Topological Data Analysis Applications in Natural Language Processing: A Survey

Adaku Uchendu; Thai Le

arxiv: 2411.10298 · v5 · submitted 2024-11-15 · 💻 cs.CL

Topological Data Analysis Applications in Natural Language Processing: A Survey

Adaku Uchendu , Thai Le This is my paper

Pith reviewed 2026-05-23 17:13 UTC · model grok-4.3

classification 💻 cs.CL

keywords Topological Data AnalysisNatural Language ProcessingSurveyTheoretical ApproachesMachine LearningLinguistic PhenomenaData Structure

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The pith

A survey compiles 137 papers on topological data analysis in natural language processing and splits them into theoretical explanations of language versus additions to machine learning pipelines.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper gathers existing research that applies topological data analysis to natural language processing tasks. It divides the collected studies into those that use topology to interpret linguistic features and those that insert TDA methods into standard machine learning workflows. The authors note that NLP has seen less of this work than fields with clearer geometric patterns, yet a focused group of researchers has produced this body of papers. By laying out the two categories and the remaining difficulties, the survey supplies a map for anyone wanting to build on the existing efforts.

Core claim

The paper establishes that a dedicated community has produced 137 papers applying topological data analysis to natural language processing. These are organized into theoretical approaches, which use topology to explain linguistic phenomena, and non-theoretical approaches, which incorporate TDA into ML-based pipelines through various numerical representations. The survey ends by outlining the key challenges and open questions that continue to define the area.

What carries the argument

The binary split of the literature into theoretical approaches (using topology to explain linguistic phenomena) and non-theoretical approaches (incorporating TDA into ML pipelines).

If this is right

Future researchers can locate prior work through the provided organization of theoretical and non-theoretical studies.
Integration of TDA into NLP pipelines becomes easier to evaluate once the numerical representations already tried are catalogued.
Open questions listed at the end can serve as starting points for new projects that address data structure in language tasks.
The survey's separation of explanation-focused work from pipeline-focused work clarifies different goals within the same research area.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Similar surveys could be written for TDA applications in other text-adjacent fields such as information retrieval or computational social science.
The non-theoretical category might expand if TDA representations are tested on newer language models that handle longer contexts.
Theoretical approaches could be strengthened by direct comparisons between topological invariants and established linguistic annotations.

Load-bearing premise

The 137 papers form a representative and exhaustive collection of all TDA-NLP work, and the division into theoretical versus non-theoretical categories remains stable and meaningful across the studies.

What would settle it

Locating a sizable set of additional papers on TDA applied to NLP that cannot be placed cleanly into either the theoretical or non-theoretical category used in the survey.

Figures

Figures reproduced from arXiv: 2411.10298 by Adaku Uchendu, Thai Le.

**Figure 2.** Figure 2: Illustration of the Persistent Homology tech [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: Illustration of Mapper from Murugan and Robertson (2019). 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 Ui . 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. 2.2 Mapper Mapper is a dimension reduction clustering technique, u… view at source ↗

**Figure 4.** Figure 4: Illustration of the TDA feature extraction [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: Taxonomy of Topological Data Analysis (TDA) for Natural Language Processing (NLP) Applications [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 6.** Figure 6: Using Watermarked vs. Non-Watermarked Texts, (a) & (b) are the distance correlation matrix of TDA [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗

**Figure 7.** Figure 7: Using Watermarked vs. Non-Watermarked Texts, (a) & (b) are Mapper plots to visualize the shape of data. entropy, perplexity, position of noun & adjective, coherence, flesh reading ease score & grade, number of stopwords, length of text, and number of unique words. Finally, we use distance correlation to measure the statistical dependence of the two non-linear sets of features. See Figures 6a & 6b for the … view at source ↗

