# Training Coupled Phase Oscillators as a Neuromorphic Platform using Equilibrium Propagation

arXiv: https://arxiv.org/abs/2402.08579 · HTML: https://mlsanity.com/paper/2402.08579/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2024.

## Built on by (most cited first, 16 of 16)

- [Training of Physical Neural Networks](https://mlsanity.com/paper/2406.03372/) (2024)
- [Quantum Equilibrium Propagation: Gradient-Descent Training of Quantum Systems](https://mlsanity.com/paper/2406.00879/) (2024)
- [Quantum Equilibrium Propagation for efficient training of quantum systems based on Onsager reciprocity](https://mlsanity.com/paper/2406.06482/) (2024)
- [Training all-mechanical neural networks for task learning through in situ backpropagation](https://mlsanity.com/paper/2404.15471/) (2024)
- [Local Learning Rules for Out-of-Equilibrium Physical Generative Models](https://mlsanity.com/paper/2506.19136/) (2025)
- [Learning at the Speed of Physics: Equilibrium Propagation on Oscillator Ising Machines](https://mlsanity.com/paper/2510.12934/) (2025)
- [Near-Equilibrium Propagation training in nonlinear wave systems](https://mlsanity.com/paper/2510.16084/) (2025)
- [Equilibrium Propagation for Non-Conservative Systems](https://mlsanity.com/paper/2602.03670/) (2026)
- [Training a Predictive Coding Network on ImageNet using Equilibrium Propagation](https://mlsanity.com/paper/2606.03584/) (2026)
- [Higher-Order Kuramoto Oscillator Network for Dense Associative Memory](https://mlsanity.com/paper/2507.21984/) (2025)
- [Energy-Based Dynamical Models for Neurocomputation, Learning, and Optimization](https://mlsanity.com/paper/2604.05042/) (2026)
- [Laser interferometry as a robust neuromorphic platform for machine learning](https://mlsanity.com/paper/2601.18047/) (2026)
- [The Phase Is the Gradient: Equilibrium Propagation for Frequency Learning in Kuramoto Networks](https://mlsanity.com/paper/2604.10272/) (2026)
- [Hybridizing Equilibrium Propagation with Ising Machines for Efficient Energy-Based Learning](https://mlsanity.com/paper/2606.09112/) (2026)
- [Optimizing Energy-based Neural Network Training with Coherent Ising Machine](https://mlsanity.com/paper/2606.09117/) (2026)
- [Optical Implementation of Equilibrium Propagation Using Spatial Photonic Ising Machines](https://mlsanity.com/paper/2606.13454/) (2026)

## Abstract (arXiv)

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 identifying promising candidates for such neuromorphic platforms is whether not only inference but also training can exploit the physical dynamics. In this work, we show that it is possible to successfully train a system of coupled phase oscillators - one of the most widely investigated nonlinear dynamical systems with a multitude of physical implementations, comprising laser arrays, coupled mechanical limit cycles, superfluids, and exciton-polaritons. To this end, we apply the approach of equilibrium propagation, which permits to extract training gradients via a physical realization of backpropagation, based only on local interactions. The complex energy landscape of the XY/ Kuramoto model leads to multistability, and we show how to address this challenge. Our study identifies coupled phase oscillators as a new general-purpose neuromorphic platform and opens the door towards future experimental implementations.