Arbitrary Time Information Modeling via Polynomial Approximation for Temporal Knowledge Graph Embedding

TL;DR

This work addresses the challenge of modeling arbitrarily evolving time information in temporal knowledge graphs by introducing PTBox, which fuses polynomial decomposition-based temporal representations with box-embedding-based entity representations. Time is represented through a Weierstrass-inspired polynomial expansion with a learnable temporal basis tensor, enabling flexible handling of unseen timestamps, while entities are modeled as Gumbel boxes and relations as affine transformations acting on these boxes, with a volume-based scoring mechanism. The method achieves state-of-the-art or competitive results on YAGO11k and WikiData for link prediction and relation prediction, and ablation studies show that both the temporal decomposition and box-based representations contribute substantially to improvements and richer inference patterns. The combination of interpretable time modeling, geometric reasoning, and efficient computation offers a practical and scalable approach for temporal knowledge graph completion and reasoning in real-world applications.

Abstract

Distinguished from traditional knowledge graphs (KGs), temporal knowledge graphs (TKGs) must explore and reason over temporally evolving facts adequately. However, existing TKG approaches still face two main challenges, i.e., the limited capability to model arbitrary timestamps continuously and the lack of rich inference patterns under temporal constraints. In this paper, we propose an innovative TKGE method (PTBox) via polynomial decomposition-based temporal representation and box embedding-based entity representation to tackle the above-mentioned problems. Specifically, we decompose time information by polynomials and then enhance the model's capability to represent arbitrary timestamps flexibly by incorporating the learnable temporal basis tensor. In addition, we model every entity as a hyperrectangle box and define each relation as a transformation on the head and tail entity boxes. The entity boxes can capture complex geometric structures and learn robust representations, improving the model's inductive capability for rich inference patterns. Theoretically, our PTBox can encode arbitrary time information or even unseen timestamps while capturing rich inference patterns and higher-arity relations of the knowledge base. Extensive experiments on real-world datasets demonstrate the effectiveness of our method.

Figures (2)

• Figure 1: the overall of our proposed PTBox. $e_h$, $e_t$, $r$ and $\tau$ denote head entity, tail entity, relation and timestamp for one quadruple fact $(h,r,t,\tau)$, respectively. $\otimes$ denotes Hadamard product. Our model obtains the time representation via the polynomial decomposition mechanism and represent the probability of the fact being established by the intersection between entity boxes.
• Figure 2: Visualization of polynomial decomposition based temporal representations on YAGO11k.