read the original abstract

The surge of data available on the Internet has driven the adoption of a wide range of computational methods for analyzing and extracting insights from large-scale data. Among these, Machine Learning (ML) has become a central paradigm, offering powerful tools for pattern discovery, prediction, and representation learning across many domains. At the same time, real-world data often exhibit properties such as noise, imbalance, sparsity, limited supervision, and high dimensionality, motivating the use of additional analytical perspectives that can complement standard ML pipelines. One such perspective is Topological Data Analysis (TDA), a statistical framework that focuses on the intrinsic shape and structural organization of data. Rather than replacing ML, TDA offers a complementary lens for characterizing geometric and topological properties that may be difficult to capture with conventional feature-based or purely predictive approaches. This has motivated a growing body of work that integrates TDA into ML workflows, particularly in settings where data structure plays an important role. Despite this promise, TDA has received relatively limited attention in Natural Language Processing (NLP) compared to domains with more overt structural regularities, such as computer vision. Nevertheless, a dedicated community of researchers has explored its use in NLP, leading to 137 papers that we comprehensively survey in this work. We organize these studies into theoretical and nontheoretical approaches. Theoretical approaches use topology to explain linguistic phenomena, whereas non-theoretical approaches incorporate TDA into ML-based pipelines through a variety of numerical representations. We conclude by discussing the key challenges and open questions that continue to shape this emerging area. Resources and a list of papers are available at: https://github.com/AdaUchendu/AwesomeTDA4NLP.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This survey gathers 137 TDA-NLP papers and offers a basic theoretical/non-theoretical split, but the missing search details make the coverage claim hard to trust.

read the letter

The paper's main contribution is a compilation of 137 papers on topological data analysis in NLP plus a new taxonomy that separates work explaining linguistic structure from work plugging TDA into ML pipelines. It also supplies a GitHub repo with the list and ends with open questions. That organization is new relative to the cited prior surveys and gives a single entry point for people who want to see what has been tried so far. The abstract is clear about scope and the authors avoid overclaiming impact outside this narrow intersection. The binary taxonomy is straightforward and matches the two main ways TDA shows up in the literature, so it is a reasonable first cut even if some papers straddle the line. The real limitation is the absence of any methods section describing the search strategy, databases, keywords, or inclusion criteria. Without that, it is impossible to judge whether 137 is close to exhaustive or whether the sample tilts toward certain venues or years. The GitHub list is helpful but does not replace a reproducible protocol. Minor issues include the usual survey risk that fast-moving sub-areas will date the list quickly, but that is not a flaw in the current draft. This paper is mainly for researchers already interested in TDA or looking for an on-ramp into the NLP-TDA niche; it will not move the broader field. It is coherent and cites external work properly, so it meets the bar for serious refereeing. I would send it out for review with a request that the authors add a clear methods paragraph and perhaps test the taxonomy on a few borderline papers.

Referee Report

2 major / 1 minor

Summary. The paper surveys applications of Topological Data Analysis (TDA) in Natural Language Processing (NLP). It identifies 137 papers, organizes them into theoretical approaches (using topology to explain linguistic phenomena) and non-theoretical approaches (integrating TDA into ML pipelines), discusses challenges and open questions, and provides a GitHub repository listing the papers.

Significance. If the survey is exhaustive and the taxonomy robust, the work would provide a useful entry point and resource for an emerging interdisciplinary area that has received less attention than TDA in computer vision or other domains. The GitHub link for the paper list is a concrete strength that supports accessibility and future work.

major comments (2)

[Abstract and §1] Abstract and §1: The central claim that the work 'comprehensively survey[s]' exactly 137 papers is load-bearing, yet the manuscript provides no description of the literature search strategy, databases (e.g., arXiv, ACL Anthology), keywords, date range, or inclusion/exclusion criteria. This absence prevents assessment of exhaustiveness or bias and directly undermines the weakest assumption identified in the review process.
[Taxonomy introduction (likely §3)] Taxonomy introduction (likely §3): The binary split into 'theoretical' versus 'non-theoretical' approaches is presented without an operational definition, decision rules for borderline cases, or any quantitative validation (e.g., coverage statistics or inter-rater reliability), making it unclear whether the organization is stable or meaningful across the 137 papers.

