A New Perspective on the Effects of Spectrum in Graph Neural Networks
This addresses a bottleneck in GNNs for researchers and practitioners in graph learning, offering an incremental improvement by removing correlation issues to enable more sophisticated filters.
The paper tackles the performance limitations of Graph Neural Networks (GNNs) by identifying that unsmooth spectra cause correlation issues, restricting the use of powerful filters and deep architectures, and proposes a correlation-free architecture that boosts graph representation learning performance.
Many improvements on GNNs can be deemed as operations on the spectrum of the underlying graph matrix, which motivates us to directly study the characteristics of the spectrum and their effects on GNN performance. By generalizing most existing GNN architectures, we show that the correlation issue caused by the $unsmooth$ spectrum becomes the obstacle to leveraging more powerful graph filters as well as developing deep architectures, which therefore restricts GNNs' performance. Inspired by this, we propose the correlation-free architecture which naturally removes the correlation issue among different channels, making it possible to utilize more sophisticated filters within each channel. The final correlation-free architecture with more powerful filters consistently boosts the performance of learning graph representations. Code is available at https://github.com/qslim/gnn-spectrum.