Graph partitioning aims to divide a graph into disjoint subsets while optimizing a specific partitioning objective. The majority of formulations related to graph partitioning exhibit NP-hardness due to their combinatorial nature. Conventional methods, like approximation algorithms or heuristics, are designed for distinct partitioning objectives and fail to achieve generalization across other important partitioning objectives. Recently machine learning-based methods have been developed that learn directly from data. Further, these methods have a distinct advantage of utilizing node features that carry additional information. However, these methods assume differentiability of target partitioning objective functions and cannot generalize for an unknown number of partitions, i.e., they assume the number of partitions is provided in advance. In this study, we develop NeuroCUT with two key innovations over previous methodologies. First, by leveraging a reinforcement learning-based framework over node representations derived from a graph neural network and positional features, NeuroCUT can accommodate any optimization objective, even those with non-differentiable functions. Second, we decouple the parameter space and the partition count making NeuroCUT inductive to any unseen number of partition, which is provided at query time. Through empirical evaluation, we demonstrate that NeuroCUT excels in identifying high-quality partitions, showcases strong generalization across a wide spectrum of partitioning objectives, and exhibits strong generalization to unseen partition count.

翻译：图分割旨在将图划分为不相交的子集，同时优化特定的分割目标。由于其组合性质，大多数与图分割相关的公式都表现出NP难度。传统方法（如近似算法或启发式算法）是为不同的分割目标而设计的，无法推广到其他重要的分割目标。最近，基于机器学习的方法得以发展，可以直接从数据中学习。此外，这些方法具有利用携带额外信息的节点特征的显著优势。然而，这些方法假设目标分割目标函数是可微的，并且无法泛化到未知数量的分区，即它们假设分区数量是预先提供的。在本研究中，我们开发了NeuroCUT，它在先前方法基础上有两项关键创新。首先，通过利用基于图神经网络和位置特征派生的节点表示的强化学习框架，NeuroCUT可以适应任何优化目标，即使是具有非可微函数的目标。其次，我们将参数空间和分区数量解耦，使得NeuroCUT能够归纳推理到任何在查询时提供的未见分区数量。通过实证评估，我们证明NeuroCUT在识别高质量分区方面表现出色，在广泛的分割目标中展现出强大的泛化能力，并且对未见过的分区数量表现出强大的泛化能力。