Graph Neural Networks (GNNs) have achieved remarkable success by extending traditional convolution to learning on non-Euclidean data. The key to the GNNs is adopting the neural message-passing paradigm with two stages: aggregation and update. The current design of GNNs considers the topology information in the aggregation stage. However, in the updating stage, all nodes share the same updating function. The identical updating function treats each node embedding as i.i.d. random variables and thus ignores the implicit relationships between neighborhoods, which limits the capacity of the GNNs. The updating function is usually implemented with a linear transformation followed by a non-linear activation function. To make the updating function topology-aware, we inject the topological information into the non-linear activation function and propose Graph-adaptive Rectified Linear Unit (GReLU), which is a new parametric activation function incorporating the neighborhood information in a novel and efficient way. The parameters of GReLU are obtained from a hyperfunction based on both node features and the corresponding adjacent matrix. To reduce the risk of overfitting and the computational cost, we decompose the hyperfunction as two independent components for nodes and features respectively. We conduct comprehensive experiments to show that our plug-and-play GReLU method is efficient and effective given different GNN backbones and various downstream tasks.

翻译：神经网络(GNNs) 取得了显著的成功。 GNNs 的关键是采用神经信息传递模式,分为两个阶段: 聚合和更新。 GNNs 目前的设计考虑汇总阶段的表层信息。 然而,在更新阶段,所有节点都具有相同的更新功能。 相同的更新功能将每个节点嵌入作为i.d. 随机变量处理,从而忽略了邻居之间的隐含关系,这限制了 GNNS 的能力。 更新功能通常是通过直线转换来实施,然后是非线性激活功能。 要将更新功能的表层了解和升级,我们将表层信息输入到非线性启动阶段。 然而,在更新阶段,所有节点共享相同的更新功能都具有相同的更新功能。 相同的更新功能将每个节点嵌入为i.d. 随机变量,从而忽略了邻居之间的隐含关系。 GRELU 参数来自基于节点特性和相应的直线性转换,然后是非线性激活功能激活功能。 将表层信息信息信息信息信息输入到 GLsurbleadal 的系统, 将测试中的风险分别用于高端和高端测试。