Cross-lingual Similarity of Multilingual Representations Revisited

Related works used indexes like CKA and variants of CCA to measure the similarity of cross-lingual representations in multilingual language models. In this paper, we argue that assumptions of CKA/CCA align poorly with one of the motivating goals of cross-lingual learning analysis, i.e., explaining zero-shot cross-lingual transfer. We highlight what valuable aspects of cross-lingual similarity these indexes fail to capture and provide a motivating case study textitdemonstrating the problem empirically. Then, we introduce textitAverage Neuron-Wise Correlation (ANC) as a straightforward alternative that is exempt from the difficulties of CKA/CCA and is good specifically in a cross-lingual context. Finally, we use ANC to construct evidence that the previously introduced ``first align, then predict'' pattern takes place not only in masked language models (MLMs) but also in multilingual models with textitcausal language modeling objectives (CLMs). Moreover, we show that the pattern extends to the textitscaled versions of the MLMs and CLMs (up to 85x original mBERT).footnoteOur code is publicly available at urlhttps://github.com/TartuNLP/xsim