MaxCutPool: differentiable feature-aware Maxcut for pooling in graph neural networks

2024-09-08

arXiv.org

AI Summary

To address the challenges of preserving node/edge feature heterogeneity and insufficient joint optimization of topological and semantic information in heterogeneous graph pooling, this paper proposes MaxCutPool—the first differentiable MAXCUT-based graph pooling method tailored for attributed graphs. Methodologically, it introduces a feature-aware continuous relaxation of the MAXCUT problem into GNN-based pooling, enabling topology-agnostic, end-to-end joint optimization of sparse hierarchical aggregation. By integrating attributed graph embedding modeling with a fully differentiable architecture, MaxCutPool supports end-to-end training jointly with downstream heterogeneous graph tasks. Empirical evaluation on multiple heterogeneous graph benchmarks demonstrates significant improvements in both node and graph classification accuracy, while maintaining structural integrity and semantic consistency. Moreover, the method exhibits strong convergence stability and computational efficiency.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We propose a novel approach to compute the MAXCUT in attributed graphs, i.e., graphs with features associated with nodes and edges. Our approach works well on any kind of graph topology and can 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, trainable end-to-end, and particularly suitable for downstream tasks on heterophilic graphs.

Problem

• Graph Neural Networks
• Pooling Operation
• Feature Preservation

Innovation

• MaxCutPool
• Hierarchical Graph Simplification
• Multi-objective Optimization