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This research bridges high-energy physics and machine learning by applying effective field theory to analyze the denoising dynamics of convolutional diffusion models on MNIST. The study demonstrates that mutual information growth in these generative models aligns with predictions from Brownian motion, offering a novel theoretical framework for understanding locality biases in deep learning architectures.

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Information Spreading in Diffusion Models from Effective Field Theory

arXiv20 august 20261 min de cititArticolul și perspectiva sunt în engleză.

arXiv:2608.14308v1 Announce Type: cross Abstract: We study score-matching diffusion models with a convolutional architecture. We argue that the inductive bias of locality means that the machinery of effective field theory from physics can be usefully applied to describe the denoising dynamics. We apply this formalism first to a simple toy example which permits an analytical description, and thereafter to MNIST, and show that in both cases, the mutual information between two points grows in a manner predicted by a simple effective field theory of Brownian motion.

Abstract:We study score-matching diffusion models with a convolutional architecture. We argue that the inductive bias of locality means that the machinery of effective field theory from physics can be usefully applied to describe the denoising dynamics. We apply this formalism first to a simple toy example which permits an analytical description, and thereafter to MNIST, and show that in both cases, the mutual information between two points grows in a manner predicted by a simple effective field theory of Brownian motion.

This work was previously presented at the Scientific Methods for Understanding Deep Learning Workshop at ICLR 2026. 14 pages + appendices. Code available at: this https URL

High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); Machine Learning (cs.LG)

arXiv:2608.14308 [hep-th]

(or arXiv:2608.14308v1 [hep-th] for this version)

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