Banana: Banach Fixed-Point Network for Pointcloud Segmentation with Inter-Part Equiv a riance - Supplementary Material - Congyue Deng 1 Jiahui Lei

This supplementary document provides proof for the statements in the main paper, as well as network and training details including the compute. We also provide a supplemental video for a quick introduction to our method and additional results. We will also make our code public upon paper acceptance. S.1.1 Well-Definednes of d As d is defined on equivalent classes, we need to show the well-definedness of d in that d is independent of the choice of representatives. Similarly, we can show that d ( ˆ y, ˆ y) 0 . Here we provide an (informal) explanation of why our SE(3) -equivariant message passing architecture is helpful to a small network Lipschitz.