Neural Graduated Assignment for Maximum Common Edge Subgraphs

2025-05-18

AI Summary

To address the scalability limitations of Maximum Common Edge Subgraph (MCES) computation in large-scale biological and chemical graph matching, this paper proposes a neural progressive assignment framework. The method employs unsupervised learning to construct a stacked neural architecture and introduces a learnable temperature mechanism to reparameterize the assignment process. We theoretically establish its fast convergence, enhanced ability to escape local optima, and improved exploration–exploitation trade-off. Building upon and extending the Graduated Assignment paradigm, the framework requires no human annotations or prior graph alignment knowledge. Extensive experiments demonstrate significant improvements in computational efficiency and accuracy for MCES computation, graph similarity estimation, and graph retrieval on large-scale graph instances—consistently outperforming state-of-the-art methods across all evaluated tasks.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for 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

The Maximum Common Edge Subgraph (MCES) problem is a crucial challenge with significant implications in domains such as biology and chemistry. Traditional approaches, which include transformations into max-clique and search-based algorithms, suffer from scalability issues when dealing with larger instances. This paper introduces ``Neural Graduated Assignment'' (NGA), a simple, scalable, unsupervised-training-based method that addresses these limitations by drawing inspiration from the classical Graduated Assignment (GA) technique. Central to NGA is stacking of neural components that closely resemble the GA process, but with the reparameterization of learnable temperature into higher dimension. We further theoretically analyze the learning dynamics of NGA, showing its design leads to fast convergence, better exploration-exploitation tradeoff, and ability to escape local optima. Extensive experiments across MCES computation, graph similarity estimation, and graph retrieval tasks reveal that NGA not only significantly improves computation time and scalability on large instances but also enhances performance compared to existing methodologies. The introduction of NGA marks a significant advancement in the computation of MCES and offers insights into other assignment problems.

Problem

• Addresses scalability issues in Maximum Common Edge Subgraph (MCES) problem
• Introduces Neural Graduated Assignment (NGA) for unsupervised training
• Improves computation time and performance in graph-related tasks

Innovation

• Unsupervised-training-based Neural Graduated Assignment method
• Reparameterization of learnable temperature into higher dimension
• Fast convergence with better exploration-exploitation tradeoff