# DyERNIE: Dynamic Evolution of Riemannian Manifold Embeddings for Temporal Knowledge Graph Completion

arXiv: https://arxiv.org/abs/2011.03984 · HTML: https://mlsanity.com/paper/2011.03984/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Nov 2020.

## Built on by (most cited first, 30 of 30)

- [Temporal Knowledge Graph Reasoning Based on Evolutional Representation Learning](https://mlsanity.com/paper/2104.10353/) (2021)
- [A Survey of Knowledge Graph Reasoning on Graph Types: Static, Dynamic, and Multimodal](https://mlsanity.com/paper/2212.05767/) (2022)
- [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)
- [Temporal Knowledge Graph Completion: A Survey](https://mlsanity.com/paper/2201.08236/) (2022)
- [Search from History and Reason for Future: Two-stage Reasoning on Temporal Knowledge Graphs](https://mlsanity.com/paper/2106.00327/) (2021)
- [Pseudo-Riemannian Graph Convolutional Networks](https://mlsanity.com/paper/2106.03134/) (2021)
- [GenTKG: Generative Forecasting on Temporal Knowledge Graph with Large Language Models](https://mlsanity.com/paper/2310.07793/) (2023)
- [A Survey on Temporal Knowledge Graph: Representation Learning and Applications](https://mlsanity.com/paper/2403.04782/) (2024)
- [A Survey on Temporal Knowledge Graph Completion: Taxonomy, Progress, and Prospects](https://mlsanity.com/paper/2308.02457/) (2023)
- [TFLEX: Temporal Feature-Logic Embedding Framework for Complex Reasoning over Temporal Knowledge Graph](https://mlsanity.com/paper/2205.14307/) (2022)
- [Hyperbolic Temporal Knowledge Graph Embeddings with Relational and Time Curvatures](https://mlsanity.com/paper/2106.04311/) (2021)
- [HiSMatch: Historical Structure Matching based Temporal Knowledge Graph Reasoning](https://mlsanity.com/paper/2210.09708/) (2022)
- [HGE: Embedding Temporal Knowledge Graphs in a Product Space of Heterogeneous Geometric Subspaces](https://mlsanity.com/paper/2312.13680/) (2023)
- [Temporal Inductive Path Neural Network for Temporal Knowledge Graph Reasoning](https://mlsanity.com/paper/2309.03251/) (2023)
- [IME: Integrating Multi-curvature Shared and Specific Embedding for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2403.19881/) (2024)
- [Few-Shot Inductive Learning on Temporal Knowledge Graphs using Concept-Aware Information](https://mlsanity.com/paper/2211.08169/) (2022)
- [Transformer-based Reasoning for Learning Evolutionary Chain of Events on Temporal Knowledge Graph](https://mlsanity.com/paper/2405.00352/) (2024)
- [ECOLA: Enhanced Temporal Knowledge Embeddings with Contextualized Language Representations](https://mlsanity.com/paper/2203.09590/) (2022)
- [Deep Active Alignment of Knowledge Graph Entities and Schemata](https://mlsanity.com/paper/2304.04389/) (2023)
- [History Repeats: Overcoming Catastrophic Forgetting For Event-Centric Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2305.18675/) (2023)
- [AMCAD: Adaptive Mixed-Curvature Representation based Advertisement Retrieval System](https://mlsanity.com/paper/2203.14683/) (2022)
- [Neurosymbolic Methods for Dynamic Knowledge Graphs](https://mlsanity.com/paper/2409.04572/) (2024)
- [Disentangled Multi-span Evolutionary Network against Temporal Knowledge Graph Reasoning](https://mlsanity.com/paper/2505.14020/) (2025)
- [Bending the Future: Autoregressive Modeling of Temporal Knowledge Graphs in Curvature-Variable Hyperbolic Spaces](https://mlsanity.com/paper/2209.05635/) (2022)
- [Knowledge-based Multiple Adaptive Spaces Fusion for Recommendation](https://mlsanity.com/paper/2308.15244/) (2023)
- [Learning Multi-graph Structure for Temporal Knowledge Graph Reasoning](https://mlsanity.com/paper/2312.03004/) (2023)
- [Arbitrary Time Information Modeling via Polynomial Approximation for Temporal Knowledge Graph Embedding](https://mlsanity.com/paper/2405.00358/) (2024)
- [Selective Temporal Knowledge Graph Reasoning](https://mlsanity.com/paper/2404.01695/) (2024)
- [Towards Improving Long-Tail Entity Predictions in Temporal Knowledge Graphs through Global Similarity and Weighted Sampling](https://mlsanity.com/paper/2507.18977/) (2025)

## Abstract (arXiv)

There has recently been increasing interest in learning representations of temporal knowledge graphs (KGs), which record the dynamic relationships between entities over time. Temporal KGs often exhibit multiple simultaneous non-Euclidean structures, such as hierarchical and cyclic structures. However, existing embedding approaches for temporal KGs typically learn entity representations and their dynamic evolution in the Euclidean space, which might not capture such intrinsic structures very well. To this end, we propose Dy- ERNIE, a non-Euclidean embedding approach that learns evolving entity representations in a product of Riemannian manifolds, where the composed spaces are estimated from the sectional curvatures of underlying data. Product manifolds enable our approach to better reflect a wide variety of geometric structures on temporal KGs. Besides, to capture the evolutionary dynamics of temporal KGs, we let the entity representations evolve according to a velocity vector defined in the tangent space at each timestamp. We analyze in detail the contribution of geometric spaces to representation learning of temporal KGs and evaluate our model on temporal knowledge graph completion tasks. Extensive experiments on three real-world datasets demonstrate significantly improved performance, indicating that the dynamics of multi-relational graph data can be more properly modeled by the evolution of embeddings on Riemannian manifolds.