Oversquashing in GNNs through the lens of information contraction and graph expansion

• URL: http://arxiv.org/abs/2208.03471v1
• Date: Sat, 6 Aug 2022 08:44:39 GMT
• Title: Oversquashing in GNNs through the lens of information contraction and graph expansion
• Authors: Pradeep Kr. Banerjee, Kedar Karhadkar, Yu Guang Wang, Uri Alon, Guido Mont\'ufar
• Abstract summary: We present a framework for analyzing oversquashing based on information contraction. We propose a graph rewiring algorithm aimed at alleviating oversquashing.
• Score: 6.8222473597904845
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The quality of signal propagation in message-passing graph neural networks (GNNs) strongly influences their expressivity as has been observed in recent works. In particular, for prediction tasks relying on long-range interactions, recursive aggregation of node features can lead to an undesired phenomenon called "oversquashing". We present a framework for analyzing oversquashing based on information contraction. Our analysis is guided by a model of reliable computation due to von Neumann that lends a new insight into oversquashing as signal quenching in noisy computation graphs. Building on this, we propose a graph rewiring algorithm aimed at alleviating oversquashing. Our algorithm employs a random local edge flip primitive motivated by an expander graph construction. We compare the spectral expansion properties of our algorithm with that of an existing curvature-based non-local rewiring strategy. Synthetic experiments show that while our algorithm in general has a slower rate of expansion, it is overall computationally cheaper, preserves the node degrees exactly and never disconnects the graph.

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