  In this paper, we propose a novel activation function tailored specifically
for graph data in Graph Neural Networks (GNNs). Motivated by the need for
graph-adaptive and flexible activation functions, we introduce DiGRAF,
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
conduct an extensive set of experiments across diverse datasets and tasks,
demonstrating a consistent and superior performance of DiGRAF compared to
traditional and graph-specific activation functions, highlighting its
effectiveness as an activation function for GNNs.
