# Mathematical Structure of Syntactic Merge

arXiv: https://arxiv.org/abs/2305.18278 · HTML: https://mlsanity.com/paper/2305.18278/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 57 references that are in the map.
- First posted on arXiv 29 May 2023.

## Builds on (most cited first, 5 of 5)

- [Topological Analysis of Syntactic Structures](https://mlsanity.com/paper/1903.05181/) (2019)
- [Semantic Spaces](https://mlsanity.com/paper/1605.04238/) (2016)
- [Syntactic Structures and Code Parameters](https://mlsanity.com/paper/1610.00311/) (2016)
- [Heat Kernel analysis of Syntactic Structures](https://mlsanity.com/paper/1803.09832/) (2018)
- [Syntactic structures and the general Markov models](https://mlsanity.com/paper/2104.08462/) (2021)

## Built on by (most cited first, 17 of 17)

- [Large Language Models](https://mlsanity.com/paper/2307.05782/) (2023)
- [How Linguistics Learned to Stop Worrying and Love the Language Models](https://mlsanity.com/paper/2501.17047/) (2025)
- [Syntax-semantics interface: an algebraic model](https://mlsanity.com/paper/2311.06189/) (2023)
- [A Comparative Investigation of Compositional Syntax and Semantics in DALL-E 2](https://mlsanity.com/paper/2403.12294/) (2024)
- [Old and New Minimalism: a Hopf algebra comparison](https://mlsanity.com/paper/2306.10270/) (2023)
- [What is a word?](https://mlsanity.com/paper/2402.12605/) (2024)
- [On the Compatibility of Generative AI and Generative Linguistics](https://mlsanity.com/paper/2411.10533/) (2024)
- [A Diagrammatic Calculus for a Functional Model of Natural Language Semantics](https://mlsanity.com/paper/2507.00782/) (2025)
- [Encoding syntactic objects and Merge operations in function spaces](https://mlsanity.com/paper/2507.13501/) (2025)
- [Language models as tools for investigating the distinction between possible and impossible natural languages](https://mlsanity.com/paper/2512.09394/) (2025)
- [Large language models have learned to use language](https://mlsanity.com/paper/2512.12447/) (2025)
- [Large language models are not about natural language](https://mlsanity.com/paper/2512.13441/) (2025)
- [Linguists should learn to love speech-based deep learning models](https://mlsanity.com/paper/2512.14506/) (2025)
- [Are Language Models Models?](https://mlsanity.com/paper/2601.10421/) (2026)
- [Across the Levels of Analysis: Explaining Predictive Processing in Humans Requires More Than Machine-Estimated Probabilities](https://mlsanity.com/paper/2604.09466/) (2026)
- [You Can't Fight in Here! This is BBS!](https://mlsanity.com/paper/2604.09501/) (2026)
- [Not-So-Strange Love: Language Models and Generative Linguistic Theories are More Compatible than They Appear](https://mlsanity.com/paper/2605.10061/) (2026)

## Abstract (arXiv)

The syntactic Merge operation of the Minimalist Program in linguistics can be described mathematically in terms of Hopf algebras, with a formalism similar to the one arising in the physics of renormalization. This mathematical formulation of Merge has good descriptive power, as phenomena empirically observed in linguistics can be justified from simple mathematical arguments. It also provides a possible mathematical model for externalization and for the role of syntactic parameters.