Generalizing Aggregation Functions in GNNs: Building High Capacity and Robust GNNs via Nonlinear Aggregation

The main aspect powering GNNs is the multi-layer network architecture to learn the nonlinear representation for graph learning task. The core operation in GNNs is the message propagation in which each node updates its information by aggregating the information from its neighbors. Existing GNNs usually adopt either linear neighborhood aggregation (e.g. mean, sum) or max aggregator in their message propagation. 1) For linear aggregators, the whole nonlinearity and network's capacity of GNNs are generally limited because deeper GNNs usually suffer from the over-smoothing issue due to their inherent information propagation mechanism. Also, linear aggregators are usually vulnerable to the spatial perturbations. 2) For max aggregator, it usually fails to be aware of the detailed information of node representations within neighborhood. To overcome these issues, we re-think the message propagation mechanism in GNNs and develop the new general nonlinear aggregators for neighborhood information aggregation in GNNs. One main aspect of our nonlinear aggregators is that they all provide the optimally balanced aggregator between max and mean/sum aggregators. Thus, they can inherit both i) high nonlinearity that enhances network's capacity, robustness and ii) detail-sensitivity that is aware of the detailed information of node representations in GNNs' message propagation. Promising experiments show the effectiveness, high capacity and robustness of the proposed methods.