# Geometric design of the tangent term in landing algorithms for orthogonality constraints

arXiv: https://arxiv.org/abs/2507.15638 · HTML: https://mlsanity.com/paper/2507.15638/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2025.

## Abstract (arXiv)

We propose a family a metrics over the set of full-rank n× p real matrices, and apply them to the landing framework for optimization under orthogonality constraints. The family of metrics we propose is a natural extension of the β-metric, defined on the Stiefel manifold.