Unveiling Topological Structures from Language: A Survey of Topological Data Analysis Applications in NLP

TL;DR

This survey maps the landscape of Topological Data Analysis (TDA) in NLP, compiling ~100 papers and organizing them into theoretical and non-theoretical strands. It explains the core TDA tools—Persistent Homology and Mapper—and examines how they are applied to semantic/syntactic spaces, topic evolution, and the topology of word representations. The work highlights case studies, taxonomies, and practical considerations (e.g., representations, tasks, and modalities), while outlining open problems such as interpretability, multilingual applications, and robustness, and it sketches directions like LLM-assisted TDA coding and Topological Deep Learning. The findings suggest TDA can complement traditional NLP features by capturing global, multi-scale structure, but wider adoption requires reducing entry barriers and improving interpretability and efficiency.

Abstract

The surge of data available on the Internet has led to the adoption of various computational methods to analyze and extract valuable insights from this wealth of information. Among these, the field of Machine Learning (ML) has thrived by leveraging data to extract meaningful insights. However, ML techniques face notable challenges when dealing with real-world data, often due to issues of imbalance, noise, insufficient labeling, and high dimensionality. To address these limitations, some researchers advocate for the adoption of Topological Data Analysis (TDA), a statistical approach that discerningly captures the intrinsic shape of data despite noise. Despite its potential, TDA has not gained as much traction within the Natural Language Processing (NLP) domain compared to structurally distinct areas like computer vision. Nevertheless, a dedicated community of researchers has been exploring the application of TDA in NLP, yielding 100 papers we comprehensively survey in this paper. Our findings categorize these efforts into theoretical and non-theoretical approaches. Theoretical approaches aim to explain linguistic phenomena from a topological viewpoint, while non-theoretical approaches merge TDA with ML features, utilizing diverse numerical representation techniques. We conclude by exploring the challenges and unresolved questions that persist in this niche field. Resources and a list of papers on this topic can be found at: https://github.com/AdaUchendu/AwesomeTDA4NLP.

Figures (9)

• Figure 1: Number of NLP papers using TDA published each year from 2012 to July-2025
• Figure 2: Illustration of the Persistent Homology technique using different radii to find the persistent features toptutorial2020. $\epsilon$ is the ball diameter.
• Figure 3: Illustration of Mapper from murugan2019introduction. The filter function $f$ is a height function, which is a projection onto the y-axis. The cover of the projected space is the four intervals $U_i$. The Mapper graph on the right is a result of applying the rest of the Mapper algorithm and clustering each preimage in the nearest neighbor.
• Figure 4: Taxonomy of Topological Data Analysis (TDA) for Natural Language Processing (NLP) Applications
• Figure 5: Illustration of the theoretical approaches researchers have employed to (1) probe texts, (2) extract TDA features, (3) use these features to explain or confirm known linguistic phenomena.