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.