Title: Ricci-GNN: Defending Against Structural Attacks Through a Geometric Approach. Abstract: Graph neural networks (GNNs) rely heavily on the underlying graph topology and thus can be vulnerable to malicious attacks targeting at graph structures. We propose a novel GNN defense algorithm against structural attacks that maliciously modify graph topology. In particular, we discover a robust representation of the input graph based on the advanced theory of graph Ricci flow, which captures the intrinsic geometry of graphs and is robust to structural perturbation. We propose an algorithm to train GNNs using re-sampled graphs based on such geometric representation. We show that this method can be effective to protect against adversarial structural attacks. Our method achieves state-of-the-art performance on synthetic and real datasets against different types of graph poisoning attacks.