The 70th Japan Society of Applied Physics Spring Meeting 2023
Highlighted Presentations Press Release
April 18, 2023

Reservoir computing utilizing spin waves: enhancement of computational performance through a practical
approach for on-chip devices

Demonstrating the potential of spin-wave-generating
devices for high-performance physical reservoir computing
Graduate School of Engineering, The Univ. of Tokyo1, International Research Center for Neurointelligence, The Univ. of Tokyo2,
Graduate School of Information Science and Technology, The Univ. of Tokyo 3
Ryosho Nakane1, Akira Hirose1, Gouhei Tanaka 1, 2, 3

Summary• In spin-wave-based reservoir computing developed by the research group, reservoir
output vectors with high dimensionality were successfully generated using a single
reservoir device on a chip by manipulating physical dynamics under different external
magnetic fields.
• Numerical experiments on a benchmark task of nonlinear time-series prediction
demonstrated that the computational performance of the spin-wave-based reservoir
computing system is comparable to that of other state-of-the-art physical reservoir
computing systems.
• This strongly suggests that spin-wave-based reservoir computing on a chip is promisingfor purpose-specific edge computing.
A research group led by Ryosho Nakane at the University of Tokyo established a methodology for improving
computational performance without increasing the number of device output terminals. They employed spin-wave-based
reservoir computing, which has been undergoing research and development, and performed a challenging benchmark
prediction task using multilevel input/output data in a physics-based numerical simulation assuming a feasible device
structure. Detailed analyses confirmed that device output signals in response to a time-series input signal change with anexternal magnetic field through the change in the spin dynamics. Reservoir output vectors were obtained by collecting
output signals under three external magnetic field conditions and used for reservoir computing. In a prediction task with a10th-order nonlinear auto-regressive moving average model (NARMA-10), it was found that the computational
performance of the proposed system is comparable to the best one reported for other state-of-the-art physical reservoir
computing systems. Thus, they succeeded in generating reservoir output vectors with high dimensionality using a single
reservoir device for computational performance improvement. Their achievement brings reservoir computing hardware,
which is currently the focus of accelerated research, one step closer to practical technology.

Details

Emerging Machine Learning Scheme: Reservoir Computing
Artificial intelligence (AI) has experienced remarkable development in recent years, while it issupported by large-scale computation through machine learning. In particular, deep learning is acomputational scheme that attempts to emulate the performance of the human brain withleveraging learning process (also referred to as training process). It is generally demonstratedusing mathematical models called artificial neural networks (ANNs) that are inspired by neuralcircuits of the human brain. Reservoir computing is currently attracting much attention as a uniquecomputational scheme in AI-related technology.
Reservoir computing uses an information “reservoir”, which is a distinctive feature. A typicalexample of reservoir computing model is the echo state network (ESN) that was originally derived
from widely-used ANNs called recurrent neural networks (RNNs). Like RNNs, the ESN has threeparts: an input part, a reservoir part (intermediate part), and a readout part. An important note isthat the intermediate part in the ESN does not have adjustable connection weights between
neurons, namely, those connection weights are fixed.
In typical RNN systems, all the connection weights, including those in the intermediate network,
are iteratively adjusted during the training phase to minimize the error between the system output
and the desired output. Hence, their physical implementations require high cost, e.g., hardware
assembly with rewritable memory storage for the weight values. Additionally, such RNN systems
have difficulties in adjusting the training algorithm and suppressing power consumption attributed
to enormous times changes in weight values. In ESN systems, on the other hand, connection
weights are adjusted only for ones between the intermediate and output parts. Because theoptimum weight values for a target task are determined by a simple training algorithm, ESN
systems have an advantage of requiring less computational process and hardware resource,
thereby potentially less power consumption than typical RNN systems.
Nevertheless, it does not straightforwardly mean that ESN systems for reservoir computing canfully replace RNN systems for deep learning. The superiority or inferiority of these twocomputational schemes depends mainly on priority specifications because of a trade-off between
versatility and training cost.
Deep learning allows subtle optimization thanks to a large number of adjustable connection
weights. Whereas it requires considerable hardware resource, it can have versatility. On the otherhand, reservoir computing has an extremely smaller number of adjustable connection weights justbetween the intermediate and output parts. Hence, it requires reasonable hardware resource but it
has less versatility. Those features are important to find advantages of reservoir computing. “Lessversatility does not mean reservoir computing is a poor-performance scheme. We are conducting
research for implementing reservoir computing in society, not as a general-purpose computing, but
as a purpose-specific and low-power-consumption computing with high performance, where
hardware resource is limited," says Ryosho Nakane of the Graduate School of Engineering at theUniversity of Tokyo.
To distinguish from reservoir computing on software, reservoir computing using physical dynamics(physical devices) in the reservoir part is called physical reservoir computing.
Physical reservoir computing has a technical merit that it can be implemented with a feasible onchip device. In addition, it can efficiently perform information processing of unstructured time-series

data, such as temporal sensing data. Hence, “We are working on a study to improve computational
performance in physical reservoir computing to develop infrastructure for advanced Internet-ofThings (IoT) society while taking its advantages,” says Nakane.

