Revisiting Anisotropy in Language Transformers: The Geometry of Learning Dynamics

Since their introduction, Transformer architectures have dominated Natural Language Processing (NLP). However, recent research has highlighted an inherent anisotropy phenomenon in these models, presenting a significant challenge to their geometric interpretation. Previous theoretical studies on this phenomenon are rarely based on the underlying representation geometry. In this paper, we extend them by providing such theoretical arguments assessing the problematic nature of this phenomenon. Furthermore, to observe geometric internal model dynamics, we apply mechanistic interpretability (MI) techniques during the model's training checkpoints rather than post-hoc, as it is commonly done in the literature. By analyzing multiple models and their checkpoints -including EuroBERT, the Pythia suite, and SmolLM2- we investigate the structure of embedding representations and their correlation with the on manifold entropy of their underlying distribution.