The Multilingual Tax Is Logarithmic: What Actually Breaks as Language Coverage Grows
TL;DR for operators Adding languages to an embedding model carries a theoretical representation cost, but the paper argues that the cost grows only logarithmically with language count. Under its formal conditions, the minimum dimensionality required to preserve useful within-language semantic structure, align translations across languages, and keep language variants distinguishable is $$ D_{X^{L}}=\Theta(\log L). $$ That changes how multilingual quality loss should be diagnosed. A sharp decline after expanding language coverage is not, by itself, evidence that embedding dimensionality has hit an unavoidable capacity wall. ...