Learning reshapes power-law anisotropy in internal representations
Power-law anisotropy in internal representations has been observed across a wide range of biological and artificial neural systems, from state-of-the-art language models to the mouse cerebral cortex. This anisotropy is a key geometric property of high-dimensional information processing and underlies a variety of theoretical analyses. However, the mechanism by which it emerges from input structure and task-driven learning has remained unclear. Here, we characterize this formation process by exactly solving the learning dynamics of a wide two-layer linear neural network in a teacher--student setting with power-law input and teacher structures. We show that, in the feature-learning regime, t...
| Authors | Asahi Nakamuta, Jun-nosuke Teramae |
|---|---|
| Primary category | cs.LG |
| Published | 15 August 2026 |
| Last updated at source | 15 August 2026 |
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