LollipopE: Bi-centered lollipop embedding for complex logic query on knowledge graph.

Answering complex First-Order Logic (FOL) query plays a vital role in multi-hop knowledge graph (KG) reasoning. Geometric methods have emerged as a promising category of approaches in this context. However, existing best-performing geometric query embedding (QE) model is still up against three-fold potential problems: (i) underutilization of embedding space, (ii) overreliance on angle information, (iii) uncaptured hierarchy structure. To bridge the gap, we propose a lollipop-like bi-centered query embedding method named LollipopE. To fully utilize embedding space, LollipopE employs learnable centroid positions to represent multiple entities distributed along the same axis. To address the potential overreliance on angular metrics, we design an angular-based and centroid-based metric. This involves calculating both an angular distance and a centroid-based geodesic distance, which empowers the model to make more informed selections of relevant answers from a wider perspective. To effectively capture the hierarchical relationships among entities within the KG, we incorporate dynamic moduli, which allows for the representation of the hierarchical structure among entities. Extensive experiments demonstrate that LollipopE surpasses the state-of-the-art geometric methods. Especially, on more hierarchical datasets, LollipopE achieves the most significant improvement.