Oversmoothing in Graph Neural Networks

Oversmoothing is a widely known problem in graph neural networks: As the network gets deeper, all of the features would converge towards some fixed point, at which point it becomes impossible to identify nodes from one another. This essentially puts a soft cap on how deep a graph neural network can be. In our project, we are theoretically analysing and empirically testing the metrics for quantifying oversmoothing in the literature, and realised that most of them are guaranteed NOT to work, unless under some very specific or non-standard setups. In this project, we are thus proposing and trying to get a theoretical proof of the convergence of the effective rank towards 1 as a more powerful and robust alternative metric.