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NeuroCUT: A Neural Approach for Robust Graph Partitioning

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.

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