Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks
The existing optimizers for deep neural networks (DNNs) typically rely on either the $\ell_2$ norm or the $\ell_\infty$ norm, resulting in optimizers that do not adapt well to substantial changes in curvature across parameter dimensions. Generally, the training process of DNNs often exhibits strong curvature anisotropy in the early period, whereas in the later period, the training process of DNNs tends to move toward flatter regions with weaker anisotropy. Particularly, optimizers based on the \(\ell_2\)-norm are usually dominated by high-curvature directions, restricting updates of optimizers along with lower curvature direction and thus leading to a slower convergence rate. While optimi...
| Authors | Jianhao Xu, Zhuang Yang |
|---|---|
| Primary category | cs.LG |
| Published | 1 June 2026 |
| Last updated at source | 1 June 2026 |
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