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

arXiv: https://arxiv.org/abs/2402.10206 · HTML: https://mlsanity.com/paper/2402.10206/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2024.

## Built on by (most cited first, 2 of 2)

- [Graph Neural Preconditioners for Iterative Solutions of Sparse Linear Systems](https://mlsanity.com/paper/2406.00809/) (2024)
- [Learning incomplete factorization preconditioners for GMRES](https://mlsanity.com/paper/2409.08262/) (2024)

## Abstract (arXiv)

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.