# On the geometry of flat minima

arXiv: https://arxiv.org/abs/2509.11386 · HTML: https://mlsanity.com/paper/2509.11386/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2025.

## Built on by (most cited first, 2 of 2)

- [Sharpness of Minima in Deep Matrix Factorization](https://mlsanity.com/paper/2509.25783/) (2025)
- [On the Loss Landscape Geometry of Regularized Deep Matrix Factorization: Uniqueness and Sharpness](https://mlsanity.com/paper/2603.27072/) (2026)

## Abstract (arXiv)

What does it mean to be flat? We propose to define it by measuring the maximal variation around a point, or from a dual perspective, the distance to neighboring level sets. After developing some calculus rules, we show how flat minima, conservation laws, and symmetries are intertwined. Gradient flows of conserved quantities are of particular interest, due to their flattening properties.