Phonological distances for linguistic typology and the origin of Indo-European languages
Authors: Marius Mavridis, Juan De Gregorio, Raul Toral, David Sanchez
Organizations: Institute for Cross-Disciplinary Physics and Complex Systems IFISC (UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain · Universit´e Paris-Saclay, ENS Paris-Saclay, DER de Physique, 91190, Gif-sur-Yvette, France
We show that short-range phoneme dependencies encode large-scale patterns of linguistic relatedness, with direct implications for quantitative typology and evolutionary linguistics. Specifically, using an information-theoretic framework, we argue that phoneme sequences modeled as second-order Markov chains essentially capture the statistical correlations of a phonological system. This finding enables us to quantify distances among 67 modern languages from a multilingual parallel corpus employing a distance metric that incorporates articulatory features of phonemes. The resulting phonological distance matrix recovers major language families and reveals signatures of contact-induced convergence. Remarkably, we obtain a clear correlation with geographic distance, allowing us to constrain a plausible homeland region for the Indo-European family, consistent with the Steppe hypothesis.
Figures & tables
Figure 1: Predictability gain Gu as a function of the phonological block size for French (for which the phoneme inventory size is L=35 ), English ( L=38 ), Russian ( L=47 ) and Greek ( L=30 ).
Figure 2: Left: Predictability gain for English phonological classes as a function of the block size. Consonants can be either all grouped together (Cons) or divided into voiced and unvoiced. Vowels can be grouped in one class (Vow) or classified in terms of openness (open, mid, or close) or backness (front, central or back). The value of L for each curve is the number of categories considered therein (i.e., L=2 for the Cons/Vow curve, L=3 for the Voiced/Unvoiced/Vowel curve, etc.). Right: Same as the left panel but for the French language.
Figure 3: Left: Distributions of English phoneme trigrams. The five most frequent 3-phones are indicated with arrows. Right: Same for French.
Figure 4: Heatmap representation of the phonological distances between all pairs of languages in our sample, calculated on the 3-phone probability distributions under a metric based on articulatory feature vectors. Languages are ordered according to the clusters found by hierarchical clustering using the Ward linkage, visualized as a hierarchical tree.
Figure 5: Same heatmap as Fig. 4 but showing only Indo-European languages Languages. The hierarchical clustering method is now applied to this family, using the Ward linkage, and is displayed as a hierarchical tree. We also order languages according to the clusters.
Figure 6: Wasserstein distance between the 3-phone probability distributions of (left) all languages pairs and (right) IE language pairs only, versus geographic distance dgeo . On each plot, a logarithmic fit is shown in black.
Figure 7: Heatmap for the sum of squared residuals χ2 between the actual and fitted geographical distances that correspond, respectively, to Indo-European language locations and potential family origins. The point with the smallest residual, and consequently the most likely homeland for the Indo-European family, is indicated with a star. We depict its 95% uncertainty region with a dashed circle, calculated from K=2000 random samples of the weights associated with the languages.
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.
Appendix
Figure 8: Comparison of four different distances between the feature vector representations of selected phoneme pairs. Each curve is normalized to its maximum value. F. (f.) e. d. stands for feature edit distance.
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 (Bokmål), 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.
Yiping Bai
Guangdong Haiqixing Marine Technology Co., Ltd., Guangzhou 510000, China
Similarities between language representations derived from Self-Supervised Speech Models (S3Ms) have been observed to primarily reflect geographic proximity or surface typological similarities driven by recent expansion or contact, potentially missing deeper genealogical signals. We investigate how scaling an S3M-based language identification system from 126 to 4,017 languages reshapes this topology, and find a non-linear effect: phylogenetic recovery stays flat up to the 1K scale, but the 4K model undergoes a qualitative shift, resolving both clear lineages and long-term linguistic contact. Most strikingly, a robust Pacific macro-cluster emerges, grouping genealogically unrelated Papuan, Oceanic, and Australian languages, and we trace its driver to a concentrated encoding that captures shared acoustic signatures such as global energy dynamics. These results suggest that massive S3Ms internalize multiple layers of language history, offering a promising perspective for computational phylogenetics and the study of language contact.
Minu Kim, Hoirin Kim, David R. Mortensen
Thomas Lord Department of Computer Science, University of Southern California, USA · School of Electrical Engineering, KAIST, Republic of Korea · Language Technologies Institute, Carnegie Mellon University, USA
Quantifying language distance among closely related languages remains a core challenge in quantitative linguistics. Our previous work [1] introduced QuanLing (Quantitative Linguistics via Pretrained Language Models), a quantitative framework combining language distance metrics (sentence embedding distance, tokenization fragmentation rate) with language property analysis (MLM prediction probability), validated on North Germanic (Danish, Norwegian Bokmål, Swedish). This paper extends QuanLing to Western Romance--French, Portuguese, Spanish, Italian--testing cross-branch applicability with the same metric family and aggregation protocol as our North Germanic study, adapted for four languages (English anchor, quadruplet construction). Using 150 four-language parallel sentences, we compute LaBSE sentence embedding distances, tokenization fragmentation rates from four monolingual BERT tokenizers, and mBERT masked language model mutual intelligibility. Results show that Portuguese--Spanish are closest (LaBSE distance 0.0229), French--Italian most distant (0.0338); LaBSE and mBERT rankings agree on 4 of 6 pairs, confirming cross-model robustness. Western Romance shows a wider absolute distance span than North Germanic (0.011 vs. 0.008) but comparable relative ratios (1.48 vs. 1.67), consistent with longer divergence time. French exhibits notably higher MLM predictability (36.12% top-1 accuracy vs. 29.28% for Italian), reflecting its orthography--phonology decoupling. This cross-branch validation provides further evidence for QuanLing's generalizability beyond a single language branch.
Yiping Bai
Guangdong Haiqixing Marine Technology Co., Ltd., Guangzhou 510000, China