Unlocking Better Knowledge Graph Reasoning: The CrossE Model Explained

Abstract

CrossE proposes a knowledge‑graph reasoning algorithm that explicitly models the crossover interaction between entities and relations. It learns both a universal embedding for each entity and relation and multiple interaction‑specific embeddings, enabling more accurate link prediction and providing interpretable explanations.

Research Background

Knowledge graphs store facts as triples (head entity, relation, tail entity) and are used in many AI tasks such as search, QA, and recommendation. Existing embedding methods (e.g., RESCAL, TransE, NTN, DistMult) map entities and relations to vector spaces but largely ignore the crossover interaction that occurs during relation inference.

Crossover Interaction

The crossover interaction refers to the mutual influence between entities and relations during inference: the predicted relation guides the selection of relevant entity information, and the entity’s information influences which inference paths for the relation are viable. This phenomenon is illustrated in the diagram below.

Algorithm Description

CrossE learns a universal embedding matrix E for entities, a relation embedding matrix R, and an interaction matrix C that provides a relation‑specific interaction vector c_r. For a given triple (h, r, ?), the head embedding h interacts with c_r to produce an interaction‑enhanced head embedding, while the relation embedding r interacts with both h and c_r. The resulting vectors are combined with a bias term and passed through an activation function to predict the tail entity embedding, which is then scored against the true tail.

The model is trained with a log‑likelihood loss. Although many interaction embeddings are generated, the only additional learnable parameters come from the interaction matrix C.

Experiments

We evaluate CrossE on link prediction and explanation quality. For link prediction, we test on three standard datasets: WN18, FB15k, and FB15k‑237. CrossE achieves notable improvements on the challenging FB15k and FB15k‑237 datasets, as shown in the tables below.

For explanation evaluation, we define six analogy‑structure types and measure two metrics: Recall (the proportion of predictions that can be explained) and AvgSupport (the average number of supporting analogical structures). CrossE attains higher Recall and AvgSupport than baselines, indicating superior explanatory power.

We also present representative explanation instances of the six analogy structures derived from CrossE’s results on FB15k‑237.

Conclusion

Crossover interaction is a pervasive phenomenon in knowledge‑graph reasoning and should be captured explicitly. CrossE demonstrates that modeling this interaction improves reasoning accuracy, especially on challenging datasets, and also enhances the model’s ability to provide interpretable explanations. The study highlights that predictive performance and explanatory capability are distinct evaluation dimensions, offering new insights for future research.