Local Learning Rules for Out-of-Equilibrium Physical Generative Models

2025-06-23

AI Summary

This work addresses the challenge of implementing online training for score-based generative models (SGMs) on physical hardware. Methodologically, it introduces a local learning framework grounded in nonequilibrium driving protocols: a network of driven, nonlinear overdamped oscillators is coupled to a thermal bath to enable physically realizable sampling; a local learning rule is designed that estimates gradients solely from measurements of local forces or dynamical responses, thereby circumventing global backpropagation. The key contribution lies in embedding SGM training within a nonequilibrium statistical physics framework, enabling hardware-efficient, online optimization. Experiments demonstrate efficacy in sampling from a 2D Gaussian mixture distribution and generating MNIST “0/1” digits using a 10×10 oscillator network. This approach establishes a novel paradigm for physics-inspired generative modeling, bridging statistical learning with analog physical implementation.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

We show that the out-of-equilibrium driving protocol of score-based generative models (SGMs) can be learned via a local learning rule. The gradient with respect to the parameters of the driving protocol are computed directly from force measurements or from observed system dynamics. As a demonstration, we implement an SGM in a network of driven, nonlinear, overdamped oscillators coupled to a thermal bath. We first apply it to the problem of sampling from a mixture of two Gaussians in 2D. Finally, we train a network of 10x10 oscillators to sample images of 0s and 1s from the MNIST dataset.

Problem

• Learning out-of-equilibrium driving protocols for SGMs
• Computing gradients from force or system dynamics
• Training oscillators to sample MNIST images

Innovation

• Local learning rules for SGMs
• Gradient computation from force measurements
• SGM implementation in nonlinear oscillators