Adaptive graph diffusion networks: compact and expressive GNNs with large receptive fields

Abstract

Graph neural networks (GNNs) are widely used in graph-based tasks, but deep GNNs often suffer from oversmoothing. Existing effective deep GNNs have various shortcomings including redundant complexity, oversimplified architecture, or predefined parameters. To address these issues, we propose adaptive graph diffusion networks (AGDNs), a class of compact and expressive GNNs that can effectively leverage deep neighborhood information. We introduce hopwise attention and hopwise convolution with positional embeddings for learning nodewise and channelwise hop weights, respectively, which overcomes oversmoothing and ensures a powerful ability to learn arbitrary filters in the spectral domain. Our experiments demonstrate that AGDNs can effectively learn various filters on images and exhibit superior performance on diverse and challenging open graph benchmark datasets for node classification and link prediction tasks while maintaining moderate complexity and fast running time.