# Special Lagrangian cones in Deep Learning

arXiv: https://arxiv.org/abs/2609.20159 · HTML: https://mlsanity.com/paper/2609.20159/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 14 references that are in the map.
- First posted on arXiv 17 Sep 2026.

## Builds on (most cited first, 4 of 4)

- [On the Optimization of Deep Networks: Implicit Acceleration by Overparameterization](https://mlsanity.com/paper/1802.06509/) (2018)
- [The geometry of the deep linear network](https://mlsanity.com/paper/2411.09004/) (2024)
- [An entropy formula for the Deep Linear Network](https://mlsanity.com/paper/2509.09088/) (2025)
- [Regularization Implies balancedness in the deep linear network](https://mlsanity.com/paper/2511.01137/) (2025)

## Abstract (arXiv)

We introduce a matrix generalization of the cone of Harvey and Lawson and prove that it is an exact special Lagrangian manifold. We further show that it belongs to a family of exact special Lagrangian manifolds that foliate the balanced manifold arising in deep learning.