A Dynamical Systems-Inspired Pruning Strategy for Addressing Oversmoothing in Graph Neural Networks

TL;DR

This paper introduces DYNAMO-GAT, a novel pruning strategy inspired by dynamical systems theory, to combat oversmoothing in deep Graph Neural Networks by maintaining node feature diversity and stability.

Contribution

It provides a dynamical systems perspective on oversmoothing and proposes a noise-driven, Anti-Hebbian pruning method that enhances GNN stability and expressiveness.

Findings

DYNAMO-GAT effectively prevents oversmoothing in deep GNNs.

Theoretical analysis explains how DYNAMO-GAT disrupts convergence to homogenized states.

Experimental results show superior performance and efficiency on benchmark datasets.

Abstract

Oversmoothing in Graph Neural Networks (GNNs) poses a significant challenge as network depth increases, leading to homogenized node representations and a loss of expressiveness. In this work, we approach the oversmoothing problem from a dynamical systems perspective, providing a deeper understanding of the stability and convergence behavior of GNNs. Leveraging insights from dynamical systems theory, we identify the root causes of oversmoothing and propose \textbf{\textit{DYNAMO-GAT}}. This approach utilizes noise-driven covariance analysis and Anti-Hebbian principles to selectively prune redundant attention weights, dynamically adjusting the network's behavior to maintain node feature diversity and stability. Our theoretical analysis reveals how DYNAMO-GAT disrupts the convergence to oversmoothed states, while experimental results on benchmark datasets demonstrate its superior performance and efficiency compared to traditional and state-of-the-art methods. DYNAMO-GAT not only advances the theoretical understanding of oversmoothing through the lens of dynamical systems but also provides a practical and effective solution for improving the stability and expressiveness of deep GNNs.