# Neural Bipartite Matching

arXiv: https://arxiv.org/abs/2005.11304 · HTML: https://mlsanity.com/paper/2005.11304/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2020.

## Built on by (most cited first, 17 of 17)

- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [The CLRS Algorithmic Reasoning Benchmark](https://mlsanity.com/paper/2205.15659/) (2022)
- [TubeR: Tubelet Transformer for Video Action Detection](https://mlsanity.com/paper/2104.00969/) (2021)
- [Explaining the Explainers in Graph Neural Networks: a Comparative Study](https://mlsanity.com/paper/2210.15304/) (2022)
- [On the Generalization of Neural Combinatorial Optimization Heuristics](https://mlsanity.com/paper/2206.00787/) (2022)
- [Dual Algorithmic Reasoning](https://mlsanity.com/paper/2302.04496/) (2023)
- [Neural Algorithmic Reasoning Without Intermediate Supervision](https://mlsanity.com/paper/2306.13411/) (2023)
- [Algorithmic Concept-based Explainable Reasoning](https://mlsanity.com/paper/2107.07493/) (2021)
- [On the Markov Property of Neural Algorithmic Reasoning: Analyses and Methods](https://mlsanity.com/paper/2403.04929/) (2024)
- [Primal-Dual Neural Algorithmic Reasoning](https://mlsanity.com/paper/2505.24067/) (2025)
- [Learning for Edge-Weighted Online Bipartite Matching with Robustness Guarantees](https://mlsanity.com/paper/2306.00172/) (2023)
- [Continuous Neural Algorithmic Planners](https://mlsanity.com/paper/2211.15839/) (2022)
- [Graph Neural Modeling of Network Flows](https://mlsanity.com/paper/2209.05208/) (2022)
- [Solving Bilevel Knapsack Problem using Graph Neural Networks](https://mlsanity.com/paper/2211.13436/) (2022)
- [Algorithmic Foundations of Deep Learning: Complexity-Theoretic Rates and a Characterization of Universal Approximation](https://mlsanity.com/paper/2606.26705/) (2026)
- [Local Vertex Colouring Graph Neural Networks](https://mlsanity.com/paper/2403.06080/) (2024)
- [Algorithm-Informed Graph Neural Networks for Leakage Detection and Localization in Water Distribution Networks](https://mlsanity.com/paper/2408.02797/) (2024)

## Abstract (arXiv)

Graph neural networks (GNNs) have found application for learning in the space of algorithms. However, the algorithms chosen by existing research (sorting, Breadth-First search, shortest path finding, etc.) usually align perfectly with a standard GNN architecture. This report describes how neural execution is applied to a complex algorithm, such as finding maximum bipartite matching by reducing it to a flow problem and using Ford-Fulkerson to find the maximum flow. This is achieved via neural execution based only on features generated from a single GNN. The evaluation shows strongly generalising results with the network achieving optimal matching almost 100% of the time.