Before revision:  The only other ingredients in our network are a spatial gradient operation, which uses dot-products of derivatives to encode tangent-invariant filters, and a multi-layer perceptron applied independently at each point . The resulting architecture, which we call DiffusionNet, is remarkably simple, efficient, and scalable. Continuously optimizing for spatial support avoids the need to pick neighborhood sizes or filter widths a priori, or worry about their impact on network size/training time. Furthermore, the principled, geometric nature of these networks makes them agnostic to the underlying representation and insensitive to discretization. In practice, this means significant robustness to mesh sampling, and even the ability to train on a mesh and evaluate on a point cloud. Our experiments demonstrate that these networks achieve state-of-the-art results for a variety of tasks on both meshes and point clouds, including surface classification, segmentation, and non-rigid correspondence.
After revision:  The only other ingredients in our network are a spatial gradient operation, which uses dot-products of derivatives to encode tangent-invariant filters, and a multi-layer perceptron applied independently at each point , and spatial gradient features to support directional filters. The resulting networks are simple, robust, and efficient. Here, we focus primarily on triangle mesh surfaces, and demonstrate state-of-the-art results for a variety of tasks on both meshes and point clouds, including surface classification, segmentation, and non-rigid correspondence.