Graph neural networks (GNNs) have become powerful tools for processing graph-based information in various domains. A desirable property of GNNs is transferability, where a trained network can swap in information from a different graph without retraining and retain its accuracy. A recent method of capturing transferability of GNNs is through the use of graphons, which are symmetric, measurable functions representing the limit of large dense graphs. In this work, we contribute to the application of graphons to GNNs by presenting an explicit two-layer graphon neural network (WNN) architecture. We prove its ability to approximate bandlimited signals within a specified error tolerance using a minimal number of network weights. We then leverage this result, to establish the transferability of an explicit two-layer GNN over all sufficiently large graphs in a sequence converging to a graphon. Our work addresses transferability between both deterministic weighted graphs and simple random graphs and overcomes issues related to the curse of dimensionality that arise in other GNN results. The proposed WNN and GNN architectures offer practical solutions for handling graph data of varying sizes while maintaining performance guarantees without extensive retraining.

通过引入显式的两层图状神经网络(WNN)架构，我们证明其能够用最少的网络权重近似带限信号在指定误差容限内，并且通过这一结果，建立了明确的两层GNN在收敛于图状函数的一系列充分大图上的可传递性。我们的工作解决了其他GNN结果中出现的维度诅咒问题，提供了处理各种大小图形数据的实际解决方案，同时保持性能保证而无需进行大量的重新训练。

使用图度及采样理论的图神经网络可转移性