Related papers: Training Coupled Phase Oscillators as a Neuromorph…
Oscillator networks represent a promising technology for unconventional computing and artificial intelligence. Thus far, these systems have primarily been demonstrated in small-scale implementations, such as Ising Machines for solving…
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…
We propose a method for training dynamical systems governed by Lagrangian mechanics using Equilibrium Propagation. Our approach extends Equilibrium Propagation - initially developed for energy-based models - to dynamical trajectories by…
The increasing resource demands of artificial neural networks have prompted the exploration of novel platforms better suited for machine learning. In this context, phase oscillators represent a promising candidate due to their intrinsic…
The widespread adoption of machine learning and artificial intelligence in all branches of science and technology has created a need for energy-efficient, alternative hardware platforms. While such neuromorphic approaches have been proposed…
The activity of collections of synchronizing neurons can be represented by weakly coupled nonlinear phase oscillators satisfying Kuramoto's equations. In this article, we build such neural-oscillator models, partly based on…
Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak…
A generalized Kuramoto model of coupled phase oscillators with slowly varying coupling matrix is studied. The dynamics of the coupling coefficients is driven by the phase difference of pairs of oscillators in such a way that the coupling…
Neural coupled oscillators are a useful building block in numerous models and applications. They were analyzed extensively in theoretical studies and more recently, in biologically realistic simulations of spiking neural networks. The…
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…
By means of numerical analysis conducted with the aid of the computer, the collective synchronization of coupled phase oscillators in the Kuramoto model in the connected regime of random networks of various sizes is studied. The oscillators…
We consider the inertial Kuramoto model of $N$ globally coupled oscillators characterized by both their phase and angular velocity, in which there is a time delay in the interaction between the oscillators. Besides the academic interest, we…
Backpropagation learning algorithm, the workhorse of modern artificial intelligence, is notoriously difficult to implement in physical neural networks. Equilibrium Propagation (EP) is an alternative with comparable efficiency and strong…
We consider a long-range model of coupled phase-only oscillators subject to a local potential and evolving in presence of thermal noise. The model is a non-trivial generalization of the celebrated Kuramoto model of collective…
This paper presents a nonlinear control framework for steering networks of coupled oscillators toward desired phase-locked configurations. Inspired by brain dynamics, where structured phase differences support cognitive functions, the focus…
We prove that in a coupled Kuramoto oscillator network at stable equilibrium, the physical phase displacement under weak output nudging is the gradient of the loss with respect to natural frequencies, with equality as the nudging strength…
The biological plausibility of the backpropagation algorithm has long been doubted by neuroscientists. Two major reasons are that neurons would need to send two different types of signal in the forward and backward phases, and that pairs of…
Kuramoto networks constitute a paradigmatic model for the investigation of collective behavior in networked systems. Despite many advances in recent years, many open questions remain on the solutions for systems composed of coupled Kuramoto…
We present a collective coordinate approach to describe coupled phase oscillators. We apply the method to study synchronisation in a Kuramoto model. In our approach an N-dimensional Kuramoto model is reduced to an n-dimensional ordinary…
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…