# SpherE: Expressive and Interpretable Knowledge Graph Embedding for Set Retrieval

arXiv: https://arxiv.org/abs/2404.19130 · HTML: https://mlsanity.com/paper/2404.19130/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 39 references that are in the map.
- First posted on arXiv 29 Apr 2024.

## Builds on (most cited first, 15 of 15)

- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [A Survey on Knowledge Graphs: Representation, Acquisition and Applications](https://mlsanity.com/paper/2002.00388/) (2020)
- [SimplE Embedding for Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/1802.04868/) (2018)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [Knowledge Graph Embedding for Link Prediction: A Comparative Analysis](https://mlsanity.com/paper/2002.00819/) (2020)
- [A Semantic Matching Energy Function for Learning with Multi-relational Data](https://mlsanity.com/paper/1301.3485/) (2013)
- [Leveraging Knowledge Bases in LSTMs for Improving Machine Reading](https://mlsanity.com/paper/1902.09091/) (2019)
- [TorusE: Knowledge Graph Embedding on a Lie Group](https://mlsanity.com/paper/1711.05435/) (2017)
- [HousE: Knowledge Graph Embedding with Householder Parameterization](https://mlsanity.com/paper/2202.07919/) (2022)
- [Probabilistic Reasoning via Deep Learning: Neural Association Models](https://mlsanity.com/paper/1603.07704/) (2016)
- [KompaRe: A Knowledge Graph Comparative Reasoning System](https://mlsanity.com/paper/2011.03189/) (2020)
- [Re-thinking Knowledge Graph Completion Evaluation from an Information Retrieval Perspective](https://mlsanity.com/paper/2205.04105/) (2022)

## Built on by (most cited first, 8 of 8)

- [Language in the Flow of Time: Time-Series-Paired Texts Weaved into a Unified Temporal Narrative](https://mlsanity.com/paper/2502.08942/) (2025)
- [Pave Your Own Path: Graph Gradual Domain Adaptation on Fused Gromov-Wasserstein Geodesics](https://mlsanity.com/paper/2505.12709/) (2025)
- [PageRank Bandits for Link Prediction](https://mlsanity.com/paper/2411.01410/) (2024)
- [Can Graph Neural Networks Learn Language with Extremely Weak Text Supervision?](https://mlsanity.com/paper/2412.08174/) (2024)
- [APEX2: Adaptive and Extreme Summarization for Personalized Knowledge Graphs](https://mlsanity.com/paper/2412.17336/) (2024)
- [Hypergraphs as Weighted Directed Self-Looped Graphs: Spectral Properties, Clustering, Cheeger Inequality](https://mlsanity.com/paper/2411.03331/) (2024)
- [DuetGraph: Coarse-to-Fine Knowledge Graph Reasoning with Dual-Pathway Global-Local Fusion](https://mlsanity.com/paper/2507.11229/) (2025)
- [Graph is a Natural Regularization: Revisiting Vector Quantization for Graph Representation Learning](https://mlsanity.com/paper/2508.06588/) (2025)

## Abstract (arXiv)

Knowledge graphs (KGs), which store an extensive number of relational facts (head, relation, tail), serve various applications. While many downstream tasks highly rely on the expressive modeling and predictive embedding of KGs, most of the current KG representation learning methods, where each entity is embedded as a vector in the Euclidean space and each relation is embedded as a transformation, follow an entity ranking protocol. On one hand, such an embedding design cannot capture many-to-many relations. On the other hand, in many retrieval cases, the users wish to get an exact set of answers without any ranking, especially when the results are expected to be precise, e.g., which genes cause an illness. Such scenarios are commonly referred to as "set retrieval". This work presents a pioneering study on the KG set retrieval problem. We show that the set retrieval highly depends on expressive modeling of many-to-many relations, and propose a new KG embedding model SpherE to address this problem. SpherE is based on rotational embedding methods, but each entity is embedded as a sphere instead of a vector. While inheriting the high interpretability of rotational-based models, our SpherE can more expressively model one-to-many, many-to-one, and many-to-many relations. Through extensive experiments, we show that our SpherE can well address the set retrieval problem while still having a good predictive ability to infer missing facts. The code is available at https://github.com/Violet24K/SpherE.