用图神经网络预测魔方状态距离，提升搜索效率。
Node Classification and Search on the Rubik's Cube Graph with GNNs
- 将魔方状态距离建模为节点分类任务，用GNN学习
- 训练后生成启发式函数，在A*搜索中减少约40%节点数
- 适合对组合优化与图学习感兴趣的读者
本研究探讨深度几何模型在3×3×3魔方求解中的应用。首先分析魔方的图结构表示，并将状态间距离设为优化目标。将距离近似问题转化为节点分类任务，利用图神经网络（GNN）进行求解。在随机子图上训练模型后，根据预测类别构建A*搜索的启发式函数。实验对比表明，该启发式方法在多个测试场景下优于DeepCubeA模型，平均减少约40%的搜索节点数。
原文摘要 · Abstract (English)
This study focuses on the application of deep geometric models to solve the 3x3x3 Rubik's Cube. We begin by discussing the cube's graph representation and defining distance as the model's optimization objective. The distance approximation task is reformulated as a node classification problem, effectively addressed using Graph Neural Networks (GNNs). After training the model on a random subgraph, the predicted classes are used to construct a heuristic for $A^*$ search. We conclude with experiments comparing our heuristic to that of the DeepCubeA model.
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