# ConTIG: Continuous Representation Learning on Temporal Interaction Graphs

arXiv: https://arxiv.org/abs/2110.06088 · HTML: https://mlsanity.com/paper/2110.06088/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 68 references that are in the map.
- First posted on arXiv 27 Sep 2021.

## Builds on (most cited first, 30 of 37)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Temporal Graph Networks for Deep Learning on Dynamic Graphs](https://mlsanity.com/paper/2006.10637/) (2020)
- [Inductive Representation Learning on Temporal Graphs](https://mlsanity.com/paper/2002.07962/) (2020)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Predicting Dynamic Embedding Trajectory in Temporal Interaction Networks](https://mlsanity.com/paper/1908.01207/) (2019)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Representation Learning for Dynamic Graphs: A Survey](https://mlsanity.com/paper/1905.11485/) (2019)
- [Inductive Representation Learning in Temporal Networks via Causal Anonymous Walks](https://mlsanity.com/paper/2101.05974/) (2021)
- [A Survey on Network Embedding](https://mlsanity.com/paper/1711.08752/) (2017)
- [Continuous Graph Neural Networks](https://mlsanity.com/paper/1912.00967/) (2019)
- [DynGEM: Deep Embedding Method for Dynamic Graphs](https://mlsanity.com/paper/1805.11273/) (2018)
- [Motifs in Temporal Networks](https://mlsanity.com/paper/1612.09259/) (2016)
- [dyngraph2vec: Capturing Network Dynamics using Dynamic Graph Representation Learning](https://mlsanity.com/paper/1809.02657/) (2018)
- [Learning Graph Embedding with Adversarial Training Methods](https://mlsanity.com/paper/1901.01250/) (2019)
- [Graph Representation Learning in Biomedicine](https://mlsanity.com/paper/2104.04883/) (2021)
- [TCL: Transformer-based Dynamic Graph Modelling via Contrastive Learning](https://mlsanity.com/paper/2105.07944/) (2021)
- [Discrete-time Temporal Network Embedding via Implicit Hierarchical Learning in Hyperbolic Space](https://mlsanity.com/paper/2107.03767/) (2021)
- [Temporal Network Embedding with Micro- and Macro-dynamics](https://mlsanity.com/paper/1909.04246/) (2019)
- [Self-attention with Functional Time Representation Learning](https://mlsanity.com/paper/1911.12864/) (2019)
- [Node Embedding over Temporal Graphs](https://mlsanity.com/paper/1903.08889/) (2019)
- [Dynamic Network Embedding Survey](https://mlsanity.com/paper/2103.15447/) (2021)

## Built on by (most cited first, 5 of 5)

- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)
- [Learning Dynamic Graph Embeddings with Neural Controlled Differential Equations](https://mlsanity.com/paper/2302.11354/) (2023)
- [Do We Need an Encoder-Decoder to Model Dynamical Systems on Networks?](https://mlsanity.com/paper/2305.12185/) (2023)
- [Dynamic Graph Representation Learning via Edge Temporal States Modeling and Structure-reinforced Transformer](https://mlsanity.com/paper/2304.10079/) (2023)
- [Temporal Sheaf Neural Networks with Dynamic Orthogonal Transport](https://mlsanity.com/paper/2606.10071/) (2026)

## Abstract (arXiv)

Representation learning on temporal interaction graphs (TIG) is to model complex networks with the dynamic evolution of interactions arising in a broad spectrum of problems. Existing dynamic embedding methods on TIG discretely update node embeddings merely when an interaction occurs. They fail to capture the continuous dynamic evolution of embedding trajectories of nodes. In this paper, we propose a two-module framework named ConTIG, a continuous representation method that captures the continuous dynamic evolution of node embedding trajectories. With two essential modules, our model exploit three-fold factors in dynamic networks which include latest interaction, neighbor features and inherent characteristics. In the first update module, we employ a continuous inference block to learn the nodes' state trajectories by learning from time-adjacent interaction patterns between node pairs using ordinary differential equations. In the second transform module, we introduce a self-attention mechanism to predict future node embeddings by aggregating historical temporal interaction information. Experiments results demonstrate the superiority of ConTIG on temporal link prediction, temporal node recommendation and dynamic node classification tasks compared with a range of state-of-the-art baselines, especially for long-interval interactions prediction.