minor comments (1)

[Resources section] The GitHub repository is referenced but the manuscript does not indicate whether it includes search strings, a PRISMA-style flow diagram, or metadata that would allow reproducibility of the 137-paper corpus.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments. We address each major comment below and indicate the revisions that will be incorporated to strengthen the manuscript.

read point-by-point responses

Referee: [Abstract and §1] Abstract and §1: The central claim that the work 'comprehensively survey[s]' exactly 137 papers is load-bearing, yet the manuscript provides no description of the literature search strategy, databases (e.g., arXiv, ACL Anthology), keywords, date range, or inclusion/exclusion criteria. This absence prevents assessment of exhaustiveness or bias and directly undermines the weakest assumption identified in the review process.

Authors: We agree that a transparent account of the literature search is required to substantiate the claim of comprehensiveness. In the revised manuscript we will insert a new subsection (Section 2.1) that explicitly describes the search strategy. This will list the databases queried (arXiv, ACL Anthology, Google Scholar, Semantic Scholar), the keyword combinations employed (e.g., “topological data analysis” OR “persistent homology” AND (“NLP” OR “natural language processing” OR “text classification”)), the temporal scope, and the inclusion/exclusion criteria used to arrive at the final set of 137 papers. Any acknowledged limitations of the search will also be noted. revision: yes
Referee: [Taxonomy introduction (likely §3)] Taxonomy introduction (likely §3): The binary split into 'theoretical' versus 'non-theoretical' approaches is presented without an operational definition, decision rules for borderline cases, or any quantitative validation (e.g., coverage statistics or inter-rater reliability), making it unclear whether the organization is stable or meaningful across the 137 papers.

Authors: We accept that the taxonomy requires clearer operational grounding. The revised Section 3 will supply explicit definitions: theoretical approaches are those whose primary goal is to employ topological invariants to model or explain linguistic structures without direct integration into machine-learning pipelines; non-theoretical approaches are those that embed TDA outputs (persistence diagrams, landscapes, etc.) as features or regularizers inside ML models. Decision rules for borderline cases will be stated, together with illustrative examples. We will also report the distribution of the 137 papers across the two categories. Although formal inter-rater reliability statistics were not computed, all classifications were discussed and reconciled among the authors; this clarification will be added without overstating validation. revision: yes

Circularity Check

0 steps flagged

No circularity in survey paper with no derivations

full rationale

This is a literature survey paper whose central claim is the identification and organization of 137 external papers on TDA-NLP. It presents no equations, no fitted parameters, no predictions, and no derivation chain that could reduce to its own inputs. The enumerated circularity patterns (self-definitional, fitted-input-called-prediction, self-citation load-bearing, etc.) do not apply because there are no mathematical or predictive steps to inspect. The survey's methodology and paper list rest on external sources rather than self-referential constructions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is a survey paper. It introduces no free parameters, mathematical axioms, or invented entities; the contribution is the curation and categorization of existing published work.

pith-pipeline@v0.9.0 · 5828 in / 1032 out tokens · 47352 ms · 2026-05-23T17:13:27.435346+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We organize these studies into theoretical and nontheoretical approaches. Theoretical approaches use topology to explain linguistic phenomena, whereas non-theoretical approaches incorporate TDA into ML-based pipelines through a variety of numerical representations.
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking echoes

?

echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

Two main techniques are used to extract TDA features – Persistent Homology and Mapper.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Topological Signatures of Grokking
cs.LG 2026-05 unverdicted novelty 7.0

Persistent homology detects a sharp increase in maximum and total H1 persistence during grokking on modular arithmetic, offering a topological diagnostic that links representation geometry to generalization.
Text Corpora as Concept Fields: Black-Box Hallucination and Novelty Measurement
cs.CL 2026-05 unverdicted novelty 7.0

