CKGConv: General Graph Convolution with Continuous Kernels

TL;DR

CKGConv introduces a flexible, continuous kernel-based graph convolution framework that unifies existing methods and achieves high expressiveness, outperforming many existing models on various datasets.

Contribution

The paper proposes CKGConv, a novel general graph convolution method using continuous kernels, unifying and extending existing approaches with superior expressiveness.

Findings

CKGConv outperforms existing graph convolutional networks.

CKGConv achieves comparable results to state-of-the-art graph transformers.

Theoretical analysis shows CKGConv's strong expressiveness.

Abstract

The existing definitions of graph convolution, either from spatial or spectral perspectives, are inflexible and not unified. Defining a general convolution operator in the graph domain is challenging due to the lack of canonical coordinates, the presence of irregular structures, and the properties of graph symmetries. In this work, we propose a novel and general graph convolution framework by parameterizing the kernels as continuous functions of pseudo-coordinates derived via graph positional encoding. We name this Continuous Kernel Graph Convolution (CKGConv). Theoretically, we demonstrate that CKGConv is flexible and expressive. CKGConv encompasses many existing graph convolutions, and exhibits a stronger expressiveness, as powerful as graph transformers in terms of distinguishing non-isomorphic graphs. Empirically, we show that CKGConv-based Networks outperform existing graph convolutional networks and perform comparably to the best graph transformers across a variety of graph datasets. The code and models are publicly available at https://github.com/networkslab/CKGConv.