数学科学学院学术报告
Low-rank optimization on Tucker tensor varieties
报告时间: 2024年7月31日星期三 10：45-11：30
报告人: 高斌（中国科学院数学与系统科学研究院）
报告地点：沙河校区国实E404
腾讯会议：453-779-534
报告摘要: In the realm of tensor optimization, the low-rank Tucker decomposition is crucial for reducing the number of parameters and for saving storage. We explore the geometry of Tucker tensor varieties—the set of tensors with bounded Tucker rank—which is notably more intricate than the well-explored matrix varieties. We give an explicit parametrization of the tangent cone of Tucker tensor varieties and leverage its geometry to develop provable gradient-related line-search methods for optimization on Tucker tensor varieties. To the best of our knowledge, this is the first work concerning geometry and optimization on Tucker tensor varieties. In practice, low-rank tensor optimization suffers from the difficulty of choosing a reliable rank parameter. To this end, we incorporate the established geometry and propose a Tucker rank-adaptive method that aims to identify an appropriate rank with guaranteed convergence. Numerical experiments on tensor completion reveal that the proposed methods are in favor of recovering performance over other state-of-the-art methods. The rank-adaptive method performs the best across various rank parameter selections and is indeed able to find an appropriate rank.
报告人简介：高斌，中国科学院数学与系统科学研究院计算数学所副研究员。2019年毕业于中国科学院数学与系统科学研究院。曾先后赴比利时、德国从事博士后研究。其主要研究兴趣是矩阵和张量流形上的优化算法。曾获中国科学院院长特别奖、钟家庆数学奖。受到中国科协青托工程、中科院青年百人、基金委国家级青年项目等项目资助。
邀请人：崔春风
