Breakdown of Local Denoising as Semantic Speciation

2026-09-29

AI Summary

This study addresses the unclear concurrent mechanisms and intrinsic relationship between semantic anchoring and non-local temporal windows in generative models. Based on the spatial distribution of semantic information, it proposes a “common cause” hypothesis. By leveraging statistical physics phase transition theory, Gaussian mixture model verification, and correlation analysis, this work defines phase transition conditions under growing system scales. It demonstrates that non-local windows are inherently embedded within anchoring windows, revealing their co-occurrence conditions and unifying these dual perspectives. Furthermore, it elucidates the conditions under which semantic labels explain long-range token correlations and confirms the phenomenon whereby the window contracts to a singular limiting time.

Abstract

The dynamics of generative models exhibit two apparently distinct temporal windows: a speciation window, in which a sample commits to a semantic class, and a nonlocality window, in which local context windows become insufficient for generation. Motivated by evidence of their near-concurrence in a variety of frontier models, we investigate their relationship through the spatial distribution of semantic information. Under a "common cause" hypothesis, we prove that the nonlocality window must lie in the speciation window. This hypothesis postulates that semantic labels explain a fraction of the correlations between distant tokens, a condition that is natural for many real datasets. We further give conditions under which both windows shrink to a single limiting time as system size grows, defining a "phase transition", and verify this behavior analytically in Gaussian mixtures. Together, these results identify conditions under which semantic information explains the concurrence of speciation and nonlocality, connecting two complementary perspectives on the emergence of semantic structure in generative modeling.

Problem

• generative models
• semantic speciation
• nonlocality window
• diffusion dynamics
• phase transition

Innovation

• Semantic Speciation
• Nonlocality Window
• Phase Transition
• Generative Models
• Gaussian Mixtures