DiGRAF: Diffeomorphic Graph-Adaptive Activation Function

Krishna Sri Ipsit Mantri, Xinzhi Wang, Carola-Bibiane Schönlieb, Bruno Ribeiro, Beatrice Bevilacqua, Moshe Eliasof

Keywords: Graph Neural Networks, Graph Activation Functions

TL;DR: We introduce DiGRAF - a novel graph-adaptive activation function for GNNs by learning flexible and efficient diffeomorphisms, and demonstrate its effectiveness on numerous benchmarks and tasks.

Abstract: In this paper, we introduce DiGRAF, a novel framework leveraging Continuous Piecewise-Affine Based (CPAB) transformations, which we augment with an additional GNN to learn a graph-adaptive diffeomorphic activation function in an end-to-end manner. In addition to its graph-adaptivity and flexibility, DiGRAF also possesses properties that are widely recognized as desirable for activation functions, such as differentiability, boundness within the domain and computational efficiency. We show the consistent and superior performance of DiGRAF across a variety of graph benchmarks, highlighting its effectiveness as an activation function for GNNs.

Submission Type: Extended abstract (max 4 main pages).

Submission Number: 33