5arXiv cs.LG (Machine Learning)·
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.
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Complexity bounds for learning projected gradient descent solver iterates via k-neighborhood data augmentation
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Ambient Diffusion Policy: imitation learning from suboptimal robot data via noise-dependent co-training
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