Probing the Latent Hierarchical Structure of Data via Diffusion Models
Keywords: data structure, hierarchical compositionality, diffusion models, statistical physics, phase transition
TL;DR: A hierarchical structure in the data induces a diverging correlation length at a phase transition in diffusion models, which is observed also in text and images.
Abstract: High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce. Likewise, accessing the latent variables underlying such a data structure remains a challenge. Forward-backward experiments in diffusion-based models, where a datum is noised and then denoised, are a promising tool to achieve these goals. We predict in simple hierarchical models that, in this process, changes in data occur by correlated chunks, with a length scale that diverges at a noise level where a phase transition is known to take place. Remarkably, we confirm this prediction in both text and image datasets using state-of-the-art diffusion models. Our results suggest that forward-backward experiments are informative on the nature of latent variables, and that the effect of changing deeper ones is revealed near the transition.
Primary Area: other topics in machine learning (i.e., none of the above)
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Submission Number: 11698
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