# Implicit regularization of normalized gradient descent

arXiv: https://arxiv.org/abs/2602.08177 · HTML: https://mlsanity.com/paper/2602.08177/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2026.

## Built on by (most cited first, 1 of 1)

- [Learning in Continuous Games from Pairwise Preference Feedback](https://mlsanity.com/paper/2610.05428/) (2026)

## Abstract (arXiv)

How to find flat minima? We propose running normalized gradient descent, usually reserved for nonsmooth optimization, with sufficiently slowly diminishing step sizes. This induces implicit regularization towards flat minima if an appropriate Lyapunov functions exists in the gradient dynamics. Our analysis shows that implicit regularization is intrinsically a question of nonsmooth analysis, for which we deploy the full power of variational analysis and stratification theory.