Concept Fields model text corpora as local Gaussian drift fields in embedding space to score sentence transitions for hallucination detection and novelty via standardized deviation.
Text Corpora as Concept Fields: Black-Box Hallucination and Novelty Measurement
cs.CL 2026-05 unverdicted novelty 6.0

Concept Fields model text corpora as local Gaussian drift fields in embedding space to score sentence transitions for groundedness and novelty without model internals.
TDA-RC: Task-Driven Alignment for Knowledge-Based Reasoning Chains in Large Language Models
cs.CL 2026-03 unverdicted novelty 6.0

TDA-RC embeds topological patterns from multi-round reasoning into CoT via persistent homology and a repair agent, yielding better accuracy-efficiency trade-offs than ToT or GoT on tested datasets.
Hallucination Detection in LLMs with Topological Divergence on Attention Graphs
cs.CL 2025-04 unverdicted novelty 6.0

TOHA detects LLM hallucinations via topological divergence on attention graphs, showing consistent patterns and competitive benchmark results with minimal data.

Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages · cited by 4 Pith papers · 2 internal anchors

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look and say

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Shape” of Words Investigate the “shape

Neural deepfake detection with factual struc- ture of text. In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Process- ing (EMNLP), pages 2461–2470. Xiaojin Zhu. 2013. Persistent homology: An introduc- tion and a new text representation for natural lan- guage processing. In IJCAI, pages 1953–1959. Y Zhu, P Feng, S Yi, Q Qu, an...

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Hallucination Detection in LLMs with Topological Divergence on Attention Graphs

A green ai methodology based on persistent homology for compressing bert. Applied Sciences, 15(1):390. Alexandra Bazarova, Aleksandr Yugay, Andrey Shulga, Alina Ermilova, Andrei V olodichev, Konstantin Polev, Julia Belikova, Rauf Parchiev, Dmitry Simakov, Maxim Savchenko, et al. 2025. Hallucina- tion detection in llms via topological divergence on attenti...

work page internal anchor Pith review Pith/arXiv arXiv 2025

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Knowledge-Based Systems, 130:102–115

Context-aware profiling of concepts from a se- mantic topological space. Knowledge-Based Systems, 130:102–115. Jatin Chauhan and Manohar Kaul. 2022. Bertops: Studying bert representations under a topological lens. In 2022 International Joint Conference on Neu- ral Networks (IJCNN), pages 1–8. IEEE. Daniil Cherniavskii, Eduard Tulchinskii, Vladislav Mikhai...

work page arXiv 2022

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Electronics, 13(18):3781

Geometry of textual data augmentation: In- sights from large language models. Electronics, 13(18):3781. Stephen Fitz. 2022. The shape of words-topological structure in natural language data. In Topological, Algebraic and Geometric Learning Workshops 2022, pages 116–123. PMLR. Stephen Fitz, Peter Romero, and Jiyan Jonas Schneider

work page 2022

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arXiv preprint arXiv:2406.05798

Hidden holes: topological aspects of language models. arXiv preprint arXiv:2406.05798. Jason S Garcia. 2022. Applications of topological data analysis to natural language processing and com- puter vision. Ph.D. thesis, Colorado State University. Alejandro García-Castellanos, Giovanni Luca Marchetti, Danica Kragic, and Martina Scolamiero. 2024. Rela- tive ...

work page arXiv 2022

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In Inter- national Conference on Learning Representations

Topological graph neural networks. In Inter- national Conference on Learning Representations. Jici Huang. 2022. A tda approach of analyzing election speeches with nlp techniques. Journal of Computing Sciences in Colleges, 38(3):215–215. Samyak Jain, Rishi Singhal, Sriram Krishna, Yaman K Singla, and Rajiv Ratn Shah. 2024. Beyond words: A topological explo...

work page arXiv 2022

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6th Interna- tional Workshop on Modern Data Science Technolo- gies

Topological structure of ukrainian tongue twisters based on speech sound analysis. 6th Interna- tional Workshop on Modern Data Science Technolo- gies. Sergei Kudriashov, Veronika Zykova, Angelina Stepanova, Jacob Raskind, and Eduard Klyshinsky

work page

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An Introduction to Topological Data Analysis for Physicists: From LGM to FRBs

