Dual Space Preconditioning for Gradient Descent in the Overparameterized Regime

ArXi:2603.10485v1 Announce Type: cross In this work we study the convergence properties of the Dual Space Preconditioned Gradient Descent, encompassing optimizers such as Normalized Gradient Descent, Gradient Clipping and Adam. We consider preconditioners of the form $\nabla K$, where $K: \mathbb{R}^p \to \mathbb{R}$ is convex and assume that the latter is applied to train an over-parameterized linear model with loss of the form $\ell({X} {W} - {Y})$, for weights ${W} \in \mathbb{R}^{d \times k}$, labels ${Y} \in \mathbb{R}^{n \times k}$ and data ${X} \in \mathbb{R}^{n \times d.