Fast Haar Transforms for Graph Neural Networks
This addresses efficiency issues for researchers and practitioners using GNNs on large-scale graph data, though it appears incremental as it builds on existing GNN frameworks.
The paper tackles the high computational cost of Graph Neural Networks (GNNs) on large graphs by introducing Haar convolution based on sparse, localized Haar basis, achieving state-of-the-art results in graph-based regression and node classification tasks.
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.