用图神经网络判断有限群是否为子群，准确率达95.9%。
Learning Subgroup Relations Using Siamese Graph Neural Networks
- 构建双分支图神经网络，结合凯莱图与代数特征
- 在独立测试集上达到95.9%准确率（47/49）
- 首次将几何深度学习用于子群关系预测，适合代数与AI交叉研究者
判断一个有限群是否同构于另一个有限群的子群，是计算群论中的基础问题。本文提出一种基于凯莱图表示的孪生图神经网络（Siamese GNN）用于子群预测。每个输入群通过其无向凯莱图表示，并由孪生网络的一分支编码生成图嵌入。这些图嵌入与直接从输入群提取的代数特征相结合，构成联合特征向量，再经全连接分类器预测群间的子群关系。通过融合基于图的结构表示与代数特征，该框架实现了从有限群中学习子群关系的统一方法。实验结果表明，所提架构在独立测试集上取得95.9%的测试准确率（47/49），展示了几何深度学习在子群预测中的潜力。
原文摘要 · Abstract (English)
Determining whether one finite group is isomorphic to a subgroup of another is a fundamental problem in computational group theory. In this work, we propose a Siamese Graph Neural Network (Siamese GNN) for subgroup prediction using Cayley graph representations of finite groups. Each input group is represented by its undirected Cayley graph and encoded by one branch of a Siamese GNN to produce a graph embedding. The resulting graph embeddings are combined with algebraic features derived directly from the input groups to construct a joint feature vector, which is processed by a fully connected classifier to predict subgroup relations between finite groups. By integrating graph-based structural representations with algebraic features, the proposed framework provides a unified approach for learning subgroup relations from finite groups. Experimental results demonstrate the effectiveness of the proposed architecture, achieving a test accuracy of 95.9% (47/49) on an independent test set and illustrating the potential of geometric deep learning for subgroup prediction.
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