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Task-adaptive physical reservoir computing

Oscar Lee, Tianyi Wei, Kilian D. Stenning, Jack C. Gartside, Dan Prestwood, Shinichiro Seki, Aisha Aqeel, Kosuke Karube, Naoya Kanazawa, Yasujiro Taguchi, Christian Back, Yoshinori Tokura, Will R. Branford, Hidekazu Kurebayashi

arXiv:2209.06962v3cond-mat.mtrl-scicond-mat.mes-hall

TL;DR

Physical reservoirs have limited means to reconfigure their properties for different tasks, unlike software reservoirs. This work uses field- and temperature-controlled magnetic phases in Cu2OSeO3 to adapt reservoir responses; skyrmion and conical phases favor forecasting and transformation, respectively. The authors report that this phase-tunable approach supports strong performance across tasks in a single physical system.

  • Problem

    Physical reservoirs typically offer a narrow, fixed set of properties, leaving a gap in task-specific control of nonlinearity, memory-capacity and complexity.

    Source: Introduction · p. 2

  • Method

    The authors use magnetic field-cycling and temperature control to select phase-dependent spin-wave responses in Cu2OSeO3 and train output weights for each task.

    Source: Introduction · p. 2, Working principle of chiral magnet… · p. 2

  • Results

    Skyrmion and conical phases favor forecasting and transformation, respectively; forecasting MSE was 3.7×10−3 for the skyrmion reservoir.

    Source: Introduction · p. 2, Working principle of chiral magnet… · p. 4

  • Takeaways & Limitations

    A single physical reservoir can be reconfigured on demand for strong performance across a broad range of tasks without fabricating additional samples or changing physical systems.

    Source: Conclusion · p. 11

Abstract

from arXiv · show

Reservoir computing is a neuromorphic architecture that potentially offers viable solutions to the growing energy costs of machine learning. In software-based machine learning, neural network properties and performance can be readily reconfigured to suit different computational tasks by changing hyperparameters. This critical functionality is missing in ``physical" reservoir computing schemes that exploit nonlinear and history-dependent memory responses of physical systems for data processing. Here, we experimentally present a `task-adaptive' approach to physical reservoir computing, capable of reconfiguring key reservoir properties (nonlinearity, memory-capacity and complexity) to optimise computational performance across a broad range of tasks. As a model case of this, we use the temperature and magnetic-field controlled spin-wave response of Cu$_2$OSeO$_3$ that hosts skyrmion, conical and helical magnetic phases, providing on-demand access to a host of different physical reservoir responses. We quantify phase-tunable reservoir performance, characterise their properties and discuss the correlation between these in physical reservoirs. This task-adaptive approach overcomes key prior limitations of physical reservoirs, opening opportunities to apply thermodynamically stable and metastable phase control across a wide variety of physical reservoir systems, as we show its transferable nature using above(near)-room-temperature demonstration with Co$_{8.5}$Zn$_{8.5}$Mn$_{3}$ (FeGe).

Introduction

Physical reservoirs lack the task-specific reconfiguration available in software, limiting their ability to suit tasks with different reservoir-property needs. This work uses phase-tunable spin dynamics in Cu2OSeO3 to adapt reservoir responses and perform forecasting and transformation tasks.

