The Routing and Filtering Structure of Attention
The attention interaction matrix $QK^{\top}$ contains two entangled computations: a skew-symmetric component that redistributes information between positions (routing) and a symmetric component that scales mutual relevance (filtering). We decompose 1776 heads across five pretrained transformers and find routing operating at low rank, well below the routing capacity allocated by the weight kernel. We introduce $S$-$D$ attention as a diagnostic parameterization that disentangles routing from filtering by construction with guaranteed stability ($\mathrm{Re}(λ) \le 0$) and trains stably without layer normalization. When disentangled and unnormalized, routing self-organizes into a spectral cas...
| Authors | Shafayeth Jamil, Rehan Kapadia |
|---|---|
| Primary category | cs.LG |
| Published | 12 May 2026 |
| Last updated at source | 12 May 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.