# The Gromov-Wasserstein distance between spheres

arXiv: https://arxiv.org/abs/2306.10586 · HTML: https://mlsanity.com/paper/2306.10586/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jun 2023.

## Built on by (most cited first, 6 of 6)

- [The Z-Gromov-Wasserstein Distance](https://mlsanity.com/paper/2408.08233/) (2024)
- [On Probabilistic Embeddings in Optimal Dimension Reduction](https://mlsanity.com/paper/2408.02433/) (2024)
- [Variational Graph Contrastive Learning](https://mlsanity.com/paper/2411.07150/) (2024)
- [Transfer Learning on Edge Connecting Probability Estimation under Graphon Model](https://mlsanity.com/paper/2510.05527/) (2025)
- [Note on computational complexity of the Gromov-Wasserstein distance](https://mlsanity.com/paper/2408.06525/) (2024)
- [Subgraph Gaussian Embedding Contrast for Self-Supervised Graph Representation Learning](https://mlsanity.com/paper/2505.23529/) (2025)

## Abstract (arXiv)

In this paper we consider a two-parameter family {dGWp,q}p,q of Gromov- Wasserstein distances between metric measure spaces. By exploiting a suitable interaction between specific values of the parameters p and q and the metric of the underlying spaces, we determine the exact value of the distance dGW4,2 between all pairs of unit spheres of different dimension endowed with their Euclidean distance and their uniform measure.