Edge-of-chaos state achieved by reservoir computing using spin-wave interference

Maki Nishimura^a^,^b, Wataru Namiki^a, Daiki Nishioka^a, Kazuya Terabe^a, Takashi Tsuchiya^a^,^b

^aResearch Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS)

^bTokyo University of Science

Proceedings of Neuronics Conference 2025 (Neuronics25)

Tsukuba, Japan, 2025 June 17th - 20th

Organizers: Takashi Tsuchiya, Chu-Chen Chueh, Sabina Spiga and Jung-Yao Chen

Poster, Maki Nishimura, 043
Publication date: 15th April 2025

The "edge of chaos" refers to the state near the boundary between order and chaos in dynamical systems. It is known that in certain types of information processing using nonlinear dynamical systems, performance peaks at the edge of chaos. For instance, theoretical calculations in physical reservoir computing (PRC) using nanowire networks have shown that the accuracy of nonlinear waveform transformation tasks is maximized at the edge of chaos [1]. Similarly, ion-gating reservoirs demonstrating high PRC performance exhibit characteristics of the edge of chaos [2]. These findings suggest that the edge of chaos is a key factor for achieving high PRC performance. Recently, based on the theoretical framework developed by Nakane et al. [3], we experimentally demonstrated high-performance PRC utilizing multi-detected spin wave interference [4]. However, although clear chaotic behaviors and the dependence on experimental parameters were observed, no edge-of-chaos state was identified, and the correlation between nonlinearity (chaos/order) and computational performance remained unclear.In this study, we controlled nonlinearity through various experimental parameters of the spin wave interference-type PRC to explore the edge-of-chaos state. We used a device with ten antennas fabricated on the surface of a Y₃Fe₅O₁₂ (YIG) single crystal. Spin wave interference was realized by using two antennas as inputs, and the system’s nonlinearity was evaluated using the Jacobian matrix estimation method. Specifically, by varying the magnetic field applied for spin wave excitation and the interval between input voltage pulses while inputting a triangular wave, we calculated the maximum Lyapunov exponent (λmax), a key indicator of chaos in the system. While positive λmax values indicating chaos were observed under many conditions, only at pulse intervals of 5 ns ~ 15 ns, λmax exhibited a very small negative value, indicating the edge-of-chaos state. We subsequently evaluated the associated computational performance using a nonlinear waveform transformation task that measures the accuracy of transformations to different waveforms. In reservoir computing, it is known that such accuracy is maximized at the edge of chaos. For all four types of nonlinear waveform transformation tasks (sine wave, square wave, π/2 phase-shifted wave, and frequency-doubled wave), computational performance (transformation accuracy) peaked as the system approached the edge of chaos from the chaotic side. This suggests that the edge of chaos is also favorable for nonlinear waveform transformation tasks using spin-wave interference-type PRC.

References:

[1] J. Hochstetter, R. Zhu, A. Loeffler, A. Diaz-Alvarez, T. Nakayama, Z. Kuncic, Avalanches and edge-of-chaos learning in neuromorphic nanowire networks. Nat. Commun.12,4008 (2021).

[2] D. Nishioka, T. Tsuchiya, W. Namiki, M. Takayanagi, M. Imura, Y. Koide, K. Terabe, Edge-of-chaos learning achieved by ion-electron–coupled dynamics in an ion-gating reservoir. Sci. Adv. 8, eade1156 (2022)

[3] R. Nakane, G. Tanaka, A. Hirose, Reservoir Computing with Spin Waves Excited in a Garnet Film. IEEE Access. 6, 4462 (2018).

[4] W. Namiki, D. Nishioka, Y. Yamaguchi, T. Tsuchiya, T. Higuchi, K. Terabe, Experimental Demonstration of High-Performance Physical Reservoir Computing with Nonlinear Interfered Spin Wave Multidetection. Adv. Intell. Syst. 5, 2300228 (2023)

Acknowledgements:

This work was supported by JSPS International Joint Research Program (JRP-LEAD with UKRI). Number: 20241712.

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