Training a multilayer dynamical spintronic network with standard machine learning tools to perform time series classification

Aug 5, 2026

Time-series processing with low energy cost is essential for edge and sensing applications, yet software recurrent neural networks can be computationally expensive. This work implements a recurrent neural network in hardware using spintronic oscillators as dynamical neurons. Multi-layer simulations show that backpropagation through time together with standard machine learning tools can train the network. Using transient oscillator dynamics, the sequential digits classification task reaches 89.83±2.91% accuracy and matches an equivalent software network, with guidelines for oscillator time constants and hyper-parameters across input timescales.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages9

Reading Time23 min

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Introduction

Motivation for low-energy time-series processing

Dynamic systems and recurrent neural networks

Spintronic oscillators and limitations of prior work

Goal and contributions

Training a multilayer dynamical spintronic network with standard machine learning tools to perform time series classification arXiv :2408 .02835v3 [ cond-mat .dis-nn] 4 Mar 2025 Erwan Plouet, D´edalo Sanz-Hern´andez, Aymeric Vecchiola, Julie Grollier, and Frank Mizrahi ∗ Laboratoire Albert Fert, CNRS, Thales, Universit´e Paris-Saclay, 91767 Palaiseau, France (Dated: March 5, 2025) The ability to process time-series at low energy cost is critical for many applications. Recurrent neural network, which can perform such tasks, are computationally expensive when implementing in software on conventional computers. Here we propose to implement a recurrent neural network in hardware using spintronic oscillators as dynamical neurons. Using numerical simulations, we build a multi-layer network and demonstrate that we can use backpropagation through time (BPTT) and standard machine learning tools to train this network. Leveraging the transient dynamics of the spintronic oscillators, we solve the sequential digits classification task with 89 .83±2 .91 % accuracy, as good as the equivalent software network. We devise guidelines on how to choose the time constant of the oscillators as well as hyper-parameters of the network to adapt to different input time scales. I. INTRODUCTION The ability to process time-series (classification, prediction, generation etc.) is important for many applications from smart sensors in industrial maintenance to personal assistants and medical devices. Using the dynamics of a physical system, leveraging its non-linearity and memory for such processing has been widely explored with the development of recurrent neural networks, both from a purely mathematical perspective [1–4] as well as from a brain-inspired perspective with spiking recurrent neural networks [5–8] . Chen et al. have shown that neural networks based on ordinary differential equations (Neural-ODEs) can be seen as residual neural networks where the time dimension acts as depth thus providing computing power [9] . These findings highlight the potential of dynamical systems to implement deep neural networks. While implementing a recurrent neural network in software on a conventional computer requires computing the evolution of each neuron step by step, a physical network would naturally perform this computation. As there is an increasing demand for learning and processing on the edge, with strong footprint and energy cost constraints, building novel hardware that directly implements dynamic recurrent neural networks is an attractive path. This motivation has led to the realisation and training of recurrent neural networks with a wide variety of dynamic systems: analogue CMOS [10], photonic systems [11], acoustic resonators [12], mechanical oscillators [13] and wave systems [14] to cite a few. Spintronic oscillators are promising building blocks for the hardware implementation of neural networks, due to their non-linear high-speed dynamics as well as potential for miniaturization and CMOS integration [15, 16] . Time-series processing using the dynamics of spintronic oscillators has been repeatedly demonstrated experimentally in the context of reservoir computing, thus validating they have the required non-linearity and memory ∗ frank.mizrahi@cnrs-thales.fr properties [17–23] . However, reservoir computing is limited because only the output classifier is trained and the dynamics is fixed. Training of spintronic oscillators for time-series processing has been limited to single layer networks [24, 25] . Ross et al. have experimentally demonstrated a multilayer network of spintronic oscillators, but with a feedforward architecture dedicated to static tasks [26] . Rodrigues et al. have shown by numerical simulations how to train the transient dynamics of a single layer network of oscillators with optimal control theory, on a static task [27] . Here we simulate and train a multi-layer network of spintronic oscillators as neurons, using st

FAQs

Why use spintronic oscillators for time-series classification instead of software RNNs?

Software RNNs require step-by-step evolution of each neuron, making them computationally expensive. Spintronic oscillators naturally compute recurrent dynamics in hardware at potentially lower energy cost through their transient and nonlinear behavior.

How is the multilayer spintronic dynamical network trained?

The network is trained using backpropagation through time (BPTT) and standard machine learning tools, implemented with PyTorch, while cascading layers of spintronic neurons.

What performance is achieved on sequential digits classification, and how does it compare to software?

The sequential digits task is solved with 89.83±2.91% accuracy, reported as comparable to the equivalent software network.

Aug 5, 2026

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