QuanLing: Cross-Branch Validation of Language Distance Quantification on Western Romance

Abstract

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 Bokm{\aa}l, 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.