Introduction

  • Physical reservoirs lack a general way to adapt nonlinearity, memory-capacity and complexity, unlike software reservoirs whose properties can be tuned in code.Physical systems typically offer a narrow, fixed set of properties tied to a particular response phenomenon.Source: Introduction · p. 2
  • Cu2OSeO3’s distinct skyrmion, helical and conical spin resonances can be selected by field and temperature, enabling task-adaptive reservoir properties and performance.The authors associate skyrmion-phase memory capacity with forecasting and conical-phase nonlinearity and complexity with transformation tasks.Source: Introduction · p. 2
  • Field-cycling encodes input time series as magnetic-field sequences, and measured spin-wave spectra form a high-dimensional reservoir response.The experiments use Mackey–Glass signals for forecasting and sinewaves for transformation; the measured spectra contain 1601 frequency channels.Source: Working principle of chiral magnet… · p. 2
  • Forecasting MSE was 3.7×10−3 for the skyrmion reservoir, while transformation MSE was 7.3×10−7 for the conical reservoir.Without the reservoirs, the corresponding MSE values were 6.2×10^2 and 5.4×10^2.Source: Working principle of chiral magnet… · p. 4
  • Ridge regression trains output weights on 70% of reservoir responses, then evaluates predictions on the remaining 30%.The demonstrated tasks forecast the Mackey–Glass signal 10 steps ahead and transform a sinewave into a square wave.Source: Working principle of chiral magnet… · p. 4

Phase-tunable physical reservoir computing

Cu2OSeO3’s magnetic phase diagram lets the reservoir’s spin-wave response be tuned through field and temperature. Field-cycling generates evolving skyrmion modes at low temperatures, while higher temperatures show conical-phase modes.

Phase-tunable physical reservoir computing

  • The metastable skyrmion phase can be generated below approximately 35 K by quenching or field-cycling, providing phase tunability for task-adaptive reservoir computing.The phase diagram also contains stable magnetic phases.Source: Phase-tunable physical reservoir… · p. 4
  • Field-cycling transforms the spectra from conical modes near 4 GHz to skyrmion modes around 2–3 GHz as cycles accumulate.At N = 100 the conical peak is sharp; skyrmion modes appear around N = 130–170 as their amplitudes evolve through skyrmion destruction and renucleation.Source: Phase-tunable physical reservoir… · p. 4, Figure 2 · p. 5
  • Changing field centre or temperature tunes the observed phases: skyrmion modes appear at 4 K and 15 K but disappear at 25 K and 35 K, where broad conical modes dominate.The spectra are measured after 920 field-cycles for the field- and temperature-dependence comparisons.Source: Phase-tunable physical reservoir… · p. 4, Figure 2 · p. 5

Reservoir Performance

Reservoir performance depends on both the magnetic phase and the computational task: skyrmion modes favor forecasting, while conical modes favor transformation. Field-cycling conditions tune these responses, and a hybrid reservoir outperforms either individual phase on a combined task.

Reservoir Performance

  • Experiments compare phase-specific performance at 4 K using field cycling, then map MSE across Hc, Hrange, and temperature.The forecasting comparison uses Mackey-Glass prediction 10 steps ahead; the parameter maps include forecasting and square-wave transformation tasks.Source: Reservoir Performance · pp. 5, 7, Figure 3 · p. 6
  • Forecasting MSE increases approximately 18-fold from skyrmion to conical, whereas conical reaches 3.7 × 10^-7 MSE on sine-to-saw transformation.Figure 3 compares forecasting, transformation, and combined forecasting/transformation across skyrmion, hybrid, and conical reservoirs.Source: Reservoir Performance · p. 5, Figure 3 · p. 6
  • The hybrid configuration outperforms both individual skyrmion and conical reservoirs on forecasting 10 steps ahead for a cubed Mackey-Glass signal.The task combines transformation of a normal Mackey-Glass input and forecasting its cubed signal.Source: Reservoir Performance · p. 7
  • Forecasting is best when field cycling stays within the skyrmion phase at lower temperatures, and worsens as cycling moves beyond that phase.Performance drops dramatically when cycling leaves the skyrmion phase at high temperatures; the passage reports a correlation with memory-capacity.Source: Reservoir Performance · p. 7
  • For transformation, larger Hrange improves performance, while cycling deeper into the helical phase performs worse; optimal performance substantially includes the conical phase.Crossing the zero-field boundary resets skyrmion-mode nucleation and suppresses its contribution; identical reservoirs can perform very differently across tasks.Source: Reservoir Performance · p. 7
  • Strong field-driven frequency shifts in conical and skyrmion spectra support transformation performance, while history-dependent skyrmion spectra provide memory for forecasting.Helical spectra shift weakly with field and show poor computational performance; skyrmion nucleation and annihilation underlie its history dependence.Source: Reservoir Performance · p. 7

Reservoir Metrics

The paper compares task performance with task-agnostic reservoir metrics and finds that the useful reservoir properties differ by task. Memory-capacity tracks forecasting, whereas nonlinearity and complexity support transformation, with correlations indicating trade-offs among properties.

