# Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness

arXiv: https://arxiv.org/abs/2502.08532 · HTML: https://mlsanity.com/paper/2502.08532/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2025.

## Built on by (most cited first, 4 of 4)

- [When the Specification Emerges: Benchmarking Faithfulness Loss in Long-Horizon Coding Agents](https://mlsanity.com/paper/2603.17104/) (2026)
- [On the Interaction of Batch Noise, Adaptivity, and Compression, under (L0,L1)-Smoothness: An SDE Approach](https://mlsanity.com/paper/2506.00181/) (2025)
- [Dual Space Preconditioning for Gradient Descent in the Overparameterized Regime](https://mlsanity.com/paper/2603.10485/) (2026)
- [Constrained Stochastic Spectral Preconditioning Converges for Nonconvex Objectives](https://mlsanity.com/paper/2605.11850/) (2026)

## Abstract (arXiv)

We analyze nonlinearly preconditioned gradient methods for solving smooth minimization problems. We introduce a generalized smoothness property, based on the notion of abstract convexity, that is broader than Lipschitz smoothness and provide sufficient first- and second-order conditions. Notably, our framework encapsulates algorithms associated with the gradient clipping method and brings out novel insights for the class of (L0,L1)-smooth functions that has received widespread interest recently, thus allowing us to extend beyond already established methods. We investigate the convergence of the proposed method in both the convex and nonconvex setting.