Sampling Strategies for Transformer-Based Mechanism Synthesis

Physical design problems offer unique opportunities for sampling strategies that go beyond standard probabilistic generation. We explore how the inherent structure and symmetries of physical systems enable specialized sampling techniques that operate outside the learned model itself. Using mechanism synthesis as an exemplar, where the goal is to design mechanical linkages that trace desired paths, we demonstrate sampling strategies that exploit physical invariances, leverage simulator-based evaluation, and provide interpretable control over the generation process. These approaches show how understanding the physics of a domain can lead to more effective sampling, yielding both accurate and diverse solutions that serve as strong starting points for traditional optimization.