Scale Invariance of Graph Neural Network for Node Classification

Qin Jiang, Chengjia Wang, Michael Lones, Wei Pang

TL;DR: Theoretical and empirical proof of scale invariance in graph neural networks

Abstract:

We address two fundamental challenges in Graph Neural Networks (GNNs) for node classification: (1) the lack of theoretical support for invariance learning, a critical property in image processing, and (2) the absence of a unified model capable of excelling on both homophilic and heterophilic graph datasets.
To tackle these issues, we establish and prove scale invariance in graphs, extending this key property to graph learning, and validate it through experiments on real-world datasets. Leveraging directed multi-scaled graphs and an adaptive self-loop strategy, we propose ScaleNet, a unified network architecture that achieves state-of-the-art performance across four homophilic and two heterophilic benchmark datasets. Furthermore, we show that through graph transformation based on scale invariance, uniform weights can replace computationally expensive edge weights in digraph inception networks while maintaining or improving performance. For another popular GNN approach to digraphs, we demonstrate the equivalence between Hermitian Laplacian methods and GraphSAGE with incidence normalization.
ScaleNet bridges the gap between homophilic and heterophilic graph learning, offering both theoretical insights into scale invariance and practical advancements in unified graph learning. Our implementation is publicly available at https://anonymous.4open.science/r/ScaleNet-B663.

Primary Area: Deep Learning->Graph Neural Networks

Keywords: scale invariance, graph neural network, directed graph, heterophilic graph

Submission Number: 783