Wednesday, October 26, 2022 - 4:00pm to 4:30pm
Event Calendar Category
LIDS & Stats Tea
IDSS & LIDS
Building and Room Number
A central challenge of building more powerful Graph Neural Networks (GNNs) is the oversmoothing phenomenon, where increasing the network depth leads to homogeneous node representations and thus worse classification performance. While previous works have only demonstrated that oversmoothing is inevitable when the number of graph convolutions tends to infinity, in this paper, we precisely characterize the mechanism behind the phenomenon via a non-asymptotic analysis. Specifically, we distinguish between two different effects when applying graph convolutions---an undesirable mixing effect that homogenizes node representations in different classes, and a desirable denoising effect that homogenizes node representations in the same class. By quantifying these two effects on random graphs sampled from the Contextual Stochastic Block Model (CSBM), we show that oversmoothing happens once the mixing effect starts to dominate the denoising effect, and the number of layers required for this transition is O(log N/log (log N)) for sufficiently dense graphs with N nodes. We also extend our analysis to study the effects of Personalized PageRank (PPR) on oversmoothing. Our results suggest that while PPR mitigates oversmoothing at deeper layers, PPR-based architectures still achieve their best performance at a shallow depth and are outperformed by the graph convolution approach on certain graphs. Finally, we support our theoretical results with numerical experiments, which further suggest that the oversmoothing phenomenon observed in practice may be exacerbated by the difficulty of optimizing deep GNN models.
Joint work with Zhengdao Chen, William Wang and Ali Jadbabaie.
Xinyi Wu is a third-year Ph.D. student at IDSS and LIDS, advised by Prof. Ali Jadbabaie. Prior to MIT, she graduated from Washington University in St. Louis with a B.A. in Mathematics. Her research interests include network science and machine learning.