Learning to Control the Smoothness of Graph Convolutional Network Features

TL;DR

This paper introduces a method for controlling the smoothness of features in graph convolutional networks, improving node classification by adaptively balancing smooth and non-smooth components based on data and task requirements.

Contribution

The paper proposes a novel augmented message-passing scheme that learns to modulate feature smoothness in GCNs, backed by geometric insights and efficient implementation.

Findings

Enhanced node classification accuracy with the proposed method

Significant improvement over standard GCNs in experiments

Effective control of feature smoothness ratio

Abstract

The pioneering work of Oono and Suzuki [ICLR, 2020] and Cai and Wang [arXiv:2006.13318] initializes the analysis of the smoothness of graph convolutional network (GCN) features. Their results reveal an intricate empirical correlation between node classification accuracy and the ratio of smooth to non-smooth feature components. However, the optimal ratio that favors node classification is unknown, and the non-smooth features of deep GCN with ReLU or leaky ReLU activation function diminish. In this paper, we propose a new strategy to let GCN learn node features with a desired smoothness -- adapting to data and tasks -- to enhance node classification. Our approach has three key steps: (1) We establish a geometric relationship between the input and output of ReLU or leaky ReLU. (2) Building on our geometric insights, we augment the message-passing process of graph convolutional layers (GCLs) with a learnable term to modulate the smoothness of node features with computational efficiency. (3) We investigate the achievable ratio between smooth and non-smooth feature components for GCNs with the augmented message-passing scheme. Our extensive numerical results show that the augmented message-passing schemes significantly improve node classification for GCN and some related models.