Message passing graph neural networks (GNNs) would appear to be powerful tools to learn distributed algorithms via gradient descent, but generate catastrophically incorrect predictions when nodes update asynchronously during inference. This failure under asynchrony effectively excludes these architectures from many potential applications, such as learning local communication policies between resource-constrained agents in, e.g., robotic swarms or sensor networks. In this work we explore why this failure occurs in common GNN architectures, and identify "implicitly-defined" GNNs as a class of architectures which is provably robust to partially asynchronous "hogwild" inference, adapting convergence guarantees from work in asynchronous and distributed optimization, e.g., Bertsekas (1982); Niu et al. (2011). We then propose a novel implicitly-defined GNN architecture, which we call an energy GNN. We show that this architecture outperforms other GNNs from this class on a variety of synthetic tasks inspired by multi-agent systems, and achieves competitive performance on real-world datasets.

翻译：消息传递图神经网络（GNNs）似乎是通过梯度下降学习分布式算法的强大工具，但在推理过程中节点异步更新时会产生灾难性的错误预测。这种异步条件下的失效实际上将这些架构排除在许多潜在应用之外，例如在机器人集群或传感器网络等场景中学习资源受限智能体间的本地通信策略。本研究探讨了常见GNN架构出现这种失效的原因，并确定"隐式定义"GNN为一类可证明对部分异步"混乱"推理具有鲁棒性的架构，其收敛性保证借鉴了异步与分布式优化领域的研究成果（如Bertsekas (1982); Niu et al. (2011)）。我们进一步提出一种新型隐式定义GNN架构——能量图神经网络。实验表明，在受多智能体系统启发的多种合成任务上，该架构优于同类其他GNN，并在真实世界数据集上取得了具有竞争力的性能。