WeaveNet: A Differentiable Solver for Non-linear Assignment Problems

Shusaku Sone, Atsushi Hashimoto, Jiaxin Ma, rintaro yanagi, Naoya Chiba, Yoshitaka Ushiku

Keywords: Non-linear assignment, Deep Learning, Stable Matching, 3D Point Cloud Matching

Abstract:

Assignment, a task to match a limited number of elements, is a fundamental problem in informatics. Traditionally, non-linear assignment is discussed as a combinatorial optimization problem with its calculation complexity. On the other hand, it is often a sub-problem of image processing tasks, such as 3D point cloud matching. This paper proposes WeaveNet, a differentiable solver for diverse non-linear assignment problems. Traditional graph convolutional networks (GCNs) suffer from an over-smoothing problem when characterizing nodes with their relationship. WeaveNet overcomes this problem by forwarding edge-wise features at each layer rather than aggregated node features.
To deal with the exponentially large input space of combinatorial optimization problems, we designed WeaveNet to be highly parameter efficient while characterizing edges through stacked set-encoder with cross-concatenation operations. Experimental results show that WeaveNet approximates two strongly NP-hard variants of stable matching in a comparative performance with the gold standard hand-crafted algorithms under the limited size of problem instances. We have also confirmed that it can boost 3D point cloud matching performance significantly.

One-sentence Summary: This paper provides a differentiable combinatorial optimization solver applicable to both NP-hard problems (e.g., fair stable matching) and image processing (e.g., 3D point cloud matching).