There is No Theoretical Curse of Multilinguality For Embedding Space Structure

A new arXiv paper (2608.17088v1) proves that the minimum dimensionality required for perfect multilingual embedding spaces grows only logarithmically with the number of languages, showing there is no theoretical curse of multilinguality for embedding space structure. The authors formalize 'perfect multilinguality' and argue that the empirical degradation in multilingual model performance stems from real-world data and training conditions, not inherent structural limits.

arXiv:2608.17088v1 Announce Type: new Abstract: A central goal of multilingual NLP is to achieve high monolingual performance per language and cross-lingual alignment for large-scale language coverage with a multilingual model. The curse of multilinguality describes the phenomenon of degradation in multilingual model performance as we increase language coverage, posing a threat to the above goal. This paper asks whether multilingual embedding spaces are inherently incapable of achieving perfect multilinguality without a prohibitive increase in required capacity. We first formalize the goal of "perfect multilinguality", embodied in two multilinguality conditions. We then prove that the minimum dimensionality required for perfect multilinguality grows only logarithmically in the number of languages. That is, we show that there is no theoretical curse of multilinguality for embedding space structure. This suggests that the empirical curse of multilinguality is a result of real world data and training conditions. We back this understanding with a small-scale empirical study. Our paper provides the first theoretical and intrinsic perspective on the curse of multilinguality, with implications for the scientific understanding of this phenomenon.