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This paper introduces a new problem in 3D point cloud: few-shot instance segmentation. Given a few annotated point clouds exemplified a target class, our goal is to segment all instances of this target class in a query point cloud. This problem has a wide range of practical applications where point-wise instance segmentation annotation is prohibitively expensive to collect. To address this problem, we present Geodesic-Former -- the first geodesic-guided transformer for 3D point cloud instance segmentation. The key idea is to leverage the geodesic distance to tackle the density imbalance of LiDAR 3D point clouds. The LiDAR 3D point clouds are dense near the object surface and sparse or empty elsewhere making the Euclidean distance less effective to distinguish different objects. The geodesic distance, on the other hand, is more suitable since it encodes the scene's geometry which can be used as a guiding signal for the attention mechanism in a transformer decoder to generate kernels representing distinct features of instances. These kernels are then used in a dynamic convolution to obtain the final instance masks. To evaluate Geodesic-Former on the new task, we propose new splits of the two common 3D point cloud instance segmentation datasets: ScannetV2 and S3DIS. Geodesic-Former consistently outperforms strong baselines adapted from state-of-the-art 3D point cloud instance segmentation approaches with a significant margin. Code is available at https://github.com/VinAIResearch/GeoFormer.