# Box Embeddings: An open-source library for representation learning using geometric structures

arXiv: https://arxiv.org/abs/2109.04997 · HTML: https://mlsanity.com/paper/2109.04997/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 30 references that are in the map.
- First posted on arXiv 10 Sep 2021.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (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)
- [Hierarchical Graph Network for Multi-hop Question Answering](https://mlsanity.com/paper/1911.03631/) (2019)
- [Probabilistic Embedding of Knowledge Graphs with Box Lattice Measures](https://mlsanity.com/paper/1805.06627/) (2018)
- [Improving Natural Language Inference Using External Knowledge in the Science Questions Domain](https://mlsanity.com/paper/1809.05724/) (2018)
- [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)
- [Probabilistic Box Embeddings for Uncertain Knowledge Graph Reasoning](https://mlsanity.com/paper/2104.04597/) (2021)
- [Hierarchical Density Order Embeddings](https://mlsanity.com/paper/1804.09843/) (2018)
- [Joint Learning of Hyperbolic Label Embeddings for Hierarchical Multi-label Classification](https://mlsanity.com/paper/2101.04997/) (2021)
- [Incorporating Domain Knowledge into Medical NLI using Knowledge Graphs](https://mlsanity.com/paper/1909.00160/) (2019)
- [Neighborhood Growth Determines Geometric Priors for Relational Representation Learning](https://mlsanity.com/paper/1910.05565/) (2019)

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

- [Interpretable Text Embeddings and Text Similarity Explanation: A Survey](https://mlsanity.com/paper/2502.14862/) (2025)
- [Representing Spatial Trajectories as Distributions](https://mlsanity.com/paper/2210.01322/) (2022)
- [Hierarchical Retrieval: The Geometry and a Pretrain-Finetune Recipe](https://mlsanity.com/paper/2509.16411/) (2025)
- [Task2Box: Box Embeddings for Modeling Asymmetric Task Relationships](https://mlsanity.com/paper/2403.17173/) (2024)
- [TaxoBell: Gaussian Box Embeddings for Self-Supervised Taxonomy Expansion](https://mlsanity.com/paper/2601.09633/) (2026)
- [Insert or Attach: Taxonomy Completion via Box Embedding](https://mlsanity.com/paper/2305.11004/) (2023)
- [Graph Neural Network based Hierarchy-Aware Embeddings of Knowledge Graphs: Applications to Yeast Phenotype Prediction](https://mlsanity.com/paper/2605.03690/) (2026)
- [Tutorial on Reasoning for IR & IR for Reasoning](https://mlsanity.com/paper/2602.03640/) (2026)
- [Hierarchy-Aware Semantic Losses for Knowledge Graph Link Prediction](https://mlsanity.com/paper/2608.22981/) (2026)

## Abstract (arXiv)

A major factor contributing to the success of modern representation learning is the ease of performing various vector operations. Recently, objects with geometric structures (eg. distributions, complex or hyperbolic vectors, or regions such as cones, disks, or boxes) have been explored for their alternative inductive biases and additional representational capacities. In this work, we introduce Box Embeddings, a Python library that enables researchers to easily apply and extend probabilistic box embeddings.