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We show that Oscillator Ising Machines (OIMs) are prime candidates for use as neuromorphic machine learning processors with Equilibrium Propagation (EP) based on-chip learning. The inherent energy gradient descent dynamics of OIMs, combined…

Disordered Systems and Neural Networks · Physics 2025-08-19 Alex Gower

Ising machines, which are hardware implementations of the Ising model of coupled spins, have been influential in the development of unsupervised learning algorithms at the origins of Artificial Intelligence (AI). However, their application…

Neural and Evolutionary Computing · Computer Science 2023-05-31 Jérémie Laydevant , Danijela Markovic , Julie Grollier

Physical systems that naturally perform energy descent offer a direct route to accelerating machine learning. Oscillator Ising Machines (OIMs) exemplify this idea: their GHz-frequency dynamics mirror both the optimization of energy-based…

Machine Learning · Computer Science 2025-11-18 Alex Gower

Given the rapidly growing scale and resource requirements of machine learning applications, the idea of building more efficient learning machines much closer to the laws of physics is an attractive proposition. One central question for…

Emerging Technologies · Computer Science 2024-10-07 Qingshan Wang , Clara C. Wanjura , Florian Marquardt

Finding spike-based learning algorithms that can be implemented within the local constraints of neuromorphic systems, while achieving high accuracy, remains a formidable challenge. Equilibrium Propagation is a promising alternative to…

Neural and Evolutionary Computing · Computer Science 2021-02-18 Erwann Martin , Maxence Ernoult , Jérémie Laydevant , Shuai Li , Damien Querlioz , Teodora Petrisor , Julie Grollier

Computing gradients of a cost function is central to design-based optimization and machine learning algorithms. Equilibrium propagation provides an exact method to compute gradients in hardware by exploiting the inherent physical laws. The…

Disordered Systems and Neural Networks · Physics 2025-08-11 Marc Berneman , Daniel Hexner

Coupled oscillator-based networks are an attractive approach for implementing hardware neural networks based on emerging nanotechnologies. However, the readout of the state of a coupled oscillator network is a difficult challenge in…

Emerging Technologies · Computer Science 2016-07-08 Damir Vodenicarevic , Nicolas Locatelli , Julie Grollier , Damien Querlioz

Machine learning has achieved remarkable advancements but at the cost of significant computational resources. This has created an urgent need for a novel and energy-efficient computational fabric and corresponding algorithms. CMOS…

Computer Vision and Pattern Recognition · Computer Science 2025-07-18 Wenxiao Cai , Zongru Li , Iris Wang , Yu-Neng Wang , Thomas H. Lee

Equilibrium propagation has been proposed as a biologically plausible alternative to the backpropagation algorithm. The local nature of gradient computations, combined with the use of convergent RNNs to reach equilibrium states, make this…

Neural and Evolutionary Computing · Computer Science 2026-03-19 Sankar Vinayak Elayedam , Gopalakrishnan Srinivasan

We introduce a principled method to train end-to-end analog neural networks by stochastic gradient descent. In these analog neural networks, the weights to be adjusted are implemented by the conductances of programmable resistive devices…

Neural and Evolutionary Computing · Computer Science 2020-06-11 Jack Kendall , Ross Pantone , Kalpana Manickavasagam , Yoshua Bengio , Benjamin Scellier

As deep learning applications continue to deploy increasingly large artificial neural networks, the associated high energy demands are creating a need for alternative neuromorphic approaches. Optics and photonics are particularly compelling…

Optics · Physics 2025-08-19 Nicola Dal Cin , Florian Marquardt , Clara C. Wanjura

A non-equilibrium open-dissipative neural network, such as a coherent Ising machine based on mutually coupled optical parametric oscillators, has been proposed and demonstrated as a novel computing machine for hard combinatorial…

Equilibrium propagation (EP) is an alternative to backpropagation (BP) that allows the training of deep neural networks with local learning rules. It thus provides a compelling framework for training neuromorphic systems and understanding…

Machine Learning · Computer Science 2022-09-02 Axel Laborieux , Friedemann Zenke

Synchronization is ubiquitous in nature, which is mathematically described by coupled oscillators. Synchronization strongly depends on the interaction network, and the network plays a crucial role in controlling the dynamics. To understand…

Adaptation and Self-Organizing Systems · Physics 2025-08-19 Akari Matsuki , Hiroshi Kori , Ryota Kobayashi

The current study uses a novel method of multilevel neurons and high order synchronization effects described by a family of special metrics, for pattern recognition in an oscillatory neural network (ONN). The output oscillator (neuron) of…

Emerging Technologies · Computer Science 2019-08-26 Andrei Velichko , Maksim Belyaev , Petr Boriskov

Pattern classification architectures leveraging the physics of coupled nano-oscillators have been demonstrated as promising alternative computing approaches, but lack effective learning algorithms. In this work, we propose a nano-oscillator…

Applied Physics · Physics 2018-10-17 Damir Vodenicarevic , Nicolas Locatelli , Julie Grollier , Damien Querlioz

When training neural networks with simulated quantization, we observe that quantized weights can, rather unexpectedly, oscillate between two grid-points. The importance of this effect and its impact on quantization-aware training (QAT) are…

Machine Learning · Computer Science 2022-06-30 Markus Nagel , Marios Fournarakis , Yelysei Bondarenko , Tijmen Blankevoort

We study the propagation of a harmonic perturbation of small amplitude on a network of coupled identical phase oscillators prepared in a state of full synchronization. The perturbation is externally applied to a single oscillator, and is…

Statistical Mechanics · Physics 2009-11-10 Damian H. Zanette

We study associative memory of an oscillator neural network with distributed native frequencies. The model is based on the use of the Hebb learning rule with random patterns ($\xi_i^{\mu}=\pm 1$), and the distribution function of native…

Disordered Systems and Neural Networks · Physics 2009-10-31 Michiko Yamana , Masatoshi Shiino , Masahiko Yoshioka

We introduce Equilibrium Propagation, a learning framework for energy-based models. It involves only one kind of neural computation, performed in both the first phase (when the prediction is made) and the second phase of training (after the…

Machine Learning · Computer Science 2017-03-30 Benjamin Scellier , Yoshua Bengio
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