Training Dynamics of Softmax Self-Attention: Fast Global Convergence via Preconditioning
We study the training dynamics of gradient descent in a softmax self-attention layer trained to perform linear regression and show that a simple first-order optimization algorithm can converge to the globally optimal self-attention parameters at a geometric rate. Our analysis proceeds in two steps. First, we show that in the infinite-data limit the regression problem solved by the self-attention layer is equivalent to a nonconvex matrix factorization problem. Second, we exploit this connection to design a novel "structure-aware" variant of gradient descent which efficiently optimizes the original finite-data regression objective. Our optimization algorithm features several innovations ove...
| Authors | Gautam Goel, Mahdi Soltanolkotabi, Peter Bartlett |
|---|---|
| Primary category | cs.LG |
| Published | 2 March 2026 |
| Last updated at source | 2 March 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 Information may be incomplete or out of date.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.