Breakdown of Local Denoising as Semantic Speciation

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.

9 pages main, 13 pages appendix, 4 figures. Comments very welcome

Machine Learning (cs.LG); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2609.38176 [cs.LG]

(or arXiv:2609.38176v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.38176 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.