Probing the Latent Hierarchical Structure of Data via Diffusion Models

2024-10-17

arXiv.org

AI Summary

This work addresses the problem of detecting and quantifying latent hierarchical structures—and their corresponding interpretable latent variables—in high-dimensional data (e.g., text and images). We propose a diffusion-based hierarchical probing framework that leverages the forward noising and backward denoising processes of diffusion models. Our method identifies critical noise-strength thresholds—phase transitions—that empirically align with divergences in hierarchical scale. We establish the first experimental paradigm enabling quantitative evaluation of both data hierarchy and latent variable interpretability. Integrating state-of-the-art models (e.g., Stable Diffusion and LLaMA-based token diffusion), our approach combines forward-backward probing, multi-scale noise analysis, and associative block dynamical modeling to yield observable, measurable, and reproducible characterizations of hierarchical structure on real-world data. This provides a novel perspective for interpreting internal representations in generative models.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Web Mining and Content Analysis: Large pretrained models with web data

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. In this work, we show that forward-backward experiments in diffusion-based models, where data is noised and then denoised to generate new samples, are a promising tool to probe the latent structure of data. 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 show how latent variable changes manifest in the data and establish how to measure these effects in real data using diffusion models.

Problem

• Quantify hierarchical structure in high-dimensional data
• Access latent variables underlying data structure
• Measure latent variable changes using diffusion models

Innovation

• Uses diffusion models for data structure analysis
• Probes latent variables via forward-backward experiments
• Measures hierarchical data changes in diffusion processes