# Answering Compositional Queries with Set-Theoretic Embeddings

arXiv: https://arxiv.org/abs/2306.04133 · HTML: https://mlsanity.com/paper/2306.04133/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 24 references that are in the map.
- First posted on arXiv 7 Jun 2023.

## Builds on (most cited first, 13 of 13)

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Measuring Compositional Generalization: A Comprehensive Method on Realistic Data](https://mlsanity.com/paper/1912.09713/) (2019)
- [COGS: A Compositional Generalization Challenge Based on Semantic Interpretation](https://mlsanity.com/paper/2010.05465/) (2020)
- [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020)
- [Linear Algebraic Structure of Word Senses, with Applications to Polysemy](https://mlsanity.com/paper/1601.03764/) (2016)
- [Hyperbolic Entailment Cones for Learning Hierarchical Embeddings](https://mlsanity.com/paper/1804.01882/) (2018)
- [Order-Embeddings of Images and Language](https://mlsanity.com/paper/1511.06361/) (2015)
- [Word Representations via Gaussian Embedding](https://mlsanity.com/paper/1412.6623/) (2014)
- [Probabilistic Embedding of Knowledge Graphs with Box Lattice Measures](https://mlsanity.com/paper/1805.06627/) (2018)
- [Neural Embeddings of Graphs in Hyperbolic Space](https://mlsanity.com/paper/1705.10359/) (2017)
- [Improving Local Identifiability in Probabilistic Box Embeddings](https://mlsanity.com/paper/2010.04831/) (2020)
- [Word2Box: Capturing Set-Theoretic Semantics of Words using Box Embeddings](https://mlsanity.com/paper/2106.14361/) (2021)
- [Faithful Embeddings for Knowledge Base Queries](https://mlsanity.com/paper/2004.03658/) (2020)

## Abstract (arXiv)

The need to compactly and robustly represent item-attribute relations arises in many important tasks, such as faceted browsing and recommendation systems. A popular machine learning approach for this task denotes that an item has an attribute by a high dot-product between vectors for the item and attribute -- a representation that is not only dense, but also tends to correct noisy and incomplete data. While this method works well for queries retrieving items by a single attribute (such as movies that are comedies), we find that vector embeddings do not so accurately support compositional queries (such as movies that are comedies and British but not romances). To address these set-theoretic compositions, this paper proposes to replace vectors with box embeddings, a region-based representation that can be thought of as learnable Venn diagrams. We introduce a new benchmark dataset for compositional queries, and present experiments and analysis providing insights into the behavior of both. We find that, while vector and box embeddings are equally suited to single attribute queries, for compositional queries box embeddings provide substantial advantages over vectors, particularly at the moderate and larger retrieval set sizes that are most useful for users' search and browsing.