# Self-Supervised Hyperboloid Representations from Logical Queries over Knowledge Graphs

arXiv: https://arxiv.org/abs/2012.13023 · HTML: https://mlsanity.com/paper/2012.13023/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2020.

## Built on by (most cited first, 30 of 35)

- [Neural-Symbolic Models for Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/2205.10128/) (2022)
- [Pseudo-Riemannian Graph Convolutional Networks](https://mlsanity.com/paper/2106.03134/) (2021)
- [Answering Complex Logical Queries on Knowledge Graphs via Query Computation Tree Optimization](https://mlsanity.com/paper/2212.09567/) (2022)
- [Probabilistic Entity Representation Model for Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2110.13522/) (2021)
- [Complex Logical Reasoning over Knowledge Graphs using Large Language Models](https://mlsanity.com/paper/2305.01157/) (2023)
- [Benchmarking the Combinatorial Generalizability of Complex Query Answering on Knowledge Graphs](https://mlsanity.com/paper/2109.08925/) (2021)
- [Graph Neural Networks: Methods, Applications, and Opportunities](https://mlsanity.com/paper/2108.10733/) (2021)
- [Wasserstein-Fisher-Rao Embedding: Logical Query Embeddings with Local Comparison and Global Transport](https://mlsanity.com/paper/2305.04034/) (2023)
- [Self-Supervised Graph Learning with Hyperbolic Embedding for Temporal Health Event Prediction](https://mlsanity.com/paper/2106.04751/) (2021)
- [Type-aware Embeddings for Multi-Hop Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2205.00782/) (2022)
- [TFLEX: Temporal Feature-Logic Embedding Framework for Complex Reasoning over Temporal Knowledge Graph](https://mlsanity.com/paper/2205.14307/) (2022)
- [Adapting Neural Link Predictors for Data-Efficient Complex Query Answering](https://mlsanity.com/paper/2301.12313/) (2023)
- [Sequential Query Encoding For Complex Query Answering on Knowledge Graphs](https://mlsanity.com/paper/2302.13114/) (2023)
- [Knowledge Graph Reasoning over Entities and Numerical Values](https://mlsanity.com/paper/2306.01399/) (2023)
- [Geometric Relational Embeddings: A Survey](https://mlsanity.com/paper/2304.11949/) (2023)
- [Is Complex Query Answering Really Complex?](https://mlsanity.com/paper/2410.12537/) (2024)
- [Effective Instruction Parsing Plugin for Complex Logical Query Answering on Knowledge Graphs](https://mlsanity.com/paper/2410.20321/) (2024)
- [Hyperbolic Graph Neural Networks at Scale: A Meta Learning Approach](https://mlsanity.com/paper/2310.18918/) (2023)
- [Conditional Logical Message Passing Transformer for Complex Query Answering](https://mlsanity.com/paper/2402.12954/) (2024)
- [HCGR: Hyperbolic Contrastive Graph Representation Learning for Session-based Recommendation](https://mlsanity.com/paper/2107.05366/) (2021)
- [FLEX: Feature-Logic Embedding Framework for CompleX Knowledge Graph Reasoning](https://mlsanity.com/paper/2205.11039/) (2022)
- [Towards Scalable Hyperbolic Neural Networks using Taylor Series Approximations](https://mlsanity.com/paper/2206.03610/) (2022)
- [Knowledge-enhanced Neural Machine Reasoning: A Review](https://mlsanity.com/paper/2302.02093/) (2023)
- [Analyzing Curriculum Learning for Sentiment Analysis along Task Difficulty, Pacing and Visualization Axes](https://mlsanity.com/paper/2102.09990/) (2021)
- [Poincar'e Heterogeneous Graph Neural Networks for Sequential Recommendation](https://mlsanity.com/paper/2205.11233/) (2022)
- [TAR: Neural Logical Reasoning across TBox and ABox](https://mlsanity.com/paper/2205.14591/) (2022)
- [A Unification Framework for Euclidean and Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/2206.04285/) (2022)
- [LogicRec: Recommendation with Users' Logical Requirements](https://mlsanity.com/paper/2304.11722/) (2023)
- [NGDB-Zoo: Towards Efficient and Scalable Neural Graph Databases Training](https://mlsanity.com/paper/2602.21597/) (2026)
- [Neural Reasoning for Robust Instance Retrieval in SHOIQ](https://mlsanity.com/paper/2510.20457/) (2025)

## Abstract (arXiv)

Knowledge Graphs (KGs) are ubiquitous structures for information storagein several real-world applications such as web search, e-commerce, social networks, and biology. Querying KGs remains a foundational and challenging problem due to their size and complexity. Promising approaches to tackle this problem include embedding the KG units (e.g., entities and relations) in a Euclidean space such that the query embedding contains the information relevant to its results. These approaches, however, fail to capture the hierarchical nature and semantic information of the entities present in the graph. Additionally, most of these approaches only utilize multi-hop queries (that can be modeled by simple translation operations) to learn embeddings and ignore more complex operations such as intersection and union of simpler queries. To tackle such complex operations, in this paper, we formulate KG representation learning as a self-supervised logical query reasoning problem that utilizes translation, intersection and union queries over KGs. We propose Hyperboloid Embeddings (HypE), a novel self-supervised dynamic reasoning framework, that utilizes positive first-order existential queries on a KG to learn representations of its entities and relations as hyperboloids in a Poincar'e ball. HypE models the positive first-order queries as geometrical translation, intersection, and union. For the problem of KG reasoning in real-world datasets, the proposed HypE model significantly outperforms the state-of-the art results. We also apply HypE to an anomaly detection task on a popular e-commerce website product taxonomy as well as hierarchically organized web articles and demonstrate significant performance improvements compared to existing baseline methods. Finally, we also visualize the learned HypE embeddings in a Poincar'e ball to clearly interpret and comprehend the representation space.