Tackling the trade-off problem between device feasibility and computational
performance
Dr. Nakane and his research group conducted physics-based simulations on a feasible on-chip
device. One of their goals was to establish a methodology that can improve computational
performance without losing robust feasibility of a device, and another was to achieve highcomputational performance in a challenging benchmark task using multilevel input/output data.
A successful reservoir computing requires "nonlinearity" (nonlinear input-output characteristics
through the reservoir), "high dimensionality" (high dimensionality in a reservoir output vector
extracted from diverse output signals), and "short term memory" (fading input information in outputsignals). To realize these three with a very simple device structure, the virtual node method has
been widely used, because it can conveniently generate a reservoir output vector throughsampling of a single time-series output signal. However, this method presumably has a limitation in
improving computational performance, from a technical perspective.
This research group has been developing spin-wave-based reservoir computing schemes, withfocusing on spin (magnetization) dynamics in a continuous magnetic film as a physical reservoir
because of its rich nonlinear physical phenomena. In this study, external magnetic fields withdifferent magnitudes were applied, aiming at achieving high dimensionality to enhance thecomputational performance.
“There is a general trade-off between device feasibility and computational performance,” says
Nakane. The ideal physical reservoir device for high computational performance has ”many-outputterminals (act as output nodes)”, to generate diverse output signals in response to a single timeseries input sequence. However, the greater the number of output nodes, the greater the numberof output terminals needed in a device. This reduces device feasibility.
The virtual node method is another root to avoid this trade-off. This method achieves “one-inputnode, many-output nodes” even using a “one-input terminal, one-output terminal” device, namely, itvirtually increases the number of output nodes through special processing. However, as the
sampling time of a time-series output signal is shortened to increase the number of output nodes,
the time-domain waveforms at output nodes tend to be similar with each other, which does not leadto higher dimensionality in a reservoir output vector. This can be a limiting factor in computationalperformance.
“We focused on the physical dynamics that determines the characteristics of a reservoir device. By
combining output signals generated under different physical conditions, we could obtain a reservoir
output vector with high dimensionality from a single reservoir device,” says Nakane.
In numerical experiments, external magnetic fields with three different magnitudes were applied totheir spin-wave-based device, and the corresponding output signals were obtained. Throughdetailed analyses, they successfully confirmed large variations in the spin dynamics using themagnetic field (Figure 1).

Highest computational performance among on-chip physical reservoir computing
Furthermore, Nakane and his colleagues evaluated whether a reservoir output vector obtained
from the collected output signals actually enhances the computational performance. According toNakane, anyone can guess that such procedure would increase the dimensionality, but the mostimportant aspect is whether the computational performance actually improves.
Nakane and his group performed spin-wave-based reservoir computing using a benchmarkprediction task with a 10th order nonlinear auto-regressive moving average model (NARMA-10)(*1). NARMA-10 is a mathematical model generating a time-series nonlinear signal that isgoverned by inputs and response outputs (reservoir output node states) in the past 10 steps. The
obtained computational performance (*2) is the highest among on-chip physical reservoir
computing, and moreover, it is comparable to those of the other state-of-the-art demonstrations(Figure 2).
“The results strongly suggest that spin-wave-based reservoir computing can approximate complex
dynamic behavior in the real world, such as those occur in nature and economics,” says Nakane.
Physical reservoir computing with an on-chip device has a high potential for practical applications
in purpose-specific edge computing because of their strengths in high adaptability through realtime training, low power consumption, and high performance for time-series data processing. They
are potentially useful to develop infrastructure for advanced IoT society in combination withsensors: highly-efficient traffic of information and telecommunication networks, sustainable social
infrastructure, and smart factories.
Annotation*1 NARMA(Nonlinear Autoregressive Moving Average): A nonlinear mathematical model that determines future
outputs based on an input and outputs in the recent past. It is useful for approximate modeling of the dynamics ofcomplex dynamical phenomena, such as ones occur in nature and economics. Furthermore, it has been widely used asa benchmark for performance evaluation in reservoir computing.
*2 Under the number of effective output nodes Ny = 360, normalized mean squared error NMSE = 0.042 in the prediction
task with a 10th order nonlinear auto-regressive moving average model (NARMA-10).

Figures

Figure 1 (Upper) Image of output waveforms under different magnetic fields. (Bottom) Characterization of the spin dynamics with an
external magnetic field (2-8 mT), where ferromagnetic resonant frequency and relaxation time were estimated to be 0.98−1.36 GHz
and 5−10 ns, respectively, under α = 0.1 condition.

Figure 2 (a) Top view of spin-wave-based device used for numerical experiments. (b) Six-valued input representation as the amplitudeof a 1-GHz carrier wave. (c) NARMA-10 signal in the testing phase: target signal (gray), predicted signal (blue).