# Graph-Time Convolutional Neural Networks: Architecture and Theoretical Analysis

arXiv: https://arxiv.org/abs/2206.15174 · HTML: https://mlsanity.com/paper/2206.15174/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 60 references that are in the map.
- First posted on arXiv 30 Jun 2022.

## Builds on (most cited first, 30 of 39)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1801.07455/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [A Deep Neural Network for Unsupervised Anomaly Detection and Diagnosis in Multivariate Time Series Data](https://mlsanity.com/paper/1811.08055/) (2018)
- [Deep Learning for Spatio-Temporal Data Mining: A Survey](https://mlsanity.com/paper/1906.04928/) (2019)
- [Multivariate Time-series Anomaly Detection via Graph Attention Network](https://mlsanity.com/paper/2009.02040/) (2020)
- [An Attention Enhanced Graph Convolutional LSTM Network for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1902.09130/) (2019)
- [Stability Properties of Graph Neural Networks](https://mlsanity.com/paper/1905.04497/) (2019)
- [Convolutional Neural Network Architectures for Signals Supported on Graphs](https://mlsanity.com/paper/1805.00165/) (2018)
- [Transferability of Spectral Graph Convolutional Neural Networks](https://mlsanity.com/paper/1907.12972/) (2019)
- [Variational Graph Recurrent Neural Networks](https://mlsanity.com/paper/1908.09710/) (2019)
- [Dynamic Graph Convolutional Networks](https://mlsanity.com/paper/1704.06199/) (2017)
- [Graph Neural Networks: Architectures, Stability and Transferability](https://mlsanity.com/paper/2008.01767/) (2020)
- [Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks](https://mlsanity.com/paper/2003.03777/) (2020)
- [Graph Learning based Recommender Systems: A Review](https://mlsanity.com/paper/2105.06339/) (2021)
- [Gated Graph Recurrent Neural Networks](https://mlsanity.com/paper/2002.01038/) (2020)
- [Bike Flow Prediction with Multi-Graph Convolutional Networks](https://mlsanity.com/paper/1807.10934/) (2018)
- [On the Transferability of Spectral Graph Filters](https://mlsanity.com/paper/1901.10524/) (2019)

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

- [Graph Deep Learning for Time Series Forecasting](https://mlsanity.com/paper/2310.15978/) (2023)
- [Continuous Product Graph Neural Networks](https://mlsanity.com/paper/2405.18877/) (2024)
- [Graph Generation Powered with LLMs for Boosting Multivariate Time-Series Representation Learning](https://mlsanity.com/paper/2403.03645/) (2024)
- [On topological descriptors for graph products](https://mlsanity.com/paper/2511.08846/) (2025)
- [On the Trade-Off between Stability and Representational Capacity in Graph Neural Networks](https://mlsanity.com/paper/2312.02372/) (2023)
- [GKNet: Graph Kalman Filtering and Model Inference via Model-based Deep Learning](https://mlsanity.com/paper/2506.22004/) (2025)
- [Second-Order Tensorial Partial Differential Equations on Graphs](https://mlsanity.com/paper/2509.02015/) (2025)
- [Graph Variate Neural Networks](https://mlsanity.com/paper/2509.20311/) (2025)
- [DWAFM: Dynamic Weighted Graph Structure Embedding Integrated with Attention and Frequency-Domain MLPs for Traffic Forecasting](https://mlsanity.com/paper/2603.00997/) (2026)
- [Spatiotemporal Kronecker Covariance Neural Networks](https://mlsanity.com/paper/2609.25326/) (2026)

## Abstract (arXiv)

Devising and analyzing learning models for spatiotemporal network data is of importance for tasks including forecasting, anomaly detection, and multi-agent coordination, among others. Graph Convolutional Neural Networks (GCNNs) are an established approach to learn from time-invariant network data. The graph convolution operation offers a principled approach to aggregate multiresolution information. However, extending the convolution principled learning and respective analysis to the spatiotemporal domain is challenging because spatiotemporal data have more intrinsic dependencies. Hence, a higher flexibility to capture jointly the spatial and the temporal dependencies is required to learn meaningful higher-order representations. Here, we leverage product graphs to represent the spatiotemporal dependencies in the data and introduce Graph-Time Convolutional Neural Networks (GTCNNs) as a principled architecture to aid learning. The proposed approach can work with any type of product graph and we also introduce a parametric product graph to learn also the spatiotemporal coupling. The convolution principle further allows a similar mathematical tractability as for GCNNs. In particular, the stability result shows GTCNNs are stable to spatial perturbations but there is an implicit trade-off between discriminability and robustness; i.e., the more complex the model, the less stable. Extensive numerical results on benchmark datasets corroborate our findings and show the GTCNN compares favorably with state-of-the-art solutions. We anticipate the GTCNN to be a starting point for more sophisticated models that achieve good performance but are also fundamentally grounded.