Fast Haar Transforms for Graph Neural Networks

TL;DR

This paper introduces a Haar basis for graph neural networks that enables fast convolution computations, significantly reducing computational costs for large graphs and achieving state-of-the-art results in graph classification and regression tasks.

Contribution

It proposes a sparse, localized Haar basis for graph Laplacians, enabling fast Haar transforms and efficient convolution in GNNs, which was not previously available.

Findings

Achieves faster convolution computation on large graphs.

Demonstrates state-of-the-art performance on regression tasks.

Improves efficiency of GNNs with Haar-based transforms.

Abstract

Graph Neural Networks (GNNs) have become a topic of intense research recently due to their powerful capability in high-dimensional classification and regression tasks for graph-structured data. However, as GNNs typically define the graph convolution by the orthonormal basis for the graph Laplacian, they suffer from high computational cost when the graph size is large. This paper introduces Haar basis which is a sparse and localized orthonormal system for a coarse-grained chain on graph. The graph convolution under Haar basis, called Haar convolution, can be defined accordingly for GNNs. The sparsity and locality of the Haar basis allow Fast Haar Transforms (FHTs) on graph, by which a fast evaluation of Haar convolution between graph data and filters can be achieved. We conduct experiments on GNNs equipped with Haar convolution, which demonstrates state-of-the-art results on graph-based regression and node classification tasks.