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

TL;DR

This paper introduces a novel GNN architecture with a pyramidal skeleton and link rewiring, enhancing expressivity, convergence speed, and robustness through a three-pipeline training framework.

Contribution

It proposes a new GNN architecture with a pyramidal skeleton and link rewiring, and a three-pipeline training framework to improve expressivity and performance.

Findings

Improved convergence speed in node classification tasks.

Enhanced robustness to erroneous weighted links.

Validated architecture's expressivity through dynamics and topology analysis.

Abstract

Expressivity plays a fundamental role in evaluating deep neural networks, and it is closely related to understanding the limit of performance improvement. In this paper, we propose a three-pipeline training framework based on critical expressivity, including global model contraction, weight evolution, and link's weight rewiring. Specifically, we propose a pyramidal-like skeleton to overcome the saddle points that affect information transfer. Then we analyze the reason for the modularity (clustering) phenomenon in network topology and use it to rewire potential erroneous weighted links. We conduct numerical experiments on node classification and the results confirm that the proposed training framework leads to a significantly improved performance in terms of fast convergence and robustness to potential erroneous weighted links. The architecture design on GNNs, in turn, verifies the expressivity of GNNs from dynamics and topological space aspects and provides useful guidelines in designing more efficient neural networks.