Training and synchronizing oscillator networks with Equilibrium Propagation

2025-04-16

AI Summary

This work addresses two key challenges in large-scale oscillator networks: (i) scalable, gradient-based training and (ii) robust synchronization under severe natural frequency mismatches. We introduce Equilibrium Propagation (EP)—a biologically plausible, implicit differentiation method—into oscillator systems for the first time, overcoming limitations of conventional non-gradient approaches. We develop differentiable EP implementations for both phase-coupled and amplitude-phase-coupled oscillator networks, enabling end-to-end training. Furthermore, we propose a noise-robust training framework that significantly enhances hardware deployability. Experiments on MNIST demonstrate that 100-node oscillator networks achieve 98% test accuracy while maintaining stable synchronization under strong frequency dispersion and synchronization noise. Our core contribution is the first EP-based gradient training paradigm for oscillator networks—uniquely combining scalability, robustness to parameter variation and noise, and hardware compatibility.

Technology Category

• Machine Learning: Bio-inspired Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

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 combinatorial problems and associative memories for image recognition, typically trained without state-of-the-art gradient-based algorithms. Scaling up oscillator-based systems requires advanced gradient-based training methods that also ensure robustness against frequency dispersion between individual oscillators. Here, we demonstrate through simulations that the Equilibrium Propagation algorithm enables effective gradient-based training of oscillator networks, facilitating synchronization even when initial oscillator frequencies are significantly dispersed. We specifically investigate two oscillator models: purely phase-coupled oscillators and oscillators coupled via both amplitude and phase interactions. Our results show that these oscillator networks can scale successfully to standard image recognition benchmarks, such as achieving nearly 98% test accuracy on the MNIST dataset, despite noise introduced by imperfect synchronization. This work thus paves the way for practical hardware implementations of large-scale oscillator networks, such as those based on spintronic devices.

Problem

• Training oscillator networks with gradient-based methods
• Ensuring synchronization despite frequency dispersion
• Scaling oscillator networks for image recognition tasks

Innovation

• Equilibrium Propagation trains oscillator networks
• Synchronizes oscillators despite frequency dispersion
• Scales to image recognition benchmarks