Revisiting Anisotropy in Language Transformers: The Geometry of Learning Dynamics

2026-04-09

AI Summary

This work addresses the anisotropy in the representation space of language Transformers, which undermines geometric interpretability. By integrating geometric analysis with concept-level mechanistic interpretability, the study introduces—during training—activation-derived low-rank tangential proxy directions and empirically demonstrates that tangential components dominate gradient energy distribution and drive anisotropy formation. Through frequency bias modeling and gradient energy decomposition, the authors show that these tangential directions significantly outperform same-rank random baselines in capturing anisotropic structure, consistently across both encoder and decoder architectures. These findings provide strong empirical support for a “tangential alignment” explanatory framework, highlighting the critical role of tangential dynamics in shaping the geometry of Transformer representations.

Technology Category

• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models
• Machine Learning: Representation Learning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

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 grounded in the underlying representation geometry. In this paper, we extend them by deriving geometric arguments for how frequency-biased sampling attenuates curvature visibility and why training preferentially amplify tangent directions. Empirically, we then use concept-based mechanistic interpretability during training, rather than only post hoc, to fit activation-derived low-rank tangent proxies and test them against ordinary backpropagated true gradients. Across encoder-style and decoder-style language models, we find that these activation-derived directions capture both unusually large gradient energy and a substantially larger share of gradient anisotropy than matched-rank normal controls, providing strong empirical support for a tangent-aligned account of anisotropy.

Problem

• anisotropy
• Transformers
• representation geometry
• language models
• gradient dynamics

Innovation

• anisotropy
• representation geometry
• tangent directions
• mechanistic interpretability
• gradient dynamics