Graph neural networks (GNNs) have gained significant interest in recent years
due to their ability to handle arbitrarily structured data represented as
graphs. GNNs generally follow the message-passing scheme to locally update node
feature representations. A graph readout function is then employed to create a
representation for the entire graph. Several studies proposed different GNNs by
modifying the aggregation and combination strategies of the message-passing
framework, often inspired by heuristics. Nevertheless, several studies have
begun exploring GNNs from a theoretical perspective based on the graph
isomorphism problem which inherently assumes countable node feature
representations. Yet, there are only a few theoretical works exploring GNNs
with uncountable node feature representations. This paper presents a new
perspective on the representational capabilities of GNNs across all levels -
node-level, neighborhood-level, and graph-level - when the space of node
feature representation is uncountable. From the results, a novel
soft-isomorphic relational graph convolution network (SIR-GCN) is proposed that
emphasizes non-linear and contextualized transformations of neighborhood
feature representations. The mathematical relationship of SIR-GCN and three
widely used GNNs is explored to highlight the contribution. Validation on
synthetic datasets then demonstrates that SIR-GCN outperforms comparable models
even in simple node and graph property prediction tasks.

本论文从理论角度探索了具有不可数节点特征表示的图神经网络的表征能力，提出了一种新颖的软同构关系图卷积网络（SIR-GCN），并通过与其他常用图神经网络的数学关系进行验证，证明其在简单节点和图属性预测任务中优于其他模型。