# TraverseNet: Unifying Space and Time in Message Passing for Traffic Forecasting

arXiv: https://arxiv.org/abs/2109.02474 · HTML: https://mlsanity.com/paper/2109.02474/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 54 references that are in the map.
- First posted on arXiv 25 Aug 2021.

## Builds on (most cited first, 30 of 34)

- [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)
- [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)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (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)
- [Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1801.07455/) (2018)
- [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)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Graph Self-Supervised Learning: A Survey](https://mlsanity.com/paper/2103.00111/) (2021)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Spatial-Temporal Fusion Graph Neural Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2012.09641/) (2020)
- [CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters](https://mlsanity.com/paper/1705.07664/) (2017)
- [Graph Neural Networks with convolutional ARMA filters](https://mlsanity.com/paper/1901.01343/) (2019)
- [Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learning](https://mlsanity.com/paper/2103.00113/) (2021)
- [GaAN: Gated Attention Networks for Learning on Large and Spatiotemporal Graphs](https://mlsanity.com/paper/1803.07294/) (2018)
- [Anomaly Detection in Dynamic Graphs via Transformer](https://mlsanity.com/paper/2106.09876/) (2021)
- [Multi-hop Attention Graph Neural Network](https://mlsanity.com/paper/2009.14332/) (2020)
- [Why Self-Attention? A Targeted Evaluation of Neural Machine Translation Architectures](https://mlsanity.com/paper/1808.08946/) (2018)
- [Spatio-Temporal Graph Scattering Transform](https://mlsanity.com/paper/2012.03363/) (2020)
- [Graph Representation Learning via Hard and Channel-Wise Attention Networks](https://mlsanity.com/paper/1907.04652/) (2019)

## Built on by (most cited first, 16 of 16)

- [Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey](https://mlsanity.com/paper/2303.14483/) (2023)
- [Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations](https://mlsanity.com/paper/2205.13479/) (2022)
- [Scalable Spatiotemporal Graph Neural Networks](https://mlsanity.com/paper/2209.06520/) (2022)
- [Taming Local Effects in Graph-based Spatiotemporal Forecasting](https://mlsanity.com/paper/2302.04071/) (2023)
- [Graph Deep Learning for Time Series Forecasting](https://mlsanity.com/paper/2310.15978/) (2023)
- [Sparse Graph Learning from Spatiotemporal Time Series](https://mlsanity.com/paper/2205.13492/) (2022)
- [Neurosymbolic AI for Reasoning over Knowledge Graphs: A Survey](https://mlsanity.com/paper/2302.07200/) (2023)
- [Correlation-aware Spatial-Temporal Graph Learning for Multivariate Time-series Anomaly Detection](https://mlsanity.com/paper/2307.08390/) (2023)
- [Graph-based Forecasting with Missing Data through Spatiotemporal Downsampling](https://mlsanity.com/paper/2402.10634/) (2024)
- [Dynamic Causal Explanation Based Diffusion-Variational Graph Neural Network for Spatio-temporal Forecasting](https://mlsanity.com/paper/2305.09703/) (2023)
- [Nearest Neighbor Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.11625/) (2025)
- [DSTCGCN: Learning Dynamic Spatial-Temporal Cross Dependencies for Traffic Forecasting](https://mlsanity.com/paper/2307.00518/) (2023)
- [SAMSGL: Series-Aligned Multi-Scale Graph Learning for Spatio-Temporal Forecasting](https://mlsanity.com/paper/2312.02646/) (2023)
- [Caformer: Rethinking Time Series Analysis from Causal Perspective](https://mlsanity.com/paper/2403.08572/) (2024)
- [A Generic Approach to Integrating Time into Spatial-Temporal Forecasting via Conditional Neural Fields](https://mlsanity.com/paper/2305.06827/) (2023)
- [AdaKernel: Learning Adaptive Kernel Parameters for Spatiotemporal Graph Neural Networks](https://mlsanity.com/paper/2606.01283/) (2026)

## Abstract (arXiv)

This paper aims to unify spatial dependency and temporal dependency in a non-Euclidean space while capturing the inner spatial-temporal dependencies for traffic data. For spatial-temporal attribute entities with topological structure, the space-time is consecutive and unified while each node's current status is influenced by its neighbors' past states over variant periods of each neighbor. Most spatial-temporal neural networks for traffic forecasting study spatial dependency and temporal correlation separately in processing, gravely impaired the spatial-temporal integrity, and ignore the fact that the neighbors' temporal dependency period for a node can be delayed and dynamic. To model this actual condition, we propose TraverseNet, a novel spatial-temporal graph neural network, viewing space and time as an inseparable whole, to mine spatial-temporal graphs while exploiting the evolving spatial-temporal dependencies for each node via message traverse mechanisms. Experiments with ablation and parameter studies have validated the effectiveness of the proposed TraverseNet, and the detailed implementation can be found from https://github.com/nnzhan/TraverseNet.