Reservoir Metrics

  • Task-agnostic nonlinearity (NL), memory-capacity (MC), and complexity (CP) are compared with normalised MSE′ across Hc values.Forecasting and transformation tasks are evaluated at 4 K, with metric scores plotted as a function of Hc.Source: Reservoir Metrics · p. 9
  • Forecasting performs best in the skyrmion phase as it worsens toward conical, while transformation shows the opposite phase trend.MC follows forecasting MSE′, and high NL and CP in conical/ferrimagnetic phases provide a physical basis for transformation performance.Source: Reservoir Metrics · p. 9
  • Forecasting performance correlates with MC at -0.89 and CP at 0.57; MC and CP correlate at -0.68, while NL and CP correlate at 0.67.For transformation, the passage reports the opposite task-property preference; NL and MC have a weak negative correlation of -0.27.Source: Reservoir Metrics · p. 9
  • Skyrmion metrics cluster at MC values of 4 to 7, while transformation reaches its potential when complexity is maximised in the conical-dominated phase.These phase-specific patterns connect memory in skyrmion textures with forecasting and conical-phase complexity with transformation.Source: Reservoir Metrics · p. 9

Above-room-temperature demonstration

At 333 K, Co8.5Zn8.5Mn3 reservoirs show task-dependent performance across magnetic phases. This above-room-temperature demonstration supports transfer of the task-adaptive concept to other materials.

Above-room-temperature demonstration

  • At 333 K, reservoirs at center fields of 15 and 60 mT show different spin-dynamics spectra during forecasting and transformation tasks.The crystal exhibits helical, skyrmion, conical, and ferromagnetic phases; the experiment temperature is marked in the susceptibility phase map.Source: Above-room-temperature demonstration · p. 9, Figure 5 · p. 10
  • For forecasting, the skyrmion-dominated reservoir outperforms the ferromagnetic reservoir, while the ferromagnetic reservoir has lower MSE for transformation.Both were tested at 333 K.Source: Above-room-temperature demonstration · p. 10
  • The above-room-temperature demonstration supports the task-adaptive concept’s transfer to a wide variety of materials.The authors note that MSE and fuller use of this material system’s task-adaptive capacity could still be improved.Source: Above-room-temperature demonstration · pp. 10–11

Conclusion

The authors conclude that phase-tunable physical reservoirs can be reconfigured on demand across tasks without fabricating additional samples. Their mapped field-cycling setup encodes time-series inputs and reads out frequency-resolved magnetic responses.

Conclusion

  • On-demand phase control lets one physical reservoir be reconfigured for different tasks without fabricating additional samples or switching physical systems.The authors identify online training and dynamic, on-the-fly reconfiguration for incoming real-time datasets as future developments.Source: Conclusion · p. 11
  • The phase-tunable approach may transfer beyond chiral magnets to other physical reservoirs, including systems with rich thermodynamic phase diagrams.The conclusion also points to possible functionality in acoustic and spin-wave physical recurrent neural networks.Source: Conclusion · p. 11

S1 Details of experimental setup

  • Mapped field-cycling modulates the field-cycle values to encode arbitrary time-series signals, with frequency-resolved FMR spectra providing reservoir outputs.The measured frequency range supplies multiple outputs for each field input; changing the magnetic field dominates the roughly two-hour task time.Source: S1 Details of experimental setup · pp. 15–16

S2 Details of reservoir computing protocols

The protocol preprocesses frequency spectra, trains ridge-regression readouts, and evaluates them on held-out data using MSE. The study uses 70% for training and 30% for testing, with task-specific forecasting and transformation targets.

