Improving Graph Convolutional Networks with Non-Parametric Activation Functions

TL;DR

This paper explores the integration of non-parametric kernel activation functions into graph convolutional networks, demonstrating significant performance improvements over traditional activation functions.

Contribution

It introduces the use of kernel activation functions in GCNs, providing a flexible, regularizable, and smooth alternative to standard nonlinearities, and shows their effectiveness through experiments.

Findings

Kernel activation functions improve GCN performance.

Adding complex activations outperforms increasing network depth or size.

Proposed method is easy to implement and regularize.

Abstract

Graph neural networks (GNNs) are a class of neural networks that allow to efficiently perform inference on data that is associated to a graph structure, such as, e.g., citation networks or knowledge graphs. While several variants of GNNs have been proposed, they only consider simple nonlinear activation functions in their layers, such as rectifiers or squashing functions. In this paper, we investigate the use of graph convolutional networks (GCNs) when combined with more complex activation functions, able to adapt from the training data. More specifically, we extend the recently proposed kernel activation function, a non-parametric model which can be implemented easily, can be regularized with standard $\ell_p$-norms techniques, and is smooth over its entire domain. Our experimental evaluation shows that the proposed architecture can significantly improve over its baseline, while similar improvements cannot be obtained by simply increasing the depth or size of the original GCN.