We propose a novel approach to compute the MAXCUT in attributed graphs, i.e., graphs with features associated with nodes and edges. Our approach is robust to the underlying graph topology and is fully differentiable, making it possible to find solutions that jointly optimize the MAXCUT along with other objectives. Based on the obtained MAXCUT partition, we implement a hierarchical graph pooling layer for Graph Neural Networks, which is sparse, differentiable, and particularly suitable for downstream tasks on heterophilic graphs.

翻译：我们提出了一种新颖的方法来计算属性图中的最大割问题，即具有与节点和边相关联特征的图。我们的方法对底层图拓扑结构具有鲁棒性，并且完全可微分，从而能够找到与其他目标联合优化最大割的解决方案。基于获得的最大割划分，我们为图神经网络实现了一个分层图池化层，该层具有稀疏性和可微分性，特别适用于异配图上的下游任务。