用图神经网络从群的凯莱图判断可解性，准确率达100%。
Graph Neural Networks for Predicting Solvability of Finite Groups
- 基于凯莱图结构设计GNN，直接学习群的可解性特征。
- 在200个群上测试，独立集准确率高达1.000，且多次实验稳定。
- 能正确识别未见过的PSL(2,q)群族，展现强泛化能力。
我们提出一种图神经网络（GNN）框架，用于根据有限群的可解性进行分类。该框架采用无向凯莱图表示，直接从图结构信息中学习区分可解与不可解群，无需依赖显式的代数特征。在包含120个可解群和80个不可解群的基准数据集上进行评估。实验考察了GNN从凯莱图中学习可解性这一代数性质的能力及其对未见有限群的泛化性能。所选的GNN架构在独立测试集上达到平衡准确率（BA）1.000。多次使用不同随机种子和学习率的实验均得到0.956至1.000之间的BA，表明该框架对训练配置具有鲁棒性。为进一步评估泛化能力，整个PSL(2,q)群族被完全排除在训练和验证集之外，仅用于测试。模型成功正确分类了该族中所有此前未见过的群，证明其对全新群族具备良好泛化能力。
原文摘要 · Abstract (English)
We present a Graph Neural Network (GNN) framework for the classification of finite groups according to their solvability. Using undirected Cayley graph representations, the proposed framework learns to distinguish solvable and non-solvable groups directly from structural graph information, without relying on explicit algebraic features. The framework is evaluated on a benchmark dataset of 200 finite groups, comprising 120 solvable and 80 non-solvable groups. The experiments investigate the extent to which GNNs can learn the algebraic property of solvability from Cayley graph representations and generalize to previously unseen finite groups. The selected GNN architecture achieved a balanced accuracy (BA) of 1.000 on the independent test set. Furthermore, repeated experiments using different random seeds and learning rates consistently produced BAs between 0.956 and 1.000, demonstrating the robustness of the proposed framework with respect to the training configuration. To further evaluate generalization, the entire PSL(2,q) family was excluded from the training and validation sets and reserved exclusively for testing. The selected model correctly classified every previously unseen group in this family, demonstrating successful generalization to an entirely unseen family of finite groups.
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