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

arXiv: https://arxiv.org/abs/2405.00358 · HTML: https://mlsanity.com/paper/2405.00358/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 37 references that are in the map.
- First posted on arXiv 1 May 2024.

## Builds on (most cited first, 23 of 23)

- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [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)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [SimplE Embedding for Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/1802.04868/) (2018)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [Learning Sequence Encoders for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/1809.03202/) (2018)
- [Multi-relational Poincar'e Graph Embeddings](https://mlsanity.com/paper/1905.09791/) (2019)
- [Tensor Decompositions for temporal knowledge base completion](https://mlsanity.com/paper/2004.04926/) (2020)
- [BoxE: A Box Embedding Model for Knowledge Base Completion](https://mlsanity.com/paper/2007.06267/) (2020)
- [Diachronic Embedding for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/1907.03143/) (2019)
- [Probabilistic Embedding of Knowledge Graphs with Box Lattice Measures](https://mlsanity.com/paper/1805.06627/) (2018)
- [TeRo: A Time-aware Knowledge Graph Embedding via Temporal Rotation](https://mlsanity.com/paper/2010.01029/) (2020)
- [TorusE: Knowledge Graph Embedding on a Lie Group](https://mlsanity.com/paper/1711.05435/) (2017)
- [Improving Local Identifiability in Probabilistic Box Embeddings](https://mlsanity.com/paper/2010.04831/) (2020)
- [ChronoR: Rotation Based Temporal Knowledge Graph Embedding](https://mlsanity.com/paper/2103.10379/) (2021)
- [Temporal Knowledge Graph Completion using Box Embeddings](https://mlsanity.com/paper/2109.08970/) (2021)
- [DyERNIE: Dynamic Evolution of Riemannian Manifold Embeddings for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2011.03984/) (2020)
- [Differentiating Concepts and Instances for Knowledge Graph Embedding](https://mlsanity.com/paper/1811.04588/) (2018)
- [Probabilistic Box Embeddings for Uncertain Knowledge Graph Reasoning](https://mlsanity.com/paper/2104.04597/) (2021)
- [Global Instance Tracking: Locating Target More Like Humans](https://mlsanity.com/paper/2202.13073/) (2022)

## Built on by (most cited first, 2 of 2)

- [Self-Aware Vector Embeddings for Retrieval-Augmented Generation: A Neuroscience-Inspired Framework for Temporal, Confidence-Weighted, and Relational Knowledge](https://mlsanity.com/paper/2604.20598/) (2026)
- [CHE-TKG: Collaborative Historical Evidence and Evolutionary Dynamics Learning for Temporal Knowledge Graph Reasoning](https://mlsanity.com/paper/2605.04652/) (2026)

## Abstract (arXiv)

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.