Reducing a graph while preserving its overall structure is an important problem with many applications. Typically, the reduction approaches either remove edges (sparsification) or merge nodes (coarsening) in an unsupervised way with no specific downstream task in mind. In this paper, we present an approach for subsampling graph structures using an Ising model defined on either the nodes or edges and learning the external magnetic field of the Ising model using a graph neural network. Our approach is task-specific as it can learn how to reduce a graph for a specific downstream task in an end-to-end fashion. The utilized loss function of the task does not even have to be differentiable. We showcase the versatility of our approach on three distinct applications: image segmentation, 3D shape sparsification, and sparse approximate matrix inverse determination.

翻译：在保留图整体结构的前提下进行图缩减是一个具有广泛应用的重要问题。典型的缩减方法通常以无监督方式（不考虑特定下游任务）移除边（稀疏化）或合并节点（粗化）。本文提出了一种基于伊辛模型的图结构子采样方法，该模型可定义在节点或边上，并通过图神经网络学习伊辛模型的外磁场。我们的方法具有任务特异性，能够以端到端方式学习如何针对特定下游任务缩减图结构，且所用任务损失函数甚至无需可微。我们通过三个不同应用展示了该方法的通用性：图像分割、三维形状稀疏化及稀疏近似逆矩阵确定。