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 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 the same expressiveness 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.

我们提出了一种新颖的连续核图卷积（CKGConv）框架，通过将核函数参数化为通过图位置编码得到的伪坐标的连续函数，从而解决了在图域中定义通用卷积算子的挑战，该框架理论上证明了 CKGConv 的灵活性和表现力，并在实证中证明 CKGConv 网络在各种图数据集上优于现有的图卷积网络，并与最佳图转换器表现相当。

CKGConv: 连续核的通用图卷积

CKGConv: General Graph Convolution with Continuous Kernels

In the last few years, graph neural networks (GNNs) have become the standard
toolkit for analyzing and learning from data on graphs. This emerging field has
witnessed an extensive growth of promising techniques that have been applied
with success to computer science, mathematics, biology, physics and chemistry.
But for any successful field to become mainstream and reliable, benchmarks must
be developed to quantify progress. This led us in March 2020 to release a
benchmark framework that i) comprises of a diverse collection of mathematical
and real-world graphs, ii) enables fair model comparison with the same
parameter budget to identify key architectures, iii) has an open-source,
easy-to-use and reproducible code infrastructure, and iv) is flexible for
researchers to experiment with new theoretical ideas. As of December 2022, the
GitHub repository has reached 2,000 stars and 380 forks, which demonstrates the
utility of the proposed open-source framework through the wide usage by the GNN
community. In this paper, we present an updated version of our benchmark with a
concise presentation of the aforementioned framework characteristics, an
additional medium-sized molecular dataset AQSOL, similar to the popular ZINC,
but with a real-world measured chemical target, and discuss how this framework
can be leveraged to explore new GNN designs and insights. As a proof of value
of our benchmark, we study the case of graph positional encoding (PE) in GNNs,
which was introduced with this benchmark and has since spurred interest of
exploring more powerful PE for Transformers and GNNs in a robust experimental
setting.

本文介绍了 Graph Neural Networks (GNNs) 领域关于基准测试框架的应用，通过该框架，可对模型进行比较，并且探索新的 GNN 设计和洞见，其中，图形位置编码 (PE) 是该基准测试框架中引入的重要设计之一。