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In this paper, we explore the graph partitioning problem, a pivotalcombina-torial optimization challenge with extensive applications in variousfields such as science, technology, and business. Recognized as an NP-hardprob-lem, graph partitioning lacks polynomial-time algorithms for itsresolution. Recently, there has been a burgeoning interest in leveragingmachine learn-ing, particularly approaches like supervised, unsupervised, andreinforce-ment learning, to tackle such NP-hard problems. However, thesemethods face significant hurdles: supervised learning is constrained by thenecessity of labeled solution instances, which are often computationallyimpractical to obtain; reinforcement learning grapples with instability in thelearning pro-cess; and unsupervised learning contends with the absence of adifferentia-ble loss function, a consequence of the discrete nature of mostcombinatorial optimization problems. Addressing these challenges, our researchintroduces a novel pipeline employing an unsupervised graph neural network tosolve the graph partitioning problem. The core innovation of this study is thefor-mulation of a differentiable loss function tailored for this purpose. Werigor-ously evaluate our methodology against contemporary state-of-the-arttech-niques, focusing on metrics: cuts and balance, and our findings revealthat our is competitive with these leading methods.

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