用神经方法加速分子图匹配，更快更准。
Neural Graduated Assignment for Maximum Common Edge Subgraphs
- 通过可微分分配与温度调节机制，实现高效图匹配。
- 在大规模图上计算速度提升5倍以上，精度更高。
- 适合生物化学中的分子结构比对与检索任务。
最大公共边子图（MCES）问题是生物和化学领域的重要挑战。传统方法如转化为最大团或基于搜索的算法，在处理大规模实例时存在可扩展性问题。本文提出「神经渐进分配」（NGA），一种简单、可扩展、无需监督训练的方法。NGA的核心是将可微分分配优化与神经组件堆叠，通过可学习的温度机制实现高维参数化匹配过程。我们进一步理论分析了NGA的学习动态，表明其设计具有快速收敛、更好的探索-利用平衡以及逃离局部最优的能力。在MCES计算、图相似性估计和图检索任务上的大量实验表明，NGA不仅在大规模实例上显著提升计算速度和可扩展性，还优于现有方法。NGA的引入标志着MCES计算的重大进展，并为其他分配问题提供新思路。
原文摘要 · Abstract (English)
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. Central to NGA is stacking of differentiable assignment optimization with neural components, enabling high-dimensional parameterization of the matching process through a learnable temperature mechanism. 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.
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