# Learning Wasserstein Embeddings

arXiv: https://arxiv.org/abs/1710.07457 · HTML: https://mlsanity.com/paper/1710.07457/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2017.

## Built on by (most cited first, 26 of 26)

- [Can Push-forward Generative Models Fit Multimodal Distributions?](https://mlsanity.com/paper/2206.14476/) (2022)
- [Meta Optimal Transport](https://mlsanity.com/paper/2206.05262/) (2022)
- [Curriculum Reinforcement Learning using Optimal Transport via Gradual Domain Adaptation](https://mlsanity.com/paper/2210.10195/) (2022)
- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [Wasserstein Task Embedding for Measuring Task Similarities](https://mlsanity.com/paper/2208.11726/) (2022)
- [Learning Generalized Gumbel-max Causal Mechanisms](https://mlsanity.com/paper/2111.06888/) (2021)
- [Wasserstein Wormhole: Scalable Optimal Transport Distance with Transformers](https://mlsanity.com/paper/2404.09411/) (2024)
- [SLOSH: Set LOcality Sensitive Hashing via Sliced-Wasserstein Embeddings](https://mlsanity.com/paper/2112.05872/) (2021)
- [Neural Embedding: Learning the Embedding of the Manifold of Physics Data](https://mlsanity.com/paper/2208.05484/) (2022)
- [Federated Wasserstein Distance](https://mlsanity.com/paper/2310.01973/) (2023)
- [Learning to Generate Wasserstein Barycenters](https://mlsanity.com/paper/2102.12178/) (2021)
- [On the Benefit of Optimal Transport for Curriculum Reinforcement Learning](https://mlsanity.com/paper/2309.14091/) (2023)
- [Bisimulation Metrics are Optimal Transport Distances, and Can be Computed Efficiently](https://mlsanity.com/paper/2406.04056/) (2024)
- [Fast Estimation of Wasserstein Distances via Regression on Sliced Wasserstein Distances](https://mlsanity.com/paper/2509.20508/) (2025)
- [Neural approximation of Wasserstein distance via a universal architecture for symmetric and factorwise group invariant functions](https://mlsanity.com/paper/2308.00273/) (2023)
- [Gromov-Wasserstein-like Distances in the Gaussian Mixture Models Space](https://mlsanity.com/paper/2310.11256/) (2023)
- [Interpolation for Robust Learning: Data Augmentation on Wasserstein Geodesics](https://mlsanity.com/paper/2302.02092/) (2023)
- [Manifold embedding data-driven mechanics](https://mlsanity.com/paper/2112.09842/) (2021)
- [Learning representations that are closed-form Monge mapping optimal with application to domain adaptation](https://mlsanity.com/paper/2305.07500/) (2023)
- [Amortized Optimal Transport from Sliced Potentials](https://mlsanity.com/paper/2604.15114/) (2026)
- [Approximating DTW with a convolutional neural network on EEG data](https://mlsanity.com/paper/2301.12873/) (2023)
- [When Sample Selection Bias Precipitates Model Collapse](https://mlsanity.com/paper/2606.13732/) (2026)
- [CLAMS: A System for Zero-Shot Model Selection for Clustering](https://mlsanity.com/paper/2407.11286/) (2024)
- [Wasserstein Hypergraph Neural Network](https://mlsanity.com/paper/2506.09682/) (2025)
- [Data Valuation and Selection in a Federated Model Marketplace](https://mlsanity.com/paper/2509.18104/) (2025)
- [How to Find and Reuse Policies for Continuous Adaptation in Lifelong Reinforcement Learning](https://mlsanity.com/paper/2610.03119/) (2026)

## Abstract (arXiv)

The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain adaptation, dimensionality reduction or generative models. However, its use is still limited by a heavy computational cost. Our goal is to alleviate this problem by providing an approximation mechanism that allows to break its inherent complexity. It relies on the search of an embedding where the Euclidean distance mimics the Wasserstein distance. We show that such an embedding can be found with a siamese architecture associated with a decoder network that allows to move from the embedding space back to the original input space. Once this embedding has been found, computing optimization problems in the Wasserstein space (e.g. barycenters, principal directions or even archetypes) can be conducted extremely fast. Numerical experiments supporting this idea are conducted on image datasets, and show the wide potential benefits of our method.