Hybridizing Equilibrium Propagation with Ising Machines for Efficient Energy-Based Learning
2026-06-08 • Machine Learning
Machine LearningArtificial Intelligence
AI summaryⓘ
The authors explore a new way to train deep neural networks inspired by the Ising model, aiming to reduce the energy needed compared to traditional GPU training. They improve an existing method called equilibrium propagation by changing how the network reaches a stable state, making the training faster and more reliable. Their approach performs well on common image recognition tasks, matching results from standard backpropagation methods. This work shows a promising alternative to energy-heavy AI training techniques.
equilibrium propagationIsing modeldeep neural networksHopfield networksphase-space dynamicsenergy-based learningconvolutional networksMNIST datasetbackpropagationenergy barriers
Authors
Chen-Rui Fan, Bo Lu, Xing-Yu Wu, Tie-Jun Wang, Chuan Wang
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.