Voltage-Controlled, Thermally Driven Superparamagnetic Ensembles for Tuneable Timescale Reservoir Computing

Abstract

Reservoir computing has been gaining traction as a bio-inspired, machine-learning approach for solving computationally hard problems, such as speech recognition and prediction of chaotic time series, that are becoming fundamental to modern technology [1]. By making use of a complex, fixed reservoir with a single output layer, the approach minimises expensive training steps. Magnetic systems are well positioned to fulfill the requirements of the reservoir, providing non-linearity, fading memory, and reproducible responses. In particular, magnetic systems subject to a temporal input sequence can perform the entire role of the reservoir, replacing complex networks of transistors whilst only requiring a single input and output [2]. This offers the potential for compact devices, with reduced energy costs for computation.Here, we propose strain-mediated, voltage controlled superparamagnetic ensembles as an ideal candidate for an ultra-low-energy reservoir. Single superparamagnetic nano-dots with uniaxial anisotropy exhibit stochastic behavior, switching between states with a characteristic timescale set by their energy barriers. Micromagnetic simulations (Fig. 1a) demonstrate this telegraphing behavior for CoFeB nano-dots, where the auto-correlation time has been verified to be below 5 ns and the strain-induced anisotropy can compete with the intrinsic anisotropy [3-6]. Borders et al. [7] have shown how tuning such telegraph noise in magnetic tunnel junctions can be used for integer factorization. Here, however, we make use of the collective behavior of extended ensembles of nano-dots such that the average magnetisation becomes predictable; thus, showing the reproducible response required for reservoir computing. Input is provided by addition of a strain-mediated anisotropy (Fig. 1b)—a technique that is predicted to achieve ultra-low-power consumption [8]. This acts to rotate the intrinsic anisotropy axis, biasing dwell time in one state over the other [9]. Whilst the internal system dynamics are driven by thermal noise, the average magnetisation obeys simple rules that, when subject to a temporally varying input, produce a complex non-linear response with fading memory (Fig. 1c).Using an analytical model of the response of the superparamagnetic ensemble [10], we simulate the physical reservoir. By inputting a temporal sequence and training a single layer of weights from the output, we can perform standard machine learning benchmarks with competitive performance over a range of input timescales. Fig. 2 presents the performance for spoken digit recognition on the TI-46 dataset and chaotic time series prediction on the NARMA10 task. In both cases the performance approaches that of competing reservoirs [1,2], despite the relative simplicity of the system. The intrinsic timescale of the system (τ) is controlled by the ratio of energy barrier (anisotropy, KV) to the thermal energy (KBT at 300 K). Fig. 2a demonstrates that by tuning the input rate and strength (relative to the intrinsic timescale and anisotropy respectively), optimal performance of 95 % recognition of the spoken digits 0-9 with five female speakers can be achieved. This is realised for τ ~ 50 ns (KV/KBT = 20) and τ ~ 1 ms (KV/KBT = 50). For the NARMA10 task (Fig. 2b), the highest performance is achieved across this entire timescale range by tuning the strength of a feedback term (i.e. the output is fed back into the input stream with a given weight).Robust performance on timescales ranging from hundreds of nanoseconds up to seconds would allow a physical realisation of such a reservoir to be tuned to provide computation in real time for a wide range of possible physical inputs: from decision-making in driverless cars (fast) to speech recognition (slow). The simplicity of the system and the ease of manufacture, coupled with the low energy consumption expected for such a, thermally driven, device makes it an ideal candidate for edge computing where high performance is needed at very low latency and power. **