# GammaE: Gamma Embeddings for Logical Queries on Knowledge Graphs arXiv: https://arxiv.org/abs/2210.15578 ยท HTML: https://mlsanity.com/paper/2210.15578/ ## Key facts - Cited by 21 papers in the map (data through 14 Oct 2026). - Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning. - Builds on 19 of its 41 references that are in the map. - First posted on arXiv 27 Oct 2022. ## Placed in - LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/) ## Builds on (most cited first, 19 of 19) - [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014) - [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019) - [DeepPath: A Reinforcement Learning Method for Knowledge Graph Reasoning](https://mlsanity.com/paper/1707.06690/) (2017) - [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020) - [Beta Embeddings for Multi-Hop Logical Reasoning in Knowledge Graphs](https://mlsanity.com/paper/2010.11465/) (2020) - [Embedding Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/1806.01445/) (2018) - [Multi-Hop Knowledge Graph Reasoning with Reward Shaping](https://mlsanity.com/paper/1808.10568/) (2018) - [Complex Query Answering with Neural Link Predictors](https://mlsanity.com/paper/2011.03459/) (2020) - [ConE: Cone Embeddings for Multi-Hop Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2110.13715/) (2021) - [Probabilistic Embedding of Knowledge Graphs with Box Lattice Measures](https://mlsanity.com/paper/1805.06627/) (2018) - [Traversing Knowledge Graphs in Vector Space](https://mlsanity.com/paper/1506.01094/) (2015) - [Knowledge Graph Embedding with Iterative Guidance from Soft Rules](https://mlsanity.com/paper/1711.11231/) (2017) - [Improving Local Identifiability in Probabilistic Box Embeddings](https://mlsanity.com/paper/2010.04831/) (2020) - [Answering Complex Queries in Knowledge Graphs with Bidirectional Sequence Encoders](https://mlsanity.com/paper/2004.02596/) (2020) - [Probabilistic Entity Representation Model for Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2110.13522/) (2021) - [Query2Particles: Knowledge Graph Reasoning with Particle Embeddings](https://mlsanity.com/paper/2204.12847/) (2022) - [Query Embedding on Hyper-relational Knowledge Graphs](https://mlsanity.com/paper/2106.08166/) (2021) - [Probabilistic Box Embeddings for Uncertain Knowledge Graph Reasoning](https://mlsanity.com/paper/2104.04597/) (2021) - [SMORE: Knowledge Graph Completion and Multi-hop Reasoning in Massive Knowledge Graphs](https://mlsanity.com/paper/2110.14890/) (2021) ## Built on by (most cited first, 21 of 21) - [Neural Graph Reasoning: Complex Logical Query Answering Meets Graph Databases](https://mlsanity.com/paper/2303.14617/) (2023) - [Complex Query Answering on Eventuality Knowledge Graph with Implicit Logical Constraints](https://mlsanity.com/paper/2305.19068/) (2023) - [Wasserstein-Fisher-Rao Embedding: Logical Query Embeddings with Local Comparison and Global Transport](https://mlsanity.com/paper/2305.04034/) (2023) - [Sequential Query Encoding For Complex Query Answering on Knowledge Graphs](https://mlsanity.com/paper/2302.13114/) (2023) - [Rethinking Complex Queries on Knowledge Graphs with Neural Link Predictors](https://mlsanity.com/paper/2304.07063/) (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) - [Effective Instruction Parsing Plugin for Complex Logical Query Answering on Knowledge Graphs](https://mlsanity.com/paper/2410.20321/) (2024) - [Knowledge Graphs Querying](https://mlsanity.com/paper/2305.14485/) (2023) - [Privacy-Preserved Neural Graph Databases](https://mlsanity.com/paper/2312.15591/) (2023) - [Conditional Logical Message Passing Transformer for Complex Query Answering](https://mlsanity.com/paper/2402.12954/) (2024) - [Learning Federated Neural Graph Databases for Answering Complex Queries from Distributed Knowledge Graphs](https://mlsanity.com/paper/2402.14609/) (2024) - [From axioms over graphs to vectors, and back again: evaluating the properties of graph-based ontology embeddings](https://mlsanity.com/paper/2303.16519/) (2023) - [Improving Multi-hop Logical Reasoning in Knowledge Graphs with Context-Aware Query Representation Learning](https://mlsanity.com/paper/2406.07034/) (2024) - [Extending Complex Logical Queries on Uncertain Knowledge Graphs](https://mlsanity.com/paper/2403.01508/) (2024) - [HyperMono: A Monotonicity-aware Approach to Hyper-Relational Knowledge Representation](https://mlsanity.com/paper/2404.09848/) (2024) - [GluMarker: A Novel Predictive Modeling of Glycemic Control Through Digital Biomarkers](https://mlsanity.com/paper/2404.12605/) (2024) - [NGDB-Zoo: Towards Efficient and Scalable Neural Graph Databases Training](https://mlsanity.com/paper/2602.21597/) (2026) - [Pathformer: Recursive Path Query Encoding for Complex Logical Query Answering](https://mlsanity.com/paper/2406.14880/) (2024) - [Efficient and Scalable Neural Symbolic Search for Knowledge Graph Complex Query Answering](https://mlsanity.com/paper/2505.08155/) (2025) - [Neural Scalable Symbolic Search Framework for Complex Logical Queries with Multiple Free Variables](https://mlsanity.com/paper/2605.25985/) (2026) ## Abstract (arXiv) Embedding knowledge graphs (KGs) for multi-hop logical reasoning is a challenging problem due to massive and complicated structures in many KGs. Recently, many promising works projected entities and queries into a geometric space to efficiently find answers. However, it remains challenging to model the negation and union operator. The negation operator has no strict boundaries, which generates overlapped embeddings and leads to obtaining ambiguous answers. An additional limitation is that the union operator is non-closure, which undermines the model to handle a series of union operators. To address these problems, we propose a novel probabilistic embedding model, namely Gamma Embeddings (GammaE), for encoding entities and queries to answer different types of FOL queries on KGs. We utilize the linear property and strong boundary support of the Gamma distribution to capture more features of entities and queries, which dramatically reduces model uncertainty. Furthermore, GammaE implements the Gamma mixture method to design the closed union operator. The performance of GammaE is validated on three large logical query datasets. Experimental results show that GammaE significantly outperforms state-of-the-art models on public benchmarks.