S2 Details of reservoir computing protocols

  • Each spectrum is background-subtracted, smoothed, and sampled at fixed intervals to form the reservoir matrix.The sampling interval is selected by an automated search for the lowest test-data MSE; sampling helps avoid overfitting from too many data points.Source: S2 Details of reservoir computing… · p. 16
  • For transformations, sine-wave inputs are trained to reproduce square- or saw-wave targets, while Mackey-Glass time series provide the forecasting benchmark.The square wave has a duty cycle of 0.5; the saw signal uses a rising-ramp width of 1.Source: S2 Details of reservoir computing… · p. 16
  • Ridge regression fits output weights to the training reservoir and target data, then applies them to the unseen test data.The regularization term penalizes large weights to stabilize fitting and prevent overfitting.Source: S2 Details of reservoir computing… · pp. 16–17
  • 70% of reservoir data is used for training and 30% for testing, with k fixed at 0.3 and N = 1000 cycles.The authors report that sufficient training data improves MSE for both tasks and that this choice of k does not significantly alter their analysis or conclusions.Source: S2 Details of reservoir computing… · p. 17
  • MSE measures average squared differences between predicted and target values, with lower values indicating better predictive performance.The protocol plots MSE against test-length factor k for forecasting and transformation tasks; the figure marks the selected k value of 0.3.Source: S2 Details of reservoir computing… · p. 17, Figure S2 · p. 17

S3 Magnetic phases and tunability in Cu2OSeO3

Cu2OSeO3’s magnetic phases produce distinct reservoir responses that can be selected through field and temperature control. The phase-dependent balance of memory, nonlinearity, and complexity aligns with different computational tasks.

S3 Magnetic phases and tunability in Cu2OSeO3

  • The magnetic phase diagram includes helical, conical, ferrimagnetic, and skyrmion phases, with metastable low-temperature skyrmions controllable by field-cycling.The skyrmion phase is anticipated below approximately 25 K and between 25 < H < 120 mT.Source: S3 Magnetic phases and tunability in… · p. 18
  • Increasing Hc shifts Cu2OSeO3 from helical-dominated responses through skyrmion and hybrid regimes toward a conical-dominated reservoir with high nonlinearity and complexity.At Hc = 185 mT, the conical reservoir is reported to perform outstandingly on transformation tasks.Source: S3 Magnetic phases and tunability in… · p. 18

S4 Computational properties associated with physical characteristics

  • In the skyrmion reservoir, spectra at the same field differ with input history, indicating short-term memory; cycling-dependent skyrmion population adds long-term memory associated with Mackey-Glass forecasting performance.The conical reservoir’s spectra are history-independent, unlike the skyrmion reservoir’s.Source: S4 Computational properties associated… · p. 18
  • Conical-mode spectra combine peak shifts that track the input field with large, diverse amplitude changes, producing nonlinear responses suited to transformation tasks.The authors characterize this mode as high in nonlinearity and complexity.Source: S4 Computational properties associated… · pp. 18–19
  • Tuning Hc selects dominant helical, skyrmion, hybrid, or conical phase spaces in the Cu2OSeO3 reservoir.The spectra evolve with microwave frequency and cycle number for a sine-wave input at 4 K and Hrange = 90 mT.Source: Figure S3 · p. 19
  • Increasing the number of spectral points generally improves MSE, except for conical-reservoir future prediction, where adding points without memory offers little improvement.The authors attribute the effectiveness of high-dimensional mapping to the differing nonlinear responses of individual spectral points.Source: S4 Computational properties associated… · p. 19

S5 Additional reservoir computing performance

Additional tests show accurate transformations across diverse target signals and explain why Mackey–Glass forecasting is evaluated at a nontrivial future step. The supplement also describes spectral analyses and how reservoir properties are assessed and related to internal hyperparameters.

