# Set2Box: Similarity Preserving Representation Learning of Sets

arXiv: https://arxiv.org/abs/2210.03282 · HTML: https://mlsanity.com/paper/2210.03282/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 48 references that are in the map.
- First posted on arXiv 7 Oct 2022.

## Builds on (most cited first, 21 of 21)

- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Similarity-Preserving Knowledge Distillation](https://mlsanity.com/paper/1907.09682/) (2019)
- [Order Matters: Sequence to sequence for sets](https://mlsanity.com/paper/1511.06391/) (2015)
- [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020)
- [Node Similarity Preserving Graph Convolutional Networks](https://mlsanity.com/paper/2011.09643/) (2020)
- [BoxE: A Box Embedding Model for Knowledge Base Completion](https://mlsanity.com/paper/2007.06267/) (2020)
- [Probabilistic Embedding of Knowledge Graphs with Box Lattice Measures](https://mlsanity.com/paper/1805.06627/) (2018)
- [VERSE: Versatile Graph Embeddings from Similarity Measures](https://mlsanity.com/paper/1803.04742/) (2018)
- [Deep Supervised Discrete Hashing](https://mlsanity.com/paper/1705.10999/) (2017)
- [Differentiable Product Quantization for End-to-End Embedding Compression](https://mlsanity.com/paper/1908.09756/) (2019)
- [Modeling Fine-Grained Entity Types with Box Embeddings](https://mlsanity.com/paper/2101.00345/) (2021)
- [Improving Local Identifiability in Probabilistic Box Embeddings](https://mlsanity.com/paper/2010.04831/) (2020)
- [Self-supervised Product Quantization for Deep Unsupervised Image Retrieval](https://mlsanity.com/paper/2109.02244/) (2021)
- [Probabilistic Box Embeddings for Uncertain Knowledge Graph Reasoning](https://mlsanity.com/paper/2104.04597/) (2021)
- [End-to-End Supervised Product Quantization for Image Search and Retrieval](https://mlsanity.com/paper/1711.08589/) (2017)
- [Predicting Visual Overlap of Images Through Interpretable Non-Metric Box Embeddings](https://mlsanity.com/paper/2008.05785/) (2020)
- [Unsupervised Neural Quantization for Compressed-Domain Similarity Search](https://mlsanity.com/paper/1908.03883/) (2019)
- [Learning K-way D-dimensional Discrete Codes for Compact Embedding Representations](https://mlsanity.com/paper/1806.09464/) (2018)
- [Efficient Pairwise Neuroimage Analysis using the Soft Jaccard Index and 3D Keypoint Sets](https://mlsanity.com/paper/2103.06966/) (2021)
- [Learning User Representations with Hypercuboids for Recommender Systems](https://mlsanity.com/paper/2011.05742/) (2020)

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

- [Distributionally Robust Set Representation Learning Under Inference-Time Element Corruption](https://mlsanity.com/paper/2605.30089/) (2026)

## Abstract (arXiv)

Sets have been used for modeling various types of objects (e.g., a document as the set of keywords in it and a customer as the set of the items that she has purchased). Measuring similarity (e.g., Jaccard Index) between sets has been a key building block of a wide range of applications, including, plagiarism detection, recommendation, and graph compression. However, as sets have grown in numbers and sizes, the computational cost and storage required for set similarity computation have become substantial, and this has led to the development of hashing and sketching based solutions. In this work, we propose Set2Box, a learning-based approach for compressed representations of sets from which various similarity measures can be estimated accurately in constant time. The key idea is to represent sets as boxes to precisely capture overlaps of sets. Additionally, based on the proposed box quantization scheme, we design Set2Box+, which yields more concise but more accurate box representations of sets. Through extensive experiments on 8 real-world datasets, we show that, compared to baseline approaches, Set2Box+ is (a) Accurate: achieving up to 40.8X smaller estimation error while requiring 60% fewer bits to encode sets, (b) Concise: yielding up to 96.8X more concise representations with similar estimation error, and (c) Versatile: enabling the estimation of four set-similarity measures from a single representation of each set.