# Cooperative Graph Neural Networks

arXiv: https://arxiv.org/abs/2310.01267 · HTML: https://mlsanity.com/paper/2310.01267/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- Builds on 60 of its 74 references that are in the map.
- First posted on arXiv 2 Oct 2023.

## Builds on (most cited first, 30 of 60)

- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Graph Transformer Networks](https://mlsanity.com/paper/1911.06455/) (2019)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [Residual Gated Graph ConvNets](https://mlsanity.com/paper/1711.07553/) (2017)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)

## Built on by (most cited first, 30 of 36)

- [Graph Mamba: Towards Learning on Graphs with State Space Models](https://mlsanity.com/paper/2402.08678/) (2024)
- [On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learning](https://mlsanity.com/paper/2502.10818/) (2025)
- [Can Classic GNNs Be Strong Baselines for Graph-level Tasks? Simple Architectures Meet Excellence](https://mlsanity.com/paper/2502.09263/) (2025)
- [Adaptive Message Passing: A General Framework to Mitigate Oversmoothing, Oversquashing, and Underreaching](https://mlsanity.com/paper/2312.16560/) (2023)
- [Bringing Graphs to the Table: Zero-shot Node Classification via Tabular Foundation Models](https://mlsanity.com/paper/2509.07143/) (2025)
- [Weisfeiler-Leman at the margin: When more expressivity matters](https://mlsanity.com/paper/2402.07568/) (2024)
- [Return of ChebNet: Understanding and Improving an Overlooked GNN on Long Range Tasks](https://mlsanity.com/paper/2506.07624/) (2025)
- [Cooperative Sheaf Neural Networks](https://mlsanity.com/paper/2507.00647/) (2025)
- [On Measuring Long-Range Interactions in Graph Neural Networks](https://mlsanity.com/paper/2506.05971/) (2025)
- [PANDA: Expanded Width-Aware Message Passing Beyond Rewiring](https://mlsanity.com/paper/2406.03671/) (2024)
- [Message-Passing State-Space Models: Improving Graph Learning with Modern Sequence Modeling](https://mlsanity.com/paper/2505.18728/) (2025)
- [What Is Missing In Homophily? Disentangling Graph Homophily For Graph Neural Networks](https://mlsanity.com/paper/2406.18854/) (2024)
- [Flock: A Knowledge Graph Foundation Model via Learning on Random Walks](https://mlsanity.com/paper/2510.01510/) (2025)
- [Depth-Adaptive Graph Neural Networks via Learnable Bakry-'Emery Curvature](https://mlsanity.com/paper/2503.01079/) (2025)
- [Mitigating Over-Squashing in Graph Neural Networks by Spectrum-Preserving Sparsification](https://mlsanity.com/paper/2506.16110/) (2025)
- [Preventing Representational Rank Collapse in MPNNs by Splitting the Computational Graph](https://mlsanity.com/paper/2409.11504/) (2024)
- [PIORF: Physics-Informed Ollivier-Ricci Flow for Long-Range Interactions in Mesh Graph Neural Networks](https://mlsanity.com/paper/2504.04052/) (2025)
- [Improving the Effective Receptive Field of Message-Passing Neural Networks](https://mlsanity.com/paper/2505.23185/) (2025)
- [Actions Speak Louder than Prompts: A Large-Scale Study of LLMs for Graph Inference](https://mlsanity.com/paper/2509.18487/) (2025)
- [Improving Graph Neural Networks by Learning Continuous Edge Directions](https://mlsanity.com/paper/2410.14109/) (2024)
- [Making Classic GNNs Strong Baselines Across Varying Homophily: A Smoothness-Generalization Perspective](https://mlsanity.com/paper/2412.09805/) (2024)
- [Efficient Learning on Large Graphs using a Densifying Regularity Lemma](https://mlsanity.com/paper/2504.18273/) (2025)
- [Early-Exit Graph Neural Networks](https://mlsanity.com/paper/2505.18088/) (2025)
- [HyperAggregation: Aggregating over Graph Edges with Hypernetworks](https://mlsanity.com/paper/2407.11596/) (2024)
- [A Decision-Based Heterogenous Graph Attention Network for Multi-Class Fake News Detection](https://mlsanity.com/paper/2501.03290/) (2025)
- [TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows](https://mlsanity.com/paper/2508.05070/) (2025)
- [gLSTM: Mitigating Over-Squashing by Increasing Storage Capacity](https://mlsanity.com/paper/2510.08450/) (2025)
- [Adaptive Graph Rewiring to Mitigate Over-Squashing in Mesh-Based GNNs for Fluid Dynamics Simulations](https://mlsanity.com/paper/2511.12709/) (2025)
- [MPM-LLM4DSE: Reaching the Pareto Frontier in HLS with Multimodal Learning and LLM-Driven Exploration](https://mlsanity.com/paper/2601.04801/) (2026)
- [Tensor-DTI: Enhancing Biomolecular Interaction Prediction with Contrastive Embedding Learning](https://mlsanity.com/paper/2601.05792/) (2026)

## Abstract (arXiv)

Graph neural networks are popular architectures for graph machine learning, based on iterative computation of node representations of an input graph through a series of invariant transformations. A large class of graph neural networks follow a standard message-passing paradigm: at every layer, each node state is updated based on an aggregate of messages from its neighborhood. In this work, we propose a novel framework for training graph neural networks, where every node is viewed as a player that can choose to either 'listen', 'broadcast', 'listen and broadcast', or to 'isolate'. The standard message propagation scheme can then be viewed as a special case of this framework where every node 'listens and broadcasts' to all neighbors. Our approach offers a more flexible and dynamic message-passing paradigm, where each node can determine its own strategy based on their state, effectively exploring the graph topology while learning. We provide a theoretical analysis of the new message-passing scheme which is further supported by an extensive empirical analysis on a synthetic dataset and on real-world datasets.