The paper "GEOM-GCN: Geometric Graph Convolutional Networks" addresses two fundamental weaknesses of message-passing neural networks (MPNNs) in representing graph-structured data: losing structural information and lacking long-range dependency capture. To overcome these issues, the authors propose a novel geometric aggregation scheme that leverages a continuous latent space underlying the graph. This scheme includes three modules: node embedding, structural neighborhood, and bi-level aggregation. The node embedding maps nodes to a latent continuous space, the structural neighborhood defines neighborhoods in both the graph and the latent space, and the bi-level aggregation updates node representations using geometric relationships. The authors implement this scheme as Geom-GCN, a graph convolutional network, and evaluate its performance on various datasets, demonstrating state-of-the-art results. The paper also discusses the contributions of the proposed scheme, compares it with related works, and provides experimental results and analysis.The paper "GEOM-GCN: Geometric Graph Convolutional Networks" addresses two fundamental weaknesses of message-passing neural networks (MPNNs) in representing graph-structured data: losing structural information and lacking long-range dependency capture. To overcome these issues, the authors propose a novel geometric aggregation scheme that leverages a continuous latent space underlying the graph. This scheme includes three modules: node embedding, structural neighborhood, and bi-level aggregation. The node embedding maps nodes to a latent continuous space, the structural neighborhood defines neighborhoods in both the graph and the latent space, and the bi-level aggregation updates node representations using geometric relationships. The authors implement this scheme as Geom-GCN, a graph convolutional network, and evaluate its performance on various datasets, demonstrating state-of-the-art results. The paper also discusses the contributions of the proposed scheme, compares it with related works, and provides experimental results and analysis.