The more polypersonal the better-a short look on space geometry of fine-tuned layers. In Interna- tional Conference on Neuroinformatics, pages 13–22. Springer. Ankit Kumar and Apurba Sarkar. 2022. Extractive text summarization using topological features. In Interna- tional Workshop on Combinatorial Image Analysis, pages 105–121. Springer. Laida Kushnareva...

work page internal anchor Pith review Pith/arXiv arXiv 2022

[8] [8]

The IJCAI-2024 AISafety Workshop

Detecting out-of-distribution text using topo- logical features of transformer-based language mod- els. The IJCAI-2024 AISafety Workshop. Alexander Port, Iulia Gheorghita, Daniel Guth, John M Clark, Crystal Liang, Shival Dasu, and Matilde Mar- colli. 2018. Persistent topology of syntax. Mathe- matics in Computer Science, 12(1):33–50. Alexander Port, Taeli...

work page 2024

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Mathematics in Computer Science, 16(1):2

Topological analysis of syntactic structures. Mathematics in Computer Science, 16(1):2. Polina Proskura and Alexey Zaytsev. 2024. Beyond sim- ple averaging: Improving nlp ensemble performance with topological-data-analysis-based weighting. In 2024 IEEE 11th International Conference on Data Science and Advanced Analytics (DSAA), pages 1–8. IEEE. Irina Pros...

work page arXiv 2024

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Ishrat Rahman Sami and Katayoun Farrahi

IEEE. Ishrat Rahman Sami and Katayoun Farrahi. 2017. A simplified topological representation of text for local and global context. In Proceedings of the 25th ACM International Conference on Multimedia, pages 1451– 1456. Luca Sassone, Marco Manetti, Mattia G Bergomi, and Massimo Ferri. 2022. Bridging Topological Persis- tence and Machine Learning for Music...

work page arXiv 2017

[11] [11]

In 2021 20th IEEE International Conference on Machine Learning and Applications (ICMLA), pages 403–408

Con connections: Detecting fraud from ab- stracts using topological data analysis. In 2021 20th IEEE International Conference on Machine Learning and Applications (ICMLA), pages 403–408. IEEE. Sarah Tymochko, Zachary New, Lucius Bynum, Em- ilie Purvine, Timothy Doster, Julien Chaput, and Tegan Emerson. 2020. Argumentative topology: Finding loop (holes) in...

work page arXiv 2021

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In Computational Topology in Image Context: 4th Inter- national Workshop, CTIC 2012, Bertinoro, Italy, May 28-30, 2012

Computational topology in text mining. In Computational Topology in Image Context: 4th Inter- national Workshop, CTIC 2012, Bertinoro, Italy, May 28-30, 2012. Proceedings, pages 68–78. Springer. Malgorzata Wamil, Abdelaali Hassaine, Shishir Rao, Yikuan Li, Mohammad Mamouei, Dexter Canoy, Milad Nazarzadeh, Zeinab Bidel, Emma Copland, Kazem Rahimi, et al. 2...

work page arXiv 2012

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look and say

Gale: Globally assessing local explanations. In Topological, Algebraic and Geometric Learning Workshops 2022, pages 322–331. PMLR. Zhandos Yessenbayev and Zhanibek Kozhirbayev. 2022. Comparison of word embeddings of unaligned audio and text data using persistent homology. In Interna- tional Conference on Speech and Computer, pages 700–711. Springer. Zhand...

work page arXiv 2022

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Shape” of Words Investigate the “shape

Neural deepfake detection with factual struc- ture of text. In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Process- ing (EMNLP), pages 2461–2470. Xiaojin Zhu. 2013. Persistent homology: An introduc- tion and a new text representation for natural lan- guage processing. In IJCAI, pages 1953–1959. Y Zhu, P Feng, S Yi, Q Qu, an...

work page 2020