A Note on Over-Smoothing for Graph Neural Networks
This work addresses the over-smoothing problem in GNNs, which is a domain-specific issue for researchers and practitioners in graph machine learning, and is incremental as it builds upon prior results.
The paper analyzes the over-smoothing effect in Graph Neural Networks (GNNs), showing that under certain conditions on the weight matrix related to the spectrum of the augmented normalized Laplacian, the Dirichlet energy of embeddings converges to zero, leading to loss of discriminative power.
Graph Neural Networks (GNNs) have achieved a lot of success on graph-structured data. However, it is observed that the performance of graph neural networks does not improve as the number of layers increases. This effect, known as over-smoothing, has been analyzed mostly in linear cases. In this paper, we build upon previous results \cite{oono2019graph} to further analyze the over-smoothing effect in the general graph neural network architecture. We show when the weight matrix satisfies the conditions determined by the spectrum of augmented normalized Laplacian, the Dirichlet energy of embeddings will converge to zero, resulting in the loss of discriminative power. Using Dirichlet energy to measure "expressiveness" of embedding is conceptually clean; it leads to simpler proofs than \cite{oono2019graph} and can handle more non-linearities.