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Analog-electronic implementation of a harmonic oscillator recurrent neural network

Pedro Carvalho1,*, Bernd Ulmann2,†, Wolf Singer1,3,‡, and Felix Effenberger1,§

  • *Contact author: pedro.carvalho@esi-frankfurt.de
  • †Contact author: ulmann@anabrid.com
  • ‡Contact author: wolf.singer@brain.mpg.de
  • §Contact author: felix.effenberger@esi-frankfurt.de
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Phys. Rev. Applied 24, 064055 – Published 22 December, 2025

DOI: https://doi.org/10.1103/bg2h-5tt8

Abstract

Oscillatory recurrent networks, such as the harmonic oscillator recurrent network (HORN) model, offer advantages in parameter efficiency, learning speed, and robustness relative to traditional nonoscillating architectures. Yet, while many implementations of physical neural networks exploiting attractor dynamics have been studied, so far implementations of oscillatory models in analog-electronic hardware that utilize the networks’ transient dynamics are lacking. This study explores the feasibility of implementing HORNs in analog-electronic hardware while maintaining the computational performance of the digital counterpart. Using a digital-twin approach, we trained a four-node HORN in silico for sMNIST (sequential Modified National Institute of Standards and Technology) classification and transferred the trained parameters to an analog-electronic implementation. A set of custom error metrics indicated that the analog system is able to successfully replicate the dynamics of the digital model in most test cases. However, despite the overall well-matching dynamics, when using the readout layer of the digital model on the data generated by the analog system, we observed only 28.39% agreement with the predictions of the digital model. An analysis shows that this mismatch is due to a precision difference between the analog hardware and the floating-point representation exploited by the digital model to perform classification tasks. When the analog system was utilized as a reservoir with a retrained linear readout, its classification performance could be recovered to that of the digital twin, indicating preserved information content within the analog dynamics. This proof of concept establishes that analog-electronic circuits can effectively implement oscillatory neural networks for computation, providing a demonstration of energy-efficient analog systems that exploit brain-inspired transient dynamics for computation.

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Phys. Rev. Applied 24, 064055– Published 22 December, 2025
  • Received 22 August 2025
  • Accepted 24 November 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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