When Do Learned Diffusion Proposals Help Constraint Solving? A Controlled Study on Continuous Algebraic Systems

Controlled study finds learned diffusion proposals offer narrow advantage over random multi-start in constraint solving

A new arXiv paper introduces MARC, a system combining graph-neural diffusion denoising, computer-algebra energy descent, and symbolic checking to solve continuous algebraic constraint systems. The paper's central finding is a careful ablation: when matched against random multi-start under the same refinement budget, learned diffusion proposals only narrowly outperform random search, and only in high-dimensional uncoupled regimes. Across eight real-world systems from robotics, positioning, and algebra, classical multi-start solved all instances, none falling in the learning-favorable regime. The work provides a principled regime map for when learned proposals actually help, serving as a cautionary calibration for the broader trend of applying learned heuristics to combinatorial/constraint problems.