# Text Has Curvature

arXiv: https://arxiv.org/abs/2602.13418 · HTML: https://mlsanity.com/paper/2602.13418/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 38 references that are in the map.
- First posted on arXiv 13 Feb 2026.

## Builds on (most cited first, 20 of 20)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [A Dataset of Information-Seeking Questions and Answers Anchored in Research Papers](https://mlsanity.com/paper/2105.03011/) (2021)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [QMSum: A New Benchmark for Query-based Multi-domain Meeting Summarization](https://mlsanity.com/paper/2104.05938/) (2021)
- [Efficient Attentions for Long Document Summarization](https://mlsanity.com/paper/2104.02112/) (2021)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [Compressing Context to Enhance Inference Efficiency of Large Language Models](https://mlsanity.com/paper/2310.06201/) (2023)
- [Retrieval Augmented Generation or Long-Context LLMs? A Comprehensive Study and Hybrid Approach](https://mlsanity.com/paper/2407.16833/) (2024)
- [Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometries](https://mlsanity.com/paper/2504.08896/) (2025)
- [Spectro-Riemannian Graph Neural Networks](https://mlsanity.com/paper/2502.00401/) (2025)

## Built on by (most cited first, 2 of 2)

- [Intrinsic Associative Memory on Riemannian Manifolds: Curvature, Capacity, and Emergent Modes](https://mlsanity.com/paper/2609.35948/) (2026)
- [Geometry-Conditioned Fixed-Scaffold Encoders for Time-Warp Robust Sequence Retrieval](https://mlsanity.com/paper/2609.36809/) (2026)

## Abstract (arXiv)

Does natural language 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. (b) Definition: We define Texture as a signed two-axis curvature of the word-in-context belief field - the differential of reconciliation between prefix and suffix - measuring, via a debiased Schr"odinger transport divergence, whether adding context from one side contracts the semantic effect of context from the other side (focus, positive) or expands it into competing continuations (fan-out, negative). (c) Utility: Texture is actionable: it serves as a general-purpose measurement and control primitive enabling geometry without geometric training; we instantiate it on two representative tasks, improving long-context inference through curvature-guided compression and retrieval-augmented generation through curvature-guided routing. Together, our results establish a text-native curvature paradigm, making Texture practically useful.