magnetic field θ correspond to the current) and output signals (resistance) of 9 pairs of different electrodes. We map the input values linearly to the angle of the magnetic field (0–360 degrees) in a plane. The resistance of the ASI reservoir to the nonlinear response of all input signals was measured in a reproducible chaotic initial state. d ASI-based reservoir computing device has fading memory. The initial states are prepared with eight long-range-ordered spin configurations Type A to Type H. Then the same 9 input signals are given to eight different long-range-ordered spin configurations. The output resistances finally converge to the same behavior. The magnetic field applied is all about 70 Oe. e The performance on different benchmark tasks Sunspot processing prediction and Mackey-Glass prediction with ASI RC. We use half the data for training and half for testing. NRMSE is used to measure the classification error.