arXiv Machine Learning September 10, 2026 By Karish Grover, Hanqing Zeng, Yinglong Xia, Christos Faloutsos, Geoffrey J. Gordon

Text Has Curvature

Read the original on arXiv Machine Learning →

The paper investigates whether natural language text possesses an intrinsic curvature, proposing a new metric called Texture that captures word-level discrete curvature. Texture is defined as a signed two-axis curvature of the word-in-context belief field, measuring how context from one side contracts or expands the semantic effect of context from the other side. The authors provide empirical and theoretical evidence of non-flat semantic inference, define Texture formally, and demonstrate its practical utility in improving long-context inference and retrieval-augmented generation.

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