Enhancing Graph Representations with Neighborhood-Contextualized Message-Passing

Graph neural networks (GNNs) have become an indispensable tool for analyzing relational data. In the literature, classical GNNs may be classified into three variants: convolutional, attentional, and message-passing. While the standard message-passing variant is highly expressive, its typical pair-wise messages nevertheless only consider the features of the center node and each neighboring node individually. This design fails to incorporate the rich contextual information contained within the broader local neighborhood, potentially hindering its ability to learn complex relationships within the entire set of neighboring nodes. To address this limitation, this work first formalizes the concept of neighborhood-contextualization, rooted in a key property of the attentional variant. This then serves as the foundation for generalizing the message-passing variant to the proposed neighborhood-contextualized message-passing (NCMP) framework. To demonstrate its utility, a simple, practical, and efficient method to parametrize and operationalize NCMP is presented, leading to the development of the proposed Soft-Isomorphic Neighborhood-Contextualized Graph Convolution Network (SINC-GCN). A preliminary analysis on a synthetic binary node classification problem then underscores both the expressivity and efficiency of the proposed GNN architecture. Overall, the paper lays the foundation for the novel NCMP framework as a practical path toward further enhancing the graph representational power of classical GNNs.

Contextualized Messages Boost Graph Representations

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.