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.

本研究引入了一种新颖的流程，利用无监督图神经网络来解决图分割问题，并提出了一个专门用于此目的的可微损失函数。对于当前先进技术，我们对度量指标：割边和平衡进行了严格评估，结果表明我们的方法具有竞争力。

一种用于图划分中无监督图神经网络的新的可微损失函数