Enhanced Computational Ability of Spin Torque Oscillator with Delayed-Feedback Circuit for Physical Reservoir Computing

Abstract

Physical reservoir computing using spin-torque oscillator (STO) has been attracting much attention after the demonstration of highly accurate human voice recognition [1]. To enhance the computational ability of STOs, there are two approaches: an array of STOs, and delayed feedback system. In the STO array, theoretical study was performed on 10-1000 STOs with interaction to obtain highly nonlinear dynamics, resulting in enhancement of computational ability that is competitive to quantum reservoir [4]. A similar highly nonlinear dynamics can be generated by using the feedback system, where outputted power from STO was reinjected in the form of electrical current or magnetic field to induce additional torque. By tuning the additional torque, complex magnetization dynamics such as amplitude modulation [5] and chaos [6,7] can be induced. These nonlinear dynamics are expected to enhance the computational ability even without interactions between STOs. Recent study showed that tunable nonlinear dynamics and delayed response by the feedback effect are adaptable for specific temporal pattern recognition task [7]. However, quantitative comparison of computational ability between the array system and the feedback system has not been investigated. In this work, we quantitatively evaluate the computational ability of STO with delayed-feedback circuit by performing a general task.The computational ability was evaluated by performing second order nonlinear autoregressive moving average (NARMA2) task [3,4]. The NARMA2 task aims to reproduce target outputs, defined by nonlinear transformation of the random inputs, from the amplitude of the STO. Figure 1 is a schematic illustration of vortex-type STO [2] with a delayed feedback circuit. To excite an auto-oscillation of the vortex core, perpendicular magnetic field of about 0.5 T and bias voltage of 350 mV were applied. In addition, we superposed random-pulse voltage with the width of 25 ns on the bias voltage. The random pulse was based on the uniform random number in the range of [-1,1] with the magnitude of 75 mV; therefore, the total input voltage varied from 275 to 425 mV. The outputted signal of the STO was amplified and converted to the RF magnetic field, which was applied to the STO with time delay of about 30 ns. The strength of the feedback signal was controlled by a tunable attenuator.Figure 2(a) shows power spectral density of the STO with delayed feedback as a function of attenuation. In the large attenuation region, the power spectra show a broad peak. With decreasing the attenuation, sharp multiple peaks appeared in the spectra below 30 dB. Such a split of spectrum is often observed when the feedback effect induces the amplitude modulation [5,6]. Figure 2(b) summarizes the dependence of normalized mean square error (NMSE) of NARMA2 task on the attenuation. It is clearly shown that NMSE can be minimized at an attenuation of 34 dB, below which the sharp multi peak structure appeared in the spectra. The observed minimum NMSE (6.4×10-6) is comparable to that theoretically obtained in the array of 16-coupled STOs [3]. This result indicates that single STO with delayed-feedback circuit can compete with the STO array.This work is supported by NEDO. **