SOS Polynomials
收藏arXiv2025-10-15 更新2025-10-17 收录
下载链接：
github.com/ZIB-IOL/Neural-Sum-of-Squares
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资源简介：
该数据集名为SOS Polynomials，由柏林Zuse研究所和柏林工业大学的研究团队创建。数据集包含了超过1亿个SOS多项式，用于训练Transformer模型，以预测给定多项式的近似最小单项式基，从而大幅度减少相应SDP问题的规模。数据集的创建过程采用了反向采样技术，确保了生成的基础具有足够的代表性。该数据集在多项式优化、控制理论、机器人等领域有着广泛的应用前景，有助于解决多项式非负性验证这一NP难题。
This dataset, named SOS Polynomials, was developed by a research team from the Zuse Institute Berlin and the Technical University of Berlin. It contains over 100 million sum-of-squares (SOS) polynomials, and is used to train Transformer models to predict the approximate minimal monomial basis of a given polynomial, thereby drastically reducing the scale of the corresponding semidefinite programming (SDP) problems. The dataset was constructed using reverse sampling techniques, which ensures that the generated basis has sufficient representativeness. This dataset has broad application prospects in fields such as polynomial optimization, control theory, robotics and other relevant domains, and can help solve the NP-hard problem of polynomial nonnegativity verification.
提供机构：
柏林Zuse研究所, 柏林工业大学, 马德里卡洛斯三世大学, ELLIS图宾根研究所, 图宾根马克斯普朗克智能系统研究所, 图宾根AI中心
创建时间：
2025-10-15
