# Discrete-time Temporal Network Embedding via Implicit Hierarchical Learning in Hyperbolic Space

arXiv: https://arxiv.org/abs/2107.03767 · HTML: https://mlsanity.com/paper/2107.03767/

## Key facts

- Cited by 67 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 42 references that are in the map.
- First posted on arXiv 8 Jul 2021.

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

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [T-GCN: A Temporal Graph ConvolutionalNetwork for Traffic Prediction](https://mlsanity.com/paper/1811.05320/) (2018)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Learning Correspondence from the Cycle-Consistency of Time](https://mlsanity.com/paper/1903.07593/) (2019)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Temporal Cycle-Consistency Learning](https://mlsanity.com/paper/1904.07846/) (2019)
- [Hyperbolic Attention Networks](https://mlsanity.com/paper/1805.09786/) (2018)
- [Variational Graph Recurrent Neural Networks](https://mlsanity.com/paper/1908.09710/) (2019)
- [Hyperbolic Graph Attention Network](https://mlsanity.com/paper/1912.03046/) (2019)
- [Graph Geometry Interaction Learning](https://mlsanity.com/paper/2010.12135/) (2020)
- [FeatureNorm: L2 Feature Normalization for Dynamic Graph Embedding](https://mlsanity.com/paper/2103.00164/) (2021)
- [Characterizing and Forecasting User Engagement with In-app Action Graph: A Case Study of Snapchat](https://mlsanity.com/paper/1906.00355/) (2019)
- [A Hierarchical Contextual Attention-based GRU Network for Sequential Recommendation](https://mlsanity.com/paper/1711.05114/) (2017)

## Built on by (most cited first, 30 of 67)

- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Temporal Graph Benchmark for Machine Learning on Temporal Graphs](https://mlsanity.com/paper/2307.01026/) (2023)
- [Towards Better Evaluation for Dynamic Link Prediction](https://mlsanity.com/paper/2207.10128/) (2022)
- [Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Space](https://mlsanity.com/paper/2407.01290/) (2024)
- [Hyperbolic Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/2202.13852/) (2022)
- [LLM4DyG: Can Large Language Models Solve Spatial-Temporal Problems on Dynamic Graphs?](https://mlsanity.com/paper/2310.17110/) (2023)
- [HRCF: Enhancing Collaborative Filtering via Hyperbolic Geometric Regularization](https://mlsanity.com/paper/2204.08176/) (2022)
- [Self-Supervised Continual Graph Learning in Adaptive Riemannian Spaces](https://mlsanity.com/paper/2211.17068/) (2022)
- [Graph Lifelong Learning: A Survey](https://mlsanity.com/paper/2202.10688/) (2022)
- [A Comprehensive Survey of Dynamic Graph Neural Networks: Models, Frameworks, Benchmarks, Experiments and Challenges](https://mlsanity.com/paper/2405.00476/) (2024)
- [Hyperbolic Fine-Tuning for Large Language Models](https://mlsanity.com/paper/2410.04010/) (2024)
- [Environment-Aware Dynamic Graph Learning for Out-of-Distribution Generalization](https://mlsanity.com/paper/2311.11114/) (2023)
- [HICF: Hyperbolic Informative Collaborative Filtering](https://mlsanity.com/paper/2207.09051/) (2022)
- [A Self-supervised Riemannian GNN with Time Varying Curvature for Temporal Graph Learning](https://mlsanity.com/paper/2208.14073/) (2022)
- [DyTed: Disentangled Representation Learning for Discrete-time Dynamic Graph](https://mlsanity.com/paper/2210.10592/) (2022)
- [Hyperbolic Representation Learning: Revisiting and Advancing](https://mlsanity.com/paper/2306.09118/) (2023)
- [Enhancing Hyperbolic Graph Embeddings via Contrastive Learning](https://mlsanity.com/paper/2201.08554/) (2022)
- [Hyperbolic Deep Learning for Foundation Models: A Survey](https://mlsanity.com/paper/2507.17787/) (2025)
- [Spectral Invariant Learning for Dynamic Graphs under Distribution Shifts](https://mlsanity.com/paper/2403.05026/) (2024)
- [Lorentzian Residual Neural Networks](https://mlsanity.com/paper/2412.14695/) (2024)
- [Contrastive Graph Clustering in Curvature Spaces](https://mlsanity.com/paper/2305.03555/) (2023)
- [kHGCN: Tree-likeness Modeling via Continuous and Discrete Curvature Learning](https://mlsanity.com/paper/2212.01793/) (2022)
- [HGWaveNet: A Hyperbolic Graph Neural Network for Temporal Link Prediction](https://mlsanity.com/paper/2304.07302/) (2023)
- [Graph-adaptive Rectified Linear Unit for Graph Neural Networks](https://mlsanity.com/paper/2202.06281/) (2022)
- [SEFraud: Graph-based Self-Explainable Fraud Detection via Interpretative Mask Learning](https://mlsanity.com/paper/2406.11389/) (2024)
- [HyperCore: The Core Framework for Building Hyperbolic Foundation Models with Comprehensive Modules](https://mlsanity.com/paper/2504.08912/) (2025)
- [UTG: Towards a Unified View of Snapshot and Event Based Models for Temporal Graphs](https://mlsanity.com/paper/2407.12269/) (2024)
- [Time-aware Random Walk Diffusion to Improve Dynamic Graph Learning](https://mlsanity.com/paper/2211.01214/) (2022)
- [TeleGraph: A Benchmark Dataset for Hierarchical Link Prediction](https://mlsanity.com/paper/2204.07703/) (2022)
- [BSAL: A Framework of Bi-component Structure and Attribute Learning for Link Prediction](https://mlsanity.com/paper/2204.09508/) (2022)

## Abstract (arXiv)

Representation learning over temporal networks has drawn considerable attention in recent years. Efforts are mainly focused on modeling structural dependencies and temporal evolving regularities in Euclidean space which, however, underestimates the inherent complex and hierarchical properties in many real-world temporal networks, leading to sub-optimal embeddings. To explore these properties of a complex temporal network, we propose a hyperbolic temporal graph network (HTGN) that fully takes advantage of the exponential capacity and hierarchical awareness of hyperbolic geometry. More specially, HTGN maps the temporal graph into hyperbolic space, and incorporates hyperbolic graph neural network and hyperbolic gated recurrent neural network, to capture the evolving behaviors and implicitly preserve hierarchical information simultaneously. Furthermore, in the hyperbolic space, we propose two important modules that enable HTGN to successfully model temporal networks: (1) hyperbolic temporal contextual self-attention (HTA) module to attend to historical states and (2) hyperbolic temporal consistency (HTC) module to ensure stability and generalization. Experimental results on multiple real-world datasets demonstrate the superiority of HTGN for temporal graph embedding, as it consistently outperforms competing methods by significant margins in various temporal link prediction tasks. Specifically, HTGN achieves AUC improvement up to 9.98% for link prediction and 11.4% for new link prediction. Moreover, the ablation study further validates the representational ability of hyperbolic geometry and the effectiveness of the proposed HTA and HTC modules.