# A Language and Its Dimensions: Intrinsic Dimensions of Language Fractal Structures

arXiv: https://arxiv.org/abs/2311.10217 · HTML: https://mlsanity.com/paper/2311.10217/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 40 references that are in the map.
- First posted on arXiv 16 Nov 2023.

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

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Intrinsic Dimension Estimation for Robust Detection of AI-Generated Texts](https://mlsanity.com/paper/2306.04723/) (2023)
- [Multiperiodic Processes: Ergodic Sources with a Sublinear Entropy](https://mlsanity.com/paper/2302.09049/) (2023)

## Built on by (most cited first, 4 of 4)

- [Token embeddings violate the manifold hypothesis](https://mlsanity.com/paper/2504.01002/) (2025)
- [The structure of the token space for large language models](https://mlsanity.com/paper/2410.08993/) (2024)
- [Probing the topology of the space of tokens with structured prompts](https://mlsanity.com/paper/2503.15421/) (2025)
- [A universal compression theory for lottery ticket hypothesis and neural scaling laws](https://mlsanity.com/paper/2510.00504/) (2025)

## Abstract (arXiv)

The present paper introduces a novel object of study - a language fractal structure. We hypothesize that a set of embeddings of all n-grams of a natural language constitutes a representative sample of this fractal set. (We use the term Hailonakea to refer to the sum total of all language fractal structures, over all n). The paper estimates intrinsic (genuine) dimensions of language fractal structures for the Russian and English languages. To this end, we employ methods based on (1) topological data analysis and (2) a minimum spanning tree of a data graph for a cloud of points considered (Steele theorem). For both languages, for all n, the intrinsic dimensions appear to be non-integer values (typical for fractal sets), close to 9 for both of the Russian and English language.