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Expressivity plays a fundamental role in evaluating deep neural networks, andit is closely related to understanding the limit of performance improvement. Inthis paper, we propose a three-pipeline training framework based on criticalexpressivity, including global model contraction, weight evolution, and link'sweight rewiring. Specifically, we propose a pyramidal-like skeleton to overcomethe saddle points that affect information transfer. Then we analyze the reasonfor the modularity (clustering) phenomenon in network topology and use it torewire potential erroneous weighted links. We conduct numerical experiments onnode classification and the results confirm that the proposed trainingframework leads to a significantly improved performance in terms of fastconvergence and robustness to potential erroneous weighted links. Thearchitecture design on GNNs, in turn, verifies the expressivity of GNNs fromdynamics and topological space aspects and provides useful guidelines indesigning more efficient neural networks.

A Deep Graph Neural Networks Architecture Design: From Global Pyramid-like Shrinkage Skeleton to Local Topology Link Rewiring