# A Novel Differentiable Loss Function for Unsupervised Graph Neural Networks in Graph Partitioning

arXiv: https://arxiv.org/abs/2312.06877 · HTML: https://mlsanity.com/paper/2312.06877/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 33 references that are in the map.
- First posted on arXiv 11 Dec 2023.

## Builds on (most cited first, 15 of 15)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [Combinatorial Optimization with Graph Convolutional Networks and Guided Tree Search](https://mlsanity.com/paper/1810.10659/) (2018)
- [Erdos Goes Neural: an Unsupervised Learning Framework for Combinatorial Optimization on Graphs](https://mlsanity.com/paper/2006.10643/) (2020)
- [Combinatorial Optimization with Physics-Inspired Graph Neural Networks](https://mlsanity.com/paper/2107.01188/) (2021)
- [Neural Graph Matching Network: Learning Lawler's Quadratic Assignment Problem with Extension to Hypergraph and Multiple-graph Matching](https://mlsanity.com/paper/1911.11308/) (2019)
- [Graph Colouring Meets Deep Learning: Effective Graph Neural Network Models for Combinatorial Problems](https://mlsanity.com/paper/1903.04598/) (2019)
- [It's Not What Machines Can Learn, It's What We Cannot Teach](https://mlsanity.com/paper/2002.09398/) (2020)
- [Machine Learning Methods in Solving the Boolean Satisfiability Problem](https://mlsanity.com/paper/2203.04755/) (2022)
- [Learning-Augmented Mechanism Design: Leveraging Predictions for Facility Location](https://mlsanity.com/paper/2204.01120/) (2022)

## Abstract (arXiv)

In this paper, we explore the graph partitioning problem, a pivotal combina-torial optimization challenge with extensive applications in various fields such as science, technology, and business. Recognized as an NP-hard prob-lem, graph partitioning lacks polynomial-time algorithms for its resolution. Recently, there has been a burgeoning interest in leveraging machine learn-ing, particularly approaches like supervised, unsupervised, and reinforce-ment learning, to tackle such NP-hard problems. However, these methods face significant hurdles: supervised learning is constrained by the necessity of labeled solution instances, which are often computationally impractical to obtain; reinforcement learning grapples with instability in the learning pro-cess; and unsupervised learning contends with the absence of a differentia-ble loss function, a consequence of the discrete nature of most combinatorial optimization problems. Addressing these challenges, our research introduces a novel pipeline employing an unsupervised graph neural network to solve the graph partitioning problem. The core innovation of this study is the for-mulation of a differentiable loss function tailored for this purpose. We rigor-ously evaluate our methodology against contemporary state-of-the-art tech-niques, focusing on metrics: cuts and balance, and our findings reveal that our is competitive with these leading methods.