Title: Learning Discrete Adaptive Receptive Fields for Graph Convolutional Networks. Abstract: Different nodes in a graph neighborhood generally yield different importance. In previous work of Graph Convolutional Networks (GCNs), such differences are typically modeled with attention mechanisms. However, as we prove in our paper, soft attention weights suffer from over-smoothness in large neighborhoods. To address this weakness, we introduce a novel framework of conducting graph convolutions, where nodes are discretely selected among multi-hop neighborhoods to construct adaptive receptive fields (ARFs). ARFs enable GCNs to get rid of the over-smoothness of soft attention weights, as well as to efficiently explore long-distance dependencies in graphs. We further propose GRARF (GCN with Reinforced Adaptive Receptive Fields) as an instance, where an optimal policy of constructing ARFs is learned with reinforcement learning. GRARF achieves or matches state-of-the-art performances on public datasets from different domains. Our further analysis corroborates that GRARF is more robust than attention models against neighborhood noises.