Hybridizing Equilibrium Propagation with Ising Machines for Efficient Energy-Based Learning

2026-06-08

AI Summary

This work addresses the high energy consumption of conventional GPU-based deep neural network training and the limitations of existing equilibrium propagation methods, which often suffer from slow convergence and susceptibility to local minima. Inspired by Ising machine dynamics, the authors propose a novel training paradigm that replaces the traditional dissipative Hopfield relaxation process with extended-phase-space dynamics incorporating conjugate variables. This approach preserves local two-phase learning rules while altering the physical trajectory by which neuronal states approach equilibrium. The method effectively lowers energy barriers, accelerates convergence, and enhances noise robustness. Experimental results on MNIST, Fashion-MNIST, and CIFAR-10 demonstrate performance comparable to backpropagation, with significantly improved training efficiency and stability.

Abstract

The rapid evolution of artificial intelligence has led to substantial advances in deep neural networks. Nonetheless, conventional GPU-based training remains highly energy-demanding, motivating the exploration of physical dynamics and compatible energy-based learning schemes, such as equilibrium propagation (EP). EP-based training, however, frequently suffers from convergence to local minima due to phase-space contraction. Here we introduce an Ising-dynamics-inspired equilibrium-propagation framework in which dissipative Hopfield relaxation is replaced by an extended phase-space dynamics with conjugate variables. The resulting training paradigm keeps the local two-phase learning rule of EP while changing the physical route by which neural states reach equilibrium. We show that this dynamics lowers effective energy barriers, accelerates convergence, improves noise robustness, and trains deep convolutional Hopfield networks on MNIST, FashionMNIST, and CIFAR-10 with performance comparable to backpropagation.

Problem

• energy-based learning
• equilibrium propagation
• local minima
• phase-space contraction
• Ising machines

Innovation

• Equilibrium Propagation
• Ising Machines
• Energy-Based Learning
• Extended Phase-Space Dynamics
• Hopfield Networks