S5 Additional reservoir computing performance

  • Transformation MSE values are 10^-3 or below across diverse target signals, including sine-squared, cosine, hysteretic, and combined waveforms.The triangle, Gaussian, and square targets are also evaluated in the broader transformation tests.Source: S5 Additional reservoir computing… · pp. 19–20
  • Figure S4 examines spectral evolution and feature changes across input cycles, including frequency and amplitude changes for skyrmion and conical modes.Source: Figure S4 · p. 20
  • Figure S5 compares spectral-size-dependent forecasting and transformation MSE for skyrmion-dominated 60 mT and conical-mode-dominated 185 mT regions.The figure distinguishes training data from task-specific test results.Source: Figure S5 · p. 21
  • The Mackey–Glass signal has an approximate period of τ ≈22, so τ = 10 tests forecasting within its first quasi-period rather than at a full period.Forecasting error varies periodically with τ; the study consistently uses τ = 10 for its nontrivial forecast evaluation.Source: S5 Additional reservoir computing… · pp. 20–21
  • Reservoir metrics are evaluated using Mackey–Glass inputs at Hrange = 90 mT, after removing unresponsive channels by retaining the 30% with the largest output range.Nonlinearity assesses prediction of current FMR-channel readouts, while memory capacity assesses retention of past input information.Source: S5 Additional reservoir computing… · pp. 21, 23
  • Complexity is measured from the average effective rank of two 480×480 readout matrices, with higher CP indicating greater sensitivity to salient input features.The authors relate phase-tunable changes in MC, NL, and CP to possible reconfiguration of internal reservoir hyperparameters such as spectral radius.Source: S5 Additional reservoir computing… · p. 23

S7 Correlation analysis and additional data

The supplement analyzes relationships among forecasting and transformation errors and reservoir metrics using log-scaled MSE and Spearman rank correlation. The reported associations differ by task and among the reservoir metrics themselves.

S7 Correlation analysis and additional data

S8 Additional ac susceptibility data for Co8.5Zn8.5Mn3

AC susceptibility measurements provide phase-diagram evidence for Co8.5Zn8.5Mn3, with the imaginary component highlighting a skyrmion-phase region. The supplement maps that component over temperature and magnetic field.

S8 Additional ac susceptibility data for Co8.5Zn8.5Mn3

S9 Task-adaptable physical reservoir computing on FeGe

FeGe demonstrates phase-tunable task adaptation at 283 K, with skyrmion and conical reservoirs trading forecasting and transformation performance. Near-room-temperature tests in Co8.5Zn8.5Mn3 and FeGe show corresponding task-dependent phase preferences.

S9 Task-adaptable physical reservoir computing on FeGe

  • For FeGe, forecasting MSE is 2.5 × 10−2 for skyrmion-dominated Hc = 31 mT versus 3.4 × 10−2 for conical Hc = 66 mT; transformation MSE is 4.6 × 10−3 versus 2.6 × 10−3, respectively.The latter comparison favors the conical reservoir for the sine-to-triangle task.Source: S9 Task-adaptable physical reservoir… · p. 25
  • The FeGe tests use 5 mT field-cycling width and compare spectra at different Hc for Mackey–Glass forecasting and sine-to-triangle transformation.The evaluated forecasting target is MG(N + 5).Source: S9 Task-adaptable physical reservoir… · p. 25, Figure S9 · p. 26

S10 High-temperature task-adaptability

  • At 333 K in Co8.5Zn8.5Mn3 and 283 K in FeGe, forecasting performs best in the skyrmion phase, while transformation performance improves toward the ferromagnetic phase.For Co8.5Zn8.5Mn3, the stated transition example is Hc = 15 to 60 mT; FeGe shows the same trend.Source: S10 High-temperature task-adaptability · p. 25
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