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Graph Neural Networks (GNNs) have succeeded in various computer scienceapplications, yet deep GNNs underperform their shallow counterparts despitedeep learning's success in other domains. Over-smoothing and over-squashing arekey challenges when stacking graph convolutional layers, hindering deeprepresentation learning and information propagation from distant nodes. Ourwork reveals that over-smoothing and over-squashing are intrinsically relatedto the spectral gap of the graph Laplacian, resulting in an inevitabletrade-off between these two issues, as they cannot be alleviatedsimultaneously. To achieve a suitable compromise, we propose adding andremoving edges as a viable approach. We introduce the Stochastic Jost and LiuCurvature Rewiring (SJLR) algorithm, which is computationally efficient andpreserves fundamental properties compared to previous curvature-based methods.Unlike existing approaches, SJLR performs edge addition and removal during GNNtraining while maintaining the graph unchanged during testing. Comprehensivecomparisons demonstrate SJLR's competitive performance in addressingover-smoothing and over-squashing.

On the Trade-off between Over-smoothing and Over-squashing in Deep Graph Neural Networks