Adaptive Message Passing: A General Framework to Mitigate Oversmoothing, Oversquashing, and Underreaching
This addresses a key limitation in graph neural networks for modeling complex systems, offering a general solution to improve long-range interaction capture, though it appears incremental as it builds on existing variational inference and message passing techniques.
The paper tackles the problem of deep graph networks failing to capture long-range dependencies due to oversmoothing, oversquashing, and underreaching, by proposing an adaptive message passing framework that learns to adjust depth and filter messages, achieving competitive results with state-of-the-art methods on five node and graph prediction datasets.
Long-range interactions are essential for the correct description of complex systems in many scientific fields. The price to pay for including them in the calculations, however, is a dramatic increase in the overall computational costs. Recently, deep graph networks have been employed as efficient, data-driven models for predicting properties of complex systems represented as graphs. These models rely on a message passing strategy that should, in principle, capture long-range information without explicitly modeling the corresponding interactions. In practice, most deep graph networks cannot really model long-range dependencies due to the intrinsic limitations of (synchronous) message passing, namely oversmoothing, oversquashing, and underreaching. This work proposes a general framework that learns to mitigate these limitations: within a variational inference framework, we endow message passing architectures with the ability to adapt their depth and filter messages along the way. With theoretical and empirical arguments, we show that this strategy better captures long-range interactions, by competing with the state of the art on five node and graph prediction datasets.