Task-adaptive physical reservoir computing

Abstract

Reservoir computing is a neuromorphic architecture that may offer viable solutions to the growing energy costs of machine learning. In software-based machine learning, computing performance can be readily reconfigured to suit different computational tasks by tuning hyperparameters. This critical functionality is missing in 'physical' reservoir computing schemes that exploit nonlinear and history-dependent responses of physical systems for data processing. Here we overcome this issue with a 'task-adaptive' approach to physical reservoir computing. By leveraging a thermodynamical phase space to reconfigure key reservoir properties, we optimize computational performance across a diverse task set. We use the spin-wave spectra of the chiral magnet Cu₂OSeO₃ that hosts skyrmion, conical and helical magnetic phases, providing on-demand access to different computational reservoir responses. The task-adaptive approach is applicable to a wide variety of physical systems, which we show in other chiral magnets via above (and near) room-temperature demonstrations in Co_8.5Zn_8.5Mn₃ (and FeGe).

Fig. 1. Working principles of physical reservoir computing with a chiral magnet.

a, Illustration of a task-adaptive reservoir computing framework. Different magnetic phases are accessed by controlling the external magnetic field (H) and temperature (T). The rightmost panel shows the experimental schematic of the VNA-assisted spin-wave spectroscopy setup. VNA, vector network analyser. b, Typical input scheme for forecasting (left: Mackey–Glass signal) and transformation (right: sine wave) tasks. The original input signal, u(t), is mapped to u'(N), which is defined by the mapped field-cycling protocol (see main text and Methods for details). Note that H_range defines the full range of applied fields, where the distance between H_low and H_high at any given N, is the width of cycling, H_range/2. A single field cycle is highlighted by the orange box in the transformation panel. c, S₁₁ (denoted as ΔS₁₁ after pre-processing; see Methods) as a function of the frequency f after accumulating N field cycles and visualization of R(N, M); a collective spectral evolution for N field cycles for skyrmion and conical phases, separated into ‘training’ and ‘test’ datasets. d, Results after applying W_out on the unseen ‘test’ dataset. Left: forecasting of a differential chaotic time-series data, Mackey–Glass signal by 10 future steps. Right: transformation of a sine wave to a square-wave signal. In both cases, reservoir prediction (transformation) results are plotted in blue (purple), the red dotted line depicts the target signal and the grey line represents the control prediction where ridge regression is performed on the raw input data without the physical reservoir. MSE_FC and MSE_TR quantify the computation performance of forecasting and transformation, respectively.

Fig. 2. Field-cycling-dependent spin-wave spectra as a physical reservoir.

a, Schematic of the temperature phase diagram for the bulk crystal Cu₂OSeO₃. The yellow dashed vertical (horizontal) line indicates the experimental conditions for our cycling experiments shown in c (d). b, The cycling number dependence of the spin-wave spectra in Cu₂OSeO₃ for H_c = 60 mT and 4 K. The evolution of the skyrmion-phase spectrum is shown for increasing values of N. Grey lines are added as a guide to the eye to keep track of the skyrmion modes. c, H_c dependence of the spin-wave spectra in Cu₂OSeO₃ for 4 K after 920 field cycles. d, Temperature dependence of the spin-wave spectra for H_c = 60 mT after 920 field cycles. e, Microwave absorption spectra as a function of f and N for different values of H_c at T = 4 K (upper row) and 35 K (lower row). The input signal in all plots is a sine wave with H_range = 90 mT.

Fig. 3. Reservoir computing performance of different magnetic phase spaces.

MSE performance comparison of different computation tasks across three distinct physical phases (skyrmion, skyrmion–conical hybrid and conical) at T = 4 K. In a–c, the red dotted and grey curves represent the target functions and the computation results without the physical reservoirs, respectively. Blue, orange and purple curves display calculations with the physical reservoirs of skyrmion, skyrmion–conical hybrid and conical phases, respectively. a, Forecasting a Mackey–Glass chaotic time series of ten steps ahead (MG(N + 10)). b, Nonlinear transformation of a sine-wave input into saw waveforms. c, Combined transform/forecasting of ten future steps of a cubed Mackey–Glass signal. d, Illustration of the mapped field-cycling protocol visualized as a modified boxplot (details in the main text). e,g, Evaluation of MSE values at a constant H_range as a variation of H_c and T, respectively, for forecasting (MG(N + 10)) (e) and transformation (square wave) (g) target applications. f, Evaluation of MSE values at a constant H_c as a variation of H_range and T for a transformation (square wave) target application. The colour scale in g also applies to f.

Fig. 4. Computation properties associated with physical characteristics.

a–c, Spin-wave spectra of the helical (a), skyrmion (b) and conical (c) magnetic phases. d, Sine-wave input sequence defining the applied field amplitudes. e–g, Spin-wave spectra of the helical (e), skyrmion (f) and conical (g) phases at nodes of the sine-wave input fields from d. h, H_c evolution of the MSE values at T = 4 K and H_range = 90 mT, for forecasting (MG(N + 10)) and transformation (square wave) target applications. Note that MSE' denotes the normalized scale of MSE for [0, 1], where 0 (1) represents the best (worst) MSE. A (meta)stable magnetic field range for each phase is colour-coded. i, MSE' and task-agnostic metric results as a function of H_c at T = 4 K. j, Correlation matrix of Spearman’s rank correlation coefficient. k, Performance of forecasting as an evolution of the MC metric. l, Performance of transformation as an evolution of the CP metric.

Fig. 5. Above-room-temperature demonstration of task adaptability using Co_8.5Zn_8.5Mn₃.

a, Two-dimensional plot of the real part of the a.c. susceptibility (χ′) to identify magnetic phases in a Co_8.5Zn_8.5Mn₃ crystal with helical, skyrmion, conical and ferromagnetic phases. The vertical dotted line represents the temperature at which we performed the reservoir computing experiments. b,c, Spin dynamics spectra measured during field cycling N showing the reservoir computing performance for forecasting (b) and transformation (c) at 333 K, at different centre fields of 15 mT (left spectra) and 60 mT (right spectra). d–g, Reservoir computing performance of predicting the nonlinear Mackey–Glass function for five future steps (d,f) and transformation from a sine input signal to triangle output function (e,g). The red dotted curves denote the target function and the blue and purple solid curves are calculations generated via our reservoir computing.