Muon moves faster along signal river directions early but converges slower or oscillates near optima than GD due to orthogonal updates removing scale information, supporting two-stage optimization.
Revisiting Anisotropy in Language Transformers: The Geometry of Learning Dynamics
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
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.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Evaluation of two latent reasoning models against controls shows observable latent patterns appear without the proposed mechanisms, have graded causal effects on behavior, and concentrate in structured low-rank directions, arguing that patterns are insufficient evidence for reasoning.
citing papers explorer
-
Towards Understanding the Power and Limits of the Muon Optimizer: A River-Valley Perspective
Muon moves faster along signal river directions early but converges slower or oscillates near optima than GD due to orthogonal updates removing scale information, supporting two-stage optimization.
-
Observable Patterns Are Not Explanations: A Causal-Geometric Analysis of Latent Reasoning Models
Evaluation of two latent reasoning models against controls shows observable latent patterns appear without the proposed mechanisms, have graded causal effects on behavior, and concentrate in structured low-rank directions, arguing that patterns are insufficient evidence for reasoning.