# Quantitative Measurement of Language Distance among Closely Related Indo-European Languages Using Pretrained Language Models: A Case Study on the North Germanic Branch

arXiv: https://arxiv.org/abs/2609.34152 · HTML: https://mlsanity.com/paper/2609.34152/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 18 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 8 of 8)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Unsupervised Cross-lingual Representation Learning at Scale](https://mlsanity.com/paper/1911.02116/) (2019)
- [Language-agnostic BERT Sentence Embedding](https://mlsanity.com/paper/2007.01852/) (2020)
- [Do All Languages Cost the Same? Tokenization in the Era of Commercial Language Models](https://mlsanity.com/paper/2305.13707/) (2023)
- [The Tatoeba Translation Challenge -- Realistic Data Sets for Low Resource and Multilingual MT](https://mlsanity.com/paper/2010.06354/) (2020)
- [Probing Multilingual BERT for Genetic and Typological Signals](https://mlsanity.com/paper/2011.02070/) (2020)
- [Identifying the Correlation Between Language Distance and Cross-Lingual Transfer in a Multilingual Representation Space](https://mlsanity.com/paper/2305.02151/) (2023)

## Abstract (arXiv)

Among closely related North Germanic languages, the quantification of language distance has traditionally relied on qualitative methods, lacking a unified multi-dimensional computational framework. Multilingual pretrained models based on the Transformer architecture can map texts from different languages into a shared vector space, enabling quantitative measurement of language distance. This paper focuses on the three North Germanic languages---Danish, Norwegian (Bokmaal), and Swedish---and proposes a three-metric quantitative framework based on pretrained language models: (1)~sentence-level semantic distance, computed as cosine similarity between LaBSE and mBERT encodings of parallel sentences; (2)~orthographic fragmentation rate, measuring subword tokenization efficiency when cross-applying monolingual BERT vocabularies to parallel texts; (3)~MLM predictability, comparing prediction confidence and entropy in masked language modeling using mBERT across languages. Using 150 trilingual parallel sentence triplets from the Tatoeba corpus as controlled samples, we obtain consistent distance rankings on two independent models: LaBSE: da--no 0.012 <  no--sv 0.016 <  da--sv 0.020; mBERT: da--no 0.016 <  no--sv 0.045 ≈  da--sv 0.046. This ranking is consistent with the historical linguistic conclusion that ``400 years of Danish rule over Norway (1380--1814) led to highly cognate written languages.'' The three metrics---semantic, orthographic, and predictability---converge on the same conclusion, providing a reproducible computational framework for the quantitative study of distance among closely related languages, extensible in principle to more branches of the Indo-European language family, pending validation on additional language groups.