# Bending the Future: Autoregressive Modeling of Temporal Knowledge Graphs in Curvature-Variable Hyperbolic Spaces

arXiv: https://arxiv.org/abs/2209.05635 · HTML: https://mlsanity.com/paper/2209.05635/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 59 references that are in the map.
- First posted on arXiv 12 Sep 2022.

## Builds on (most cited first, 30 of 36)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [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)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Know-Evolve: Deep Temporal Reasoning for Dynamic Knowledge Graphs](https://mlsanity.com/paper/1705.05742/) (2017)
- [Learning Sequence Encoders for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/1809.03202/) (2018)
- [DKN: Deep Knowledge-Aware Network for News Recommendation](https://mlsanity.com/paper/1801.08284/) (2018)
- [Multi-relational Poincar'e Graph Embeddings](https://mlsanity.com/paper/1905.09791/) (2019)
- [Hyperbolic Attention Networks](https://mlsanity.com/paper/1805.09786/) (2018)
- [Temporal Knowledge Graph Reasoning Based on Evolutional Representation Learning](https://mlsanity.com/paper/2104.10353/) (2021)
- [Diachronic Embedding for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/1907.03143/) (2019)
- [Learning from History: Modeling Temporal Knowledge Graphs with Sequential Copy-Generation Networks](https://mlsanity.com/paper/2012.08492/) (2020)
- [Lorentzian Graph Convolutional Networks](https://mlsanity.com/paper/2104.07477/) (2021)
- [TimeTraveler: Reinforcement Learning for Temporal Knowledge Graph Forecasting](https://mlsanity.com/paper/2109.04101/) (2021)
- [Temporal Knowledge Graph Forecasting with Neural ODE](https://mlsanity.com/paper/2101.05151/) (2021)
- [A Hyperbolic-to-Hyperbolic Graph Convolutional Network](https://mlsanity.com/paper/2104.06942/) (2021)
- [RepeatNet: A Repeat Aware Neural Recommendation Machine for Session-based Recommendation](https://mlsanity.com/paper/1812.02646/) (2018)
- [Learning the Predictability of the Future](https://mlsanity.com/paper/2101.01600/) (2021)
- [Search from History and Reason for Future: Two-stage Reasoning on Temporal Knowledge Graphs](https://mlsanity.com/paper/2106.00327/) (2021)
- [Entity-Duet Neural Ranking: Understanding the Role of Knowledge Graph Semantics in Neural Information Retrieval](https://mlsanity.com/paper/1805.07591/) (2018)
- [Knowledge Association with Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2010.02162/) (2020)
- [Hyperbolic Interaction Model For Hierarchical Multi-Label Classification](https://mlsanity.com/paper/1905.10802/) (2019)

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

- [ProWorld: Progress-Aware Hyperbolic World Models for Long-Horizon Visual Goal Reaching](https://mlsanity.com/paper/2608.01926/) (2026)
- [From Semantics to Hierarchy: A Hybrid Euclidean-Tangent-Hyperbolic Space Model for Temporal Knowledge Graph Reasoning](https://mlsanity.com/paper/2409.00149/) (2024)

## Abstract (arXiv)

Recently there is an increasing scholarly interest in time-varying knowledge graphs, or temporal knowledge graphs (TKG). Previous research suggests diverse approaches to TKG reasoning that uses historical information. However, less attention has been given to the hierarchies within such information at different timestamps. Given that TKG is a sequence of knowledge graphs based on time, the chronology in the sequence derives hierarchies between the graphs. Furthermore, each knowledge graph has its hierarchical level which may differ from one another. To address these hierarchical characteristics in TKG, we propose HyperVC, which utilizes hyperbolic space that better encodes the hierarchies than Euclidean space. The chronological hierarchies between knowledge graphs at different timestamps are represented by embedding the knowledge graphs as vectors in a common hyperbolic space. Additionally, diverse hierarchical levels of knowledge graphs are represented by adjusting the curvatures of hyperbolic embeddings of their entities and relations. Experiments on four benchmark datasets show substantial improvements, especially on the datasets with higher hierarchical levels.