# Probabilistic Embedding of Knowledge Graphs with Box Lattice Measures

arXiv: https://arxiv.org/abs/1805.06627 · HTML: https://mlsanity.com/paper/1805.06627/

## Key facts

- Cited by 64 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 May 2018.

## Built on by (most cited first, 30 of 64)

- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)
- [Mask and Reason: Pre-Training Knowledge Graph Transformers for Complex Logical Queries](https://mlsanity.com/paper/2208.07638/) (2022)
- [Modeling Heterogeneous Hierarchies with Relation-specific Hyperbolic Cones](https://mlsanity.com/paper/2110.14923/) (2021)
- [Modeling Fine-Grained Entity Types with Box Embeddings](https://mlsanity.com/paper/2101.00345/) (2021)
- [Contextual Semantic Embeddings for Ontology Subsumption Prediction](https://mlsanity.com/paper/2202.09791/) (2022)
- [QUEST: A Retrieval Dataset of Entity-Seeking Queries with Implicit Set Operations](https://mlsanity.com/paper/2305.11694/) (2023)
- [Probabilistic Entity Representation Model for Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2110.13522/) (2021)
- [Faithiful Embeddings for EL++ Knowledge Bases](https://mlsanity.com/paper/2201.09919/) (2022)
- [Probabilistic Box Embeddings for Uncertain Knowledge Graph Reasoning](https://mlsanity.com/paper/2104.04597/) (2021)
- [GammaE: Gamma Embeddings for Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/2210.15578/) (2022)
- [FALCON: Fast Visual Concept Learning by Integrating Images, Linguistic descriptions, and Conceptual Relations](https://mlsanity.com/paper/2203.16639/) (2022)
- [Question Answering Infused Pre-training of General-Purpose Contextualized Representations](https://mlsanity.com/paper/2106.08190/) (2021)
- [Ultra-fine Entity Typing with Indirect Supervision from Natural Language Inference](https://mlsanity.com/paper/2202.06167/) (2022)
- [Rethinking Knowledge Graph Evaluation Under the Open-World Assumption](https://mlsanity.com/paper/2209.08858/) (2022)
- [ExpressivE: A Spatio-Functional Embedding For Knowledge Graph Completion](https://mlsanity.com/paper/2206.04192/) (2022)
- [Shrinking Embeddings for Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2306.02199/) (2023)
- [Ontology Embedding: A Survey of Methods, Applications and Resources](https://mlsanity.com/paper/2406.10964/) (2024)
- [Word2Box: Capturing Set-Theoretic Semantics of Words using Box Embeddings](https://mlsanity.com/paper/2106.14361/) (2021)
- [Box Embeddings: An open-source library for representation learning using geometric structures](https://mlsanity.com/paper/2109.04997/) (2021)
- [Geometric Relational Embeddings: A Survey](https://mlsanity.com/paper/2304.11949/) (2023)
- [A Unified Taxonomy-Guided Instruction Tuning Framework for Entity Set Expansion and Taxonomy Expansion](https://mlsanity.com/paper/2402.13405/) (2024)
- [Learning Visual Hierarchies in Hyperbolic Space for Image Retrieval](https://mlsanity.com/paper/2411.17490/) (2024)
- [PHyCLIP: ℓ1-Product of Hyperbolic Factors Unifies Hierarchy and Compositionality in Vision-Language Representation Learning](https://mlsanity.com/paper/2510.08919/) (2025)
- [Time in a Box: Advancing Knowledge Graph Completion with Temporal Scopes](https://mlsanity.com/paper/2111.06854/) (2021)
- [Concept2Box: Joint Geometric Embeddings for Learning Two-View Knowledge Graphs](https://mlsanity.com/paper/2307.01933/) (2023)
- [Representing Spatial Trajectories as Distributions](https://mlsanity.com/paper/2210.01322/) (2022)
- [Ontology Completion with Natural Language Inference and Concept Embeddings: An Analysis](https://mlsanity.com/paper/2403.17216/) (2024)
- [Self-supervised Topic Taxonomy Discovery in the Box Embedding Space](https://mlsanity.com/paper/2408.15050/) (2024)
- [Quasi-random Multi-Sample Inference for Large Language Models](https://mlsanity.com/paper/2411.06251/) (2024)
- [Hierarchical Retrieval: The Geometry and a Pretrain-Finetune Recipe](https://mlsanity.com/paper/2509.16411/) (2025)

## Abstract (arXiv)

Embedding methods which enforce a partial order or lattice structure over the concept space, such as Order Embeddings (OE) (Vendrov et al., 2016), are a natural way to model transitive relational data (e.g. entailment graphs). However, OE learns a deterministic knowledge base, limiting expressiveness of queries and the ability to use uncertainty for both prediction and learning (e.g. learning from expectations). Probabilistic extensions of OE (Lai and Hockenmaier, 2017) have provided the ability to somewhat calibrate these denotational probabilities while retaining the consistency and inductive bias of ordered models, but lack the ability to model the negative correlations found in real-world knowledge. In this work we show that a broad class of models that assign probability measures to OE can never capture negative correlation, which motivates our construction of a novel box lattice and accompanying probability measure to capture anticorrelation and even disjoint concepts, while still providing the benefits of probabilistic modeling, such as the ability to perform rich joint and conditional queries over arbitrary sets of concepts, and both learning from and predicting calibrated uncertainty. We show improvements over previous approaches in modeling the Flickr and WordNet entailment graphs, and investigate the power of the model.