# Gromov-Wasserstein at Scale, Beyond Squared Norms

arXiv: https://arxiv.org/abs/2602.06658 · HTML: https://mlsanity.com/paper/2602.06658/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2026.

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

- [On sparsity, extremal structure, and monotonicity properties of Wasserstein and Gromov-Wasserstein optimal transport plans](https://mlsanity.com/paper/2602.16265/) (2026)
- [Gromov-Wasserstein Quantization and Clustering: Structure, Rates, and Algorithms](https://mlsanity.com/paper/2608.11016/) (2026)
- [Averaged Mirror Descent and Dual Gradient Methods: Convergent Algorithms for Entropic Gromov-Wasserstein Problems](https://mlsanity.com/paper/2609.31848/) (2026)
- [A Unified Dual Method for Matching Problems](https://mlsanity.com/paper/2609.39339/) (2026)

## Abstract (arXiv)

A fundamental challenge in data science is to match disparate point sets with each other. While optimal transport efficiently minimizes point displacements under a bijectivity constraint, it is inherently sensitive to rotations. Conversely, minimizing distortions via the Gromov-Wasserstein (GW) framework addresses this limitation but introduces a non-convex, computationally demanding optimization problem. In this work, we identify a broad class of distortion penalties that reduce to a simple alignment problem within a lifted feature space. Leveraging this insight, we introduce an iterative GW solver with a linear memory footprint and quadratic (rather than cubic) time complexity. Our method is differentiable, comes with strong theoretical guarantees, and scales to hundreds of thousands of points in minutes. This efficiency unlocks a wide range of geometric applications and enables the exploration of the GW energy landscape, whose local minima encode the symmetries of the matching problem.