Graph Neural Networks over the Air for Decentralized Tasks in Wireless Networks
This addresses the challenge of implementing GNNs in real-world wireless networks for decentralized tasks, offering a more robust solution, though it is incremental as it builds on existing GNN frameworks.
The paper tackles the problem of graph neural networks (GNNs) degrading in performance due to wireless channel impairments like fading and noise, and proposes AirGNNs, a novel architecture that incorporates communication models, showing superior performance in experiments on tasks like decentralized source localization and multi-robot flocking.
Graph neural networks (GNNs) model representations from networked data and allow for decentralized inference through localized communications. Existing GNN architectures often assume ideal communications and ignore potential channel effects, such as fading and noise, leading to performance degradation in real-world implementation. Considering a GNN implemented over nodes connected through wireless links, this paper conducts a stability analysis to study the impact of channel impairments on the performance of GNNs, and proposes graph neural networks over the air (AirGNNs), a novel GNN architecture that incorporates the communication model. AirGNNs modify graph convolutional operations that shift graph signals over random communication graphs to take into account channel fading and noise when aggregating features from neighbors, thus, improving architecture robustness to channel impairments during testing. We develop a channel-inversion signal transmission strategy for AirGNNs when channel state information (CSI) is available, and propose a stochastic gradient descent based method to train AirGNNs when CSI is unknown. The convergence analysis shows that the training procedure approaches a stationary solution of an associated stochastic optimization problem and the variance analysis characterizes the statistical behavior of the trained model. Experiments on decentralized source localization and multi-robot flocking corroborate theoretical findings and show superior performance of AirGNNs over wireless communication channels.