A theory of platonic representations in language models
Darshil Doshi, Wenjie Zhou, Corinna Elena Wegner, Daniel J. Korchinski, Santiago Acevedo, Matthieu Wyart
Abstract
Representations of translated sentences are similar in the inner layers of multilingual language models -- an observation connected to the platonic representation hypothesis, yet unexplained theoretically. We provide an explanation based on the assumption that data have a hidden hierarchical structure whose abstract levels are shared across languages while surface levels are modality- or language-specific. Concretely, we generate synthetic languages from probabilistic context-free grammars sharing upper-level but not lower-level production rules. In this setting the Bayes-optimal next-token predictor is belief propagation (BP); encoding its messages in successive layers yields analytical predictions that agree well with transformers trained on the same data. The framework explains why cross-lingual similarity peaks in middle layers, coexists with language-specific structure, and strengthens with language proximity, model quality and data exposure. It distinguishes similarity (shared neighborhood geometry) from alignment (shared coordinates), showing that the latter occurs when code-switched data, i.e. mixed-language sentences, are abundant enough. It further predicts that subtracting from each layer the component linearly predictable from the preceding one increases cross-lingual similarity, which we confirm in pretrained LLMs.