SpherE: Expressive and Interpretable Knowledge Graph Embedding for Set Retrieval

TL;DR

The paper introduces Knowledge Graph Set Retrieval and proposes SpherE, a model that embeds entities as spheres and relations as rotations to produce exact answer sets rather than ranked lists. By interpreting the sphere radii as entity universality and using overlapping transformed spheres to indicate factuality, SpherE achieves expressive modeling of one-to-many, many-to-one, and many-to-many relations while maintaining interpretability. Across FB15K237 and WN18RR, SpherE variants outperform rotation- and box-based baselines on set retrieval metrics and retain competitive link inference, with radii aligning with entity frequency. This approach offers a principled, interpretable alternative for precise KG querying with practical impact on bioinformatics and other domains requiring exact answer sets.

Abstract

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.

Figures (2)

• Figure 1: Illustration of Rotational-based embedding methods (left) and SpherE (right) in 2D Euclidean space. The user asks the tail query $(Max\_Born, advised, ?)$. In the KG, $Robert\_Oppenheimer, Pascual\_Jordan$, or $Carl\_Hermann$ are correct answers to this query, but $Geoffrey\_Hinton$ is not. While the left returns a ranked list of all entities in the KG and disproportionately ranks incorrect answers highly, our SpherE method returns a set that exclusively comprises all correct tail entities. The radius of each sphere is learned.
• Figure 2: The relation between radius and occurrence count.

Theorems & Definitions (3)

• theorem 1
• theorem 2
• theorem 3