Assur-KB 表示法让平面机构学习样本效率提升 1.8 倍
Efficient Learning of Mechanism Designs and Compositionality
一篇把机构拆成模块再学的研究，同样数据量下预测效率高了 1.8 倍，做结构化学习或 CAD 生成的话有参考价值。
一篇 arXiv 论文提出 Assur-KB 表示法，将平面机构拆解为不可约模块、边界接口和求解依赖关系，同时保留源几何信息。在 50-10000 个机构的训练预算下，Assur 衍生特征相比展平的邻接与位置输入，样本效率几何平均提升 1.8 倍。实验还验证了关节重标记下的不变性、二元组合下更高的有效生成率，并在 1002 万个机构上构建了更粗粒度的结构索引。理论部分刻画了通过模块接口的迁移机制，以及接口信息缺失和敏感性累积带来的物理极限。
Efficient Learning of Mechanism Designs and Compositionality
Learning mechanism behaviour requires a representation of how connected parts jointly constrain motion. We study whether exposing reusable constraint subassemblies improves prediction from limited data. Assur-KB represents planar mechanisms through irreducible modules, boundary interfaces, and solve dependencies while retaining source geometry. Our theoretical results characterize transfer through module interfaces and establish physical limits arising from missing interface information and accumulated sensitivity. To test the representation claim directly, the experimental design compares matched mechanism-curve pairs across training budgets within the same multilayer-perceptron family. This controlled comparison establishes the utility of the complete representation in the evaluated learning setting. Assur-derived features provide a geometric-mean $1.8\times$ advantage in sample efficiency over flattened adjacency and position inputs across budgets of 50-10,000 mechanisms. Separate experiments establish invariance under tested joint relabelings, higher valid-generation rates under dyadic composition, and a coarser structural index over 10.02 million mechanisms. In summary, the theory and experiments identify how physical constraint structure supports limited-data prediction and which interface conditions govern compositional reuse.