GPNet: Simplifying Graph Neural Networks via Multi-channel Geometric Polynomials

TL;DR

GPNet is a simple, efficient one-layer graph neural network that addresses common limitations of GNNs by integrating multi-channel geometric polynomials, and it outperforms many baselines in various tasks.

Contribution

The paper introduces GPNet, a novel GNN model combining dilated convolution, multi-channel learning, self-attention, and sign factors, with theoretical analysis and superior empirical performance.

Findings

GPNet outperforms baseline models in accuracy and complexity.

Theoretical analysis shows GPNet can approximate various graph filters.

GPNet achieves competitive results on inductive learning tasks.

Abstract

Graph Neural Networks (GNNs) are a promising deep learning approach for circumventing many real-world problems on graph-structured data. However, these models usually have at least one of four fundamental limitations: over-smoothing, over-fitting, difficult to train, and strong homophily assumption. For example, Simple Graph Convolution (SGC) is known to suffer from the first and fourth limitations. To tackle these limitations, we identify a set of key designs including (D1) dilated convolution, (D2) multi-channel learning, (D3) self-attention score, and (D4) sign factor to boost learning from different types (i.e. homophily and heterophily) and scales (i.e. small, medium, and large) of networks, and combine them into a graph neural network, GPNet, a simple and efficient one-layer model. We theoretically analyze the model and show that it can approximate various graph filters by adjusting the self-attention score and sign factor. Experiments show that GPNet consistently outperforms baselines in terms of average rank, average accuracy, complexity, and parameters on semi-supervised and full-supervised tasks, and achieves competitive performance compared to state-of-the-art model with inductive learning task.