# WeaveNet for Approximating Two-sided Matching Problems

arXiv: https://arxiv.org/abs/2310.12515 · HTML: https://mlsanity.com/paper/2310.12515/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 35 references that are in the map.
- First posted on arXiv 19 Oct 2023.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Balanced Stable Marriage: How Close is Close Enough?](https://mlsanity.com/paper/1707.09545/) (2017)
- [Stable Marriage with Multi-Modal Preferences](https://mlsanity.com/paper/1801.02693/) (2018)

## Abstract (arXiv)

Matching, a task to optimally assign limited resources under constraints, is a fundamental technology for society. The task potentially has various objectives, conditions, and constraints; however, the efficient neural network architecture for matching is underexplored. This paper proposes a novel graph neural network (GNN), textitWeaveNet, designed for bipartite graphs. Since a bipartite graph is generally dense, general GNN architectures lose node-wise information by over-smoothing when deeply stacked. Such a phenomenon is undesirable for solving matching problems. WeaveNet avoids it by preserving edge-wise information while passing messages densely to reach a better solution. To evaluate the model, we approximated one of the textitstrongly NP-hard problems, textitfair stable matching. Despite its inherent difficulties and the network's general purpose design, our model reached a comparative performance with state-of-the-art algorithms specially designed for stable matching for small numbers of agents.