  Learning to autonomously assemble shapes is a crucial skill for many robotic
applications. While the majority of existing part assembly methods focus on
correctly posing semantic parts to recreate a whole object, we interpret
assembly more literally: as mating geometric parts together to achieve a snug
fit. By focusing on shape alignment rather than semantic cues, we can achieve
across-category generalization. In this paper, we introduce a novel task,
pairwise 3D geometric shape mating, and propose Neural Shape Mating (NSM) to
tackle this problem. Given the point clouds of two object parts of an unknown
category, NSM learns to reason about the fit of the two parts and predict a
pair of 3D poses that tightly mate them together. We couple the training of NSM
with an implicit shape reconstruction task to make NSM more robust to imperfect
point cloud observations. To train NSM, we present a self-supervised data
collection pipeline that generates pairwise shape mating data with ground truth
by randomly cutting an object mesh into two parts, resulting in a dataset that
consists of 200K shape mating pairs from numerous object meshes with diverse
cut types. We train NSM on the collected dataset and compare it with several
point cloud registration methods and one part assembly baseline. Extensive
experimental results and ablation studies under various settings demonstrate
the effectiveness of the proposed algorithm. Additional material is available
at: https://neural-shape-mating.github.io/
