# On the Equivalence Between Temporal and Static Graph Representations for Observational Predictions

arXiv: https://arxiv.org/abs/2103.07016 · HTML: https://mlsanity.com/paper/2103.07016/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 65 references that are in the map.
- First posted on arXiv 12 Mar 2021.

## Builds on (most cited first, 30 of 38)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Temporal Graph Networks for Deep Learning on Dynamic Graphs](https://mlsanity.com/paper/2006.10637/) (2020)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Inductive Representation Learning on Temporal Graphs](https://mlsanity.com/paper/2002.07962/) (2020)
- [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)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Representation Learning for Dynamic Graphs: A Survey](https://mlsanity.com/paper/1905.11485/) (2019)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [On the Universality of Invariant Networks](https://mlsanity.com/paper/1901.09342/) (2019)
- [Relational Pooling for Graph Representations](https://mlsanity.com/paper/1903.02541/) (2019)
- [Foundations and modelling of dynamic networks using Dynamic Graph Neural Networks: A survey](https://mlsanity.com/paper/2005.07496/) (2020)
- [DynGEM: Deep Embedding Method for Dynamic Graphs](https://mlsanity.com/paper/1805.11273/) (2018)
- [Streaming Graph Neural Networks](https://mlsanity.com/paper/1810.10627/) (2018)
- [dyngraph2vec: Capturing Network Dynamics using Dynamic Graph Representation Learning](https://mlsanity.com/paper/1809.02657/) (2018)
- [Variational Graph Recurrent Neural Networks](https://mlsanity.com/paper/1908.09710/) (2019)
- [Dynamic Graph Convolutional Networks](https://mlsanity.com/paper/1704.06199/) (2017)
- [On the Expressive Power of Deep Polynomial Neural Networks](https://mlsanity.com/paper/1905.12207/) (2019)

## Built on by (most cited first, 10 of 10)

- [Provably expressive temporal graph networks](https://mlsanity.com/paper/2209.15059/) (2022)
- [Deep Temporal Graph Clustering](https://mlsanity.com/paper/2305.10738/) (2023)
- [TMac: Temporal Multi-Modal Graph Learning for Acoustic Event Classification](https://mlsanity.com/paper/2309.11845/) (2023)
- [Representation Learning in Continuous-Time Dynamic Signed Networks](https://mlsanity.com/paper/2207.03408/) (2022)
- [arXiv4TGC: Large-Scale Datasets for Temporal Graph Clustering](https://mlsanity.com/paper/2306.04962/) (2023)
- [Temporal Graph Network Embedding with Causal Anonymous Walks Representations](https://mlsanity.com/paper/2108.08754/) (2021)
- [Heterogeneous Graph Neural Networks for Short-term State Forecasting in Power Systems across Domains and Time Scales: A Hydroelectric Power Plant Case Study](https://mlsanity.com/paper/2507.06694/) (2025)
- [Deep Temporal Graph Clustering: A Comprehensive Benchmark and Datasets](https://mlsanity.com/paper/2601.12903/) (2026)
- [RepSPD: Enhancing SPD Manifold Representation in EEGs via Dynamic Graphs](https://mlsanity.com/paper/2602.22981/) (2026)
- [Modern Structure-Aware Simplicial Spatiotemporal Neural Network](https://mlsanity.com/paper/2604.15833/) (2026)

## Abstract (arXiv)

This work formalizes the associational task of predicting node attribute evolution in temporal graphs from the perspective of learning equivariant representations. We show that node representations in temporal graphs can be cast into two distinct frameworks: (a) The most popular approach, which we denote as time-and-graph, where equivariant graph (e.g., GNN) and sequence (e.g., RNN) representations are intertwined to represent the temporal evolution of node attributes in the graph; and (b) an approach that we denote as time-then-graph, where the sequences describing the node and edge dynamics are represented first, then fed as node and edge attributes into a static equivariant graph representation that comes after. Interestingly, we show that time-then-graph representations have an expressivity advantage over time-and-graph representations when both use component GNNs that are not most-expressive (e.g., 1-Weisfeiler-Lehman GNNs). Moreover, while our goal is not necessarily to obtain state-of-the-art results, our experiments show that time-then-graph methods are capable of achieving better performance and efficiency than state-of-the-art time-and-graph methods in some real-world tasks, thereby showcasing that the time-then-graph framework is a worthy addition to the graph ML toolbox.