Enhancing Graph Representations with Neighborhood-Contextualized Message-Passing

TL;DR

The paper tackles the limited expressivity of classic one-hop GNNs by incorporating neighborhood context into message passing. It formalizes neighborhood-contextualization and proposes the NCMP framework, with SINC-GCN as a practical, efficient instantiation that uses contextualized messages and neighborhood-aware aggregation, expressed as $\bigoplus_{v \in \mathcal{N}(u)} \psi(\boldsymbol{h_u}, \boldsymbol{h_v}, \{\boldsymbol{h_w}: w \in \mathcal{N}(u)\})$. A conceptual proof of SINC-GCN shows a permutation-invariant architecture with a shared neighborhood transform, achieving complexity $O(|\mathcal{V}| d_{hidden} d_{in} + |\mathcal{E}| d_{hidden} + |\mathcal{V}| d_{out} d_{hidden})$ and reducing to $\text{SIR-GCN}$ when $\boldsymbol{W_N}=0$. On a synthetic UniqueSignature task, SINC-GCN exhibits strong expressivity and efficiency, attaining perfect accuracy where baselines struggle, and maintains competitive runtime relative to traditional one-hop GNNs, highlighting the practical impact of NCMP for enhancing graph representations.

Abstract

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.

Figures (2)

• Figure 1: Graph Neural Network Architecture Variants.
• Figure 2: Neighborhood-Contextualized Message-Passing.