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

Abstract: 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.