# Revisiting invariances and introducing priors in Gromov-Wasserstein distances

arXiv: https://arxiv.org/abs/2307.10093 · HTML: https://mlsanity.com/paper/2307.10093/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 19 Jul 2023.

## Builds on (most cited first, 10 of 10)

- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Caffe: Convolutional Architecture for Fast Feature Embedding](https://mlsanity.com/paper/1408.5093/) (2014)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [Geometric Dataset Distances via Optimal Transport](https://mlsanity.com/paper/2002.02923/) (2020)
- [Linear-Time Gromov Wasserstein Distances using Low Rank Couplings and Costs](https://mlsanity.com/paper/2106.01128/) (2021)
- [Learning Generative Models across Incomparable Spaces](https://mlsanity.com/paper/1905.05461/) (2019)
- [Cross-Domain Imitation Learning via Optimal Transport](https://mlsanity.com/paper/2110.03684/) (2021)
- [CO-Optimal Transport](https://mlsanity.com/paper/2002.03731/) (2020)
- [Quantized Gromov-Wasserstein](https://mlsanity.com/paper/2104.02013/) (2021)

## Built on by (most cited first, 1 of 1)

- [Identifying Sub-networks in Neural Networks via Functionally Similar Representations](https://mlsanity.com/paper/2410.16484/) (2024)

## Abstract (arXiv)

Gromov-Wasserstein distance has found many applications in machine learning due to its ability to compare measures across metric spaces and its invariance to isometric transformations. However, in certain applications, this invariance property can be too flexible, thus undesirable. Moreover, the Gromov-Wasserstein distance solely considers pairwise sample similarities in input datasets, disregarding the raw feature representations. We propose a new optimal transport-based distance, called Augmented Gromov-Wasserstein, that allows for some control over the level of rigidity to transformations. It also incorporates feature alignments, enabling us to better leverage prior knowledge on the input data for improved performance. We present theoretical insights into the proposed metric. We then demonstrate its usefulness for single-cell multi-omic alignment tasks and a transfer learning scenario in machine learning.