Graph neural networks (GNNs) are information processing architectures that model representations from networked data and allow for decentralized implementation through localized communications. Existing GNN architectures often assume ideal communication links, and ignore channel effects, such as fading and noise, leading to performance degradation in real-world implementation. This paper proposes graph neural networks over the air (AirGNNs), a novel GNN architecture that incorporates the communication model into the architecture. The AirGNN modifies the graph convolutional operation that shifts graph signals over random communication graphs to take into account channel fading and noise when aggregating features from neighbors, thus, improving the architecture robustness to channel impairments during testing. We propose a stochastic gradient descent based method to train the AirGNN, and show that the training procedure converges to a stationary solution. Numerical simulations on decentralized source localization and multi-robot flocking corroborate theoretical findings and show superior performance of the AirGNN over wireless communication channels.

翻译：图神经网络（GNNs）是一种信息处理架构，能够对网络化数据进行建模表示，并可通过局部通信实现分布式部署。现有GNN架构通常假设理想通信链路，忽略信道效应（如衰落和噪声），导致在实际部署中性能下降。本文提出空中图神经网络（AirGNN），一种将通信模型融入架构的新型GNN。AirGNN改进了图卷积操作——该操作在随机通信图上对图信号进行移位——在聚合邻域特征时考虑信道衰落与噪声，从而提升架构对测试期间信道损伤的鲁棒性。我们提出基于随机梯度下降的方法训练AirGNN，并证明训练过程收敛至平稳解。针对分布式源定位与多机器人集群的数值仿真验证了理论结论，并展示了AirGNN在无线信道上优越的性能。