Learning at the Speed of Physics: Equilibrium Propagation on Oscillator Ising Machines
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Abstract (arXiv)
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 models (EBMs) and gradient descent on loss landscapes, while intrinsic noise corresponds to Langevin dynamics - supporting sampling as well as optimization. Equilibrium Propagation (EP) unifies these processes into descent on a single total energy landscape, enabling local learning rules without global backpropagation. We show that EP on OIMs achieves competitive accuracy (~ 97.2 ± 0.1 % on MNIST, ~ 88.0 ± 0.1 % on Fashion-MNIST), while maintaining robustness under realistic hardware constraints such as parameter quantization and phase noise. These results establish OIMs as a fast, energy-efficient substrate for neuromorphic learning, and suggest that EBMs - often bottlenecked by conventional processors - may find practical realization on physical hardware whose dynamics directly perform their optimization.
Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 10 of its 18 references that are in the map. First posted on arXiv 14 Oct 2025.
Builds on
10 of 18 references.
References · 10
- 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,349
- 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,611
- 2023Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecturecited by 1,039
- 2016Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagationcited by 259
- 2020Temporal Spike Sequence Learning via Backpropagation for Deep Spiking Neural Networkscited by 100
- 2020Scaling Equilibrium Propagation to Deep ConvNets by Drastically Reducing its Gradient Estimator Biascited by 64
- 2023Training an Ising Machine with Equilibrium Propagationcited by 29
- 2023Training Deep Boltzmann Networks with Sparse Ising Machinescited by 24
- 2024Training Coupled Phase Oscillators as a Neuromorphic Platform using Equilibrium Propagationcited by 16
- 2023A Note on Analyzing the Stability of Oscillator Ising Machinescited by 2
Built on by
Citing papers per year: 2026: 3.
3 papers.
- 2026The Phase Is the Gradient: Equilibrium Propagation for Frequency Learning in Kuramoto Networkscited by 0
- 2026Hybridizing Equilibrium Propagation with Ising Machines for Efficient Energy-Based Learningcited by 0
- 2026Graph Coloring Approach to Solving Sudoku with Oscillatory Neural Networkscited by 0
- 2026Graph Coloring Approach to Solving Sudoku with Oscillatory Neural Networks17 Jul 2026
- 2026Hybridizing Equilibrium Propagation with Ising Machines for Efficient Energy-Based Learning8 Jun 2026
- 2026The Phase Is the Gradient: Equilibrium Propagation for Frequency Learning in Kuramoto Networks11 Apr 2026
Similar, not cited
Close in wording, no citation either way
- 2021Training Dynamical Binary Neural Networks with Equilibrium Propagation
- 2026Boltzmann Reinforcement Learning for Noise resilience in Analog Ising Machines
- 2023The Copycat Perceptron: Smashing Barriers Through Collective Learning
- 2025Local Learning Rules for Out-of-Equilibrium Physical Generative Models
- 2022Frequency propagation: Multi-mechanism learning in nonlinear physical networks
- 2026Ultrafast On-Chip Online Learning via Spline Locality in Kolmogorov-Arnold Networks
- 2026Symmetric Equilibrium Propagation for Thermodynamic Diffusion Training
- 2026Bridging Control, Inference, Transport, and Thermodynamics: From Theory to Applications in Learning