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[2602.13418] Text Has Curvature
Summary
The paper 'Text Has Curvature' explores the concept of intrinsic curvature in language, proposing a new measurement called Texture to analyze and utilize this curvature in natural language processing tasks.
Why It Matters
Understanding the intrinsic curvature of text can enhance natural language processing models by providing new insights into semantic relationships and improving tasks like context inference and generation. This research could lead to more effective AI applications in language understanding.
Key Takeaways
- Language exhibits intrinsic curvature, which can be measured and defined.
- The proposed Texture signal reconciles context beliefs to yield actionable insights.
- Curvature can enhance long-context inference and retrieval-augmented generation tasks.
Computer Science > Machine Learning arXiv:2602.13418 (cs) [Submitted on 13 Feb 2026] Title:Text Has Curvature Authors:Karish Grover, Hanqing Zeng, Yinglong Xia, Christos Faloutsos, Geoffrey J. Gordon View a PDF of the paper titled Text Has Curvature, by Karish Grover and 4 other authors View PDF HTML (experimental) Abstract:Does text have an intrinsic curvature? Language is increasingly modeled in curved geometries - hyperbolic spaces for hierarchy, mixed-curvature manifolds for compositional structure - yet a basic scientific question remains unresolved: what does curvature mean for text itself, in a way that is native to language rather than an artifact of the embedding space we choose? We argue that text does indeed have curvature, and show how to detect it, define it, and use it. To this end, we propose Texture, a text-native, word-level discrete curvature signal, and make three contributions. (a) Existence: We provide empirical and theoretical certificates that semantic inference in natural corpora is non-flat, i.e. language has inherent curvature. (b) Definition: We define Texture by reconciling left- and right-context beliefs around a masked word through a Schrodinger bridge, yielding a curvature field that is positive where context focuses meaning and negative where it fans out into competing continuations. (c) Utility: Texture is actionable: it serves as a general-purpose measurement and control primitive enabling geometry without geometric training; we instantiat...
