AdaptedNorm: An Adaptive Modeling Strategy for Graph Convolutional Network-Based Deep Learning Tasks

Graph neural networks (GNNs), particularly graph convolutional networks (GCNs), have demonstrated remarkable success in modeling graph-structured data across diverse applications. A critical yet underexplored aspect of GCN design lies in graph representation normalization, where the choice of normalization scheme significantly influences model performance on learning tasks. Despite its importance, existing research lacks systematic analysis on determining optimal task-specific normalization strategies. This study proposes AdaptedNorm, a principled framework that establishes connections between normalization schemes and GCN task objectives, while introducing three key contributions: 1) A novel random walk re-normalized transformation (RWRT) technique for graph representation normalization; 2) A task-aligned modeling paradigm demonstrating that symmetric re-normalized transformation (SRT) enhances node classification accuracy, while RWRT achieves superior performance in link prediction; 3) Integration of normalization schemes with GNN sparsification strategies, enabling effective model compression without sacrificing performance. Extensive experiments on benchmark datasets (Cora, Citeseer, and PubMed) confirm the generalizability of the findings. The implementation is publicly available at: https://www.github.com/ChuanDai/AdaptedNorm.