What if I ask in \textit{alia lingua}? Measuring Functional Similarity Across Languages

How similar are model outputs across languages? In this work, we study this question using a recently proposed model similarity metric $κ_p$ applied to 20 languages and 47 subjects in GlobalMMLU. Our analysis reveals that a model's responses become increasingly consistent across languages as its size and capability grow. Interestingly, models exhibit greater cross-lingual consistency within themselves than agreement with other models prompted in the same language. These results highlight not only the value of $κ_p$ as a practical tool for evaluating multilingual reliability, but also its potential to guide the development of more consistent multilingual systems.