Ising on the Graph: Task-specific Graph Subsampling via the Ising Model

Maria Bånkestad, Jennifer R. Andersson, Sebastian Mair, Jens Sjölund

Keywords: Graph neural networks, graph coarsening, graph sparsification, energy-based models, explainability

TL;DR: Using an Ising model, we propose a task-specific approach for reducing graph structures and showcase this approach in image segmentation, graph explainability, 3D shape sparsification, and matrix inverse approximation.

Abstract: Reducing a graph while preserving its overall properties is an important problem with many applications. Typically, 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 without requiring a differentiable loss function for the task. We showcase the versatility of our approach on four distinct applications: image segmentation, explainability for graph classification, 3D shape sparsification, and sparse approximate matrix inverse determination.

Submission Type: Full paper proceedings track submission (max 9 main pages).

Software: https://github.com/mariabankestad/IsingOnGraphs

Submission Number: 161