# COOL: A Conjoint Perspective on Spatio-Temporal Graph Neural Network for Traffic Forecasting

arXiv: https://arxiv.org/abs/2403.01091 · HTML: https://mlsanity.com/paper/2403.01091/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 65 references that are in the map.
- First posted on arXiv 2 Mar 2024.

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [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)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2106.12931/) (2021)
- [Dynamic Graph Convolutional Recurrent Network for Traffic Prediction: Benchmark and Solution](https://mlsanity.com/paper/2104.14917/) (2021)
- [PDFormer: Propagation Delay-Aware Dynamic Long-Range Transformer for Traffic Flow Prediction](https://mlsanity.com/paper/2301.07945/) (2023)
- [Pre-training Enhanced Spatial-temporal Graph Neural Network for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2206.09113/) (2022)
- [TransRefer3D: Entity-and-Relation Aware Transformer for Fine-Grained 3D Visual Grounding](https://mlsanity.com/paper/2108.02388/) (2021)
- [A Comprehensive Survey on Deep Graph Representation Learning](https://mlsanity.com/paper/2304.05055/) (2023)
- [Cross-Node Federated Graph Neural Network for Spatio-Temporal Data Modeling](https://mlsanity.com/paper/2106.05223/) (2021)
- [Target-Driven Structured Transformer Planner for Vision-Language Navigation](https://mlsanity.com/paper/2207.11201/) (2022)
- [AutoCTS: Automated Correlated Time Series Forecasting -- Extended Version](https://mlsanity.com/paper/2112.11174/) (2021)
- [STDEN: Towards Physics-Guided Neural Networks for Traffic Flow Prediction](https://mlsanity.com/paper/2209.00225/) (2022)
- [Multi-Behavior Hypergraph-Enhanced Transformer for Sequential Recommendation](https://mlsanity.com/paper/2207.05584/) (2022)
- [A Physics-Informed Deep Learning Paradigm for Car-Following Models](https://mlsanity.com/paper/2012.13376/) (2020)
- [Self-Supervised Hypergraph Transformer for Recommender Systems](https://mlsanity.com/paper/2207.14338/) (2022)
- [A Survey on Autonomous Vehicle Control in the Era of Mixed-Autonomy: From Physics-Based to AI-Guided Driving Policy Learning](https://mlsanity.com/paper/2007.05156/) (2020)
- [Learning on Graphs under Label Noise](https://mlsanity.com/paper/2306.08194/) (2023)
- [GLCC: A General Framework for Graph-Level Clustering](https://mlsanity.com/paper/2210.11879/) (2022)
- [TGNN: A Joint Semi-supervised Framework for Graph-level Classification](https://mlsanity.com/paper/2304.11688/) (2023)
- [A Survey of Data-Efficient Graph Learning](https://mlsanity.com/paper/2402.00447/) (2024)
- [Towards Semi-supervised Universal Graph Classification](https://mlsanity.com/paper/2305.19598/) (2023)
- [Dynamic Hypergraph Structure Learning for Traffic Flow Forecasting](https://mlsanity.com/paper/2309.12028/) (2023)

## Built on by (most cited first, 2 of 2)

- [From Graphs to Qubits: A Critical Review of Quantum Graph Neural Networks](https://mlsanity.com/paper/2408.06524/) (2024)
- [GraphEdge: Dynamic Graph Partition and Task Scheduling for GNNs Computing in Edge Network](https://mlsanity.com/paper/2504.15905/) (2025)

## Abstract (arXiv)

This paper investigates traffic forecasting, which attempts to forecast the future state of traffic based on historical situations. This problem has received ever-increasing attention in various scenarios and facilitated the development of numerous downstream applications such as urban planning and transportation management. However, the efficacy of existing methods remains sub-optimal due to their tendency to model temporal and spatial relationships independently, thereby inadequately accounting for complex high-order interactions of both worlds. Moreover, the diversity of transitional patterns in traffic forecasting makes them challenging to capture for existing approaches, warranting a deeper exploration of their diversity. Toward this end, this paper proposes Conjoint Spatio-Temporal graph neural network (abbreviated as COOL), which models heterogeneous graphs from prior and posterior information to conjointly capture high-order spatio-temporal relationships. On the one hand, heterogeneous graphs connecting sequential observation are constructed to extract composite spatio-temporal relationships via prior message passing. On the other hand, we model dynamic relationships using constructed affinity and penalty graphs, which guide posterior message passing to incorporate complementary semantic information into node representations. Moreover, to capture diverse transitional properties to enhance traffic forecasting, we propose a conjoint self-attention decoder that models diverse temporal patterns from both multi-rank and multi-scale views. Experimental results on four popular benchmark datasets demonstrate that our proposed COOL provides state-of-the-art performance compared with the competitive baselines.