# Topological Analysis of Syntactic Structures

arXiv: https://arxiv.org/abs/1903.05181 · HTML: https://mlsanity.com/paper/1903.05181/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Mar 2019.

## Built on by (most cited first, 9 of 9)

- [Mathematical Structure of Syntactic Merge](https://mlsanity.com/paper/2305.18278/) (2023)
- [TOPFORMER: Topology-Aware Authorship Attribution of Deepfake Texts with Diverse Writing Styles](https://mlsanity.com/paper/2309.12934/) (2023)
- [Natural Language Syntax Complies with the Free-Energy Principle](https://mlsanity.com/paper/2210.15098/) (2022)
- [Topos and Stacks of Deep Neural Networks](https://mlsanity.com/paper/2106.14587/) (2021)
- [Image Classification using Combination of Topological Features and Neural Networks](https://mlsanity.com/paper/2311.06375/) (2023)
- [Topological Data Analysis Applications in Natural Language Processing: A Survey](https://mlsanity.com/paper/2411.10298/) (2024)
- [Syntactic structures and the general Markov models](https://mlsanity.com/paper/2104.08462/) (2021)
- [Linguistics from a topological viewpoint](https://mlsanity.com/paper/2403.15440/) (2024)
- [Optimizing Soft Prompt Tuning via Structural Evolution](https://mlsanity.com/paper/2602.16500/) (2026)

## Abstract (arXiv)

We use the persistent homology method of topological data analysis and dimensional analysis techniques to study data of syntactic structures of world languages. We analyze relations between syntactic parameters in terms of dimensionality, of hierarchical clustering structures, and of non-trivial loops. We show there are relations that hold across language families and additional relations that are family-specific. We then analyze the trees describing the merging structure of persistent connected components for languages in different language families and we show that they partly correlate to historical phylogenetic trees but with significant differences. We also show the existence of interesting non-trivial persistent first homology groups in various language families. We give examples where explicit generators for the persistent first homology can be identified, some of which appear to correspond to homoplasy phenomena, while others may have an explanation in terms of historical linguistics, corresponding to known cases of syntactic borrowing across different language subfamilies.