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

2024-02-15

arXiv.org

AI Summary

Graph structure reduction must preserve global properties while adapting to downstream tasks; however, existing methods are predominantly unsupervised and task-agnostic. This paper proposes the first task-driven graph sub-sampling framework: it models node/edge selection as an Ising model and employs graph neural networks to learn external magnetic fields, enabling end-to-end differentiable optimization. Crucially, it introduces Ising energy minimization to graph reduction for the first time—jointly optimizing structural fidelity and task performance without requiring explicit differentiable task losses. The method balances topological preservation with task-specific adaptation. Empirical evaluation across four diverse tasks—image segmentation, explainable graph classification, 3D shape sparsification, and sparse matrix inversion—demonstrates substantial improvements in both computational efficiency and accuracy.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Task-specific graph subsampling using Ising model
• Learning graph reduction for downstream tasks
• Versatile applications in segmentation, classification, sparsification

Innovation

• Task-specific graph subsampling via Ising model
• Learning external magnetic field with GNN
• End-to-end reduction without differentiable loss