# SLOSH: Set LOcality Sensitive Hashing via Sliced-Wasserstein Embeddings

arXiv: https://arxiv.org/abs/2112.05872 · HTML: https://mlsanity.com/paper/2112.05872/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 78 references that are in the map.
- First posted on arXiv 11 Dec 2021.

## Builds on (most cited first, 30 of 38)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Fine-tuning CNN Image Retrieval with No Human Annotation](https://mlsanity.com/paper/1711.02512/) (2017)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Sliced Wasserstein Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1903.04064/) (2019)
- [DeepJDOT: Deep Joint Distribution Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1803.10081/) (2018)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [Geometric Dataset Distances via Optimal Transport](https://mlsanity.com/paper/2002.02923/) (2020)
- [Wasserstein Weisfeiler-Lehman Graph Kernels](https://mlsanity.com/paper/1906.01277/) (2019)
- [Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs](https://mlsanity.com/paper/1811.01900/) (2018)
- [Subspace Robust Wasserstein Distances](https://mlsanity.com/paper/1901.08949/) (2019)
- [On the Limitations of Representing Functions on Sets](https://mlsanity.com/paper/1901.09006/) (2019)
- [Wasserstein Adversarial Examples via Projected Sinkhorn Iterations](https://mlsanity.com/paper/1902.07906/) (2019)
- [Statistical and Topological Properties of Sliced Probability Divergences](https://mlsanity.com/paper/2003.05783/) (2020)
- [Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusions](https://mlsanity.com/paper/1806.08141/) (2018)
- [Sliced Wasserstein Kernels for Probability Distributions](https://mlsanity.com/paper/1511.03198/) (2015)
- [Wasserstein Embedding for Graph Learning](https://mlsanity.com/paper/2006.09430/) (2020)
- [FSPool: Learning Set Representations with Featurewise Sort Pooling](https://mlsanity.com/paper/1906.02795/) (2019)
- [Approximate Nearest Neighbor Search in High Dimensions](https://mlsanity.com/paper/1806.09823/) (2018)
- [Optimal Data-Dependent Hashing for Approximate Near Neighbors](https://mlsanity.com/paper/1501.01062/) (2015)
- [Cross-dimensional Weighting for Aggregated Deep Convolutional Features](https://mlsanity.com/paper/1512.04065/) (2015)
- [Deep CNNs Meet Global Covariance Pooling: Better Representation and Generalization](https://mlsanity.com/paper/1904.06836/) (2019)
- [Covariance Pooling For Facial Expression Recognition](https://mlsanity.com/paper/1805.04855/) (2018)
- [The Radon cumulative distribution transform and its application to image classification](https://mlsanity.com/paper/1511.03206/) (2015)

## Built on by (most cited first, 9 of 9)

- [Characterizing Out-of-Distribution Error via Optimal Transport](https://mlsanity.com/paper/2305.15640/) (2023)
- [Fourier Sliced-Wasserstein Embedding for Multisets and Measures](https://mlsanity.com/paper/2504.02544/) (2025)
- [Teaching Networks to Solve Optimization Problems](https://mlsanity.com/paper/2202.04104/) (2022)
- [Advances in Set Function Learning: A Survey of Techniques and Applications](https://mlsanity.com/paper/2501.14991/) (2025)
- [PTLp: Partial Transport Lp Distances](https://mlsanity.com/paper/2307.13571/) (2023)
- [Constrained Sliced Wasserstein Embedding](https://mlsanity.com/paper/2506.02203/) (2025)
- [Linear optimal transport subspaces for point set classification](https://mlsanity.com/paper/2403.10015/) (2024)
- [Sliced Inner Product Gromov-Wasserstein Distances](https://mlsanity.com/paper/2605.08546/) (2026)
- [Fourier Sliced-Wasserstein Embedding for Multisets and Measures](https://mlsanity.com/paper/2405.16519/) (2024)

## Abstract (arXiv)

Learning from set-structured data is an essential problem with many applications in machine learning and computer vision. This paper focuses on non-parametric and data-independent learning from set-structured data using approximate nearest neighbor (ANN) solutions, particularly locality-sensitive hashing. We consider the problem of set retrieval from an input set query. Such retrieval problem requires: 1) an efficient mechanism to calculate the distances/dissimilarities between sets, and 2) an appropriate data structure for fast nearest neighbor search. To that end, we propose Sliced-Wasserstein set embedding as a computationally efficient "set-2-vector" mechanism that enables downstream ANN, with theoretical guarantees. The set elements are treated as samples from an unknown underlying distribution, and the Sliced-Wasserstein distance is used to compare sets. We demonstrate the effectiveness of our algorithm, denoted as Set-LOcality Sensitive Hashing (SLOSH), on various set retrieval datasets and compare our proposed embedding with standard set embedding approaches, including Generalized Mean (GeM) embedding/pooling, Featurewise Sort Pooling (FSPool), and Covariance Pooling and show consistent improvement in retrieval results. The code for replicating our results is available here: hrefhttps://github.com/mint-vu/SLOSHhttps://github.com/mint-vu/SLOSH.