机器学习与数据科学博士生系列论坛（第一百零三期）—— A Geometric Perspective on Random Tensor Injective Norms
报告人：向彦瑾（mksport体育）
时间：2026-05-28 16:00-17:00
地点：腾讯会议：928-6293-8217
摘要：
This talk introduces a recent geometric approach to estimating the lp injective norm of sums of random tensors. The main idea is to view the random tensor norm as the supremum of a Gaussian process, apply Dudley's entropy integral, and reduce the problem to covering number estimates under the induced Gaussian metric. We will explain how random shifts in lp balls, uniform convexity, and volume arguments lead to the key entropy bound in the diagonal-free symmetric case. We will then discuss how symmetric embedding extends the result to general symmetric tensors, and how the main theorem yields bounds for the type-2 constant of tensor spaces.
论坛简介：该线上论坛是由张志华教授机器学习实验室组织，每两周主办一次（除了公共假期）。论坛每次邀请一位博士生就某个前沿课题做较为系统深入的介绍，主题包括但不限于机器学习、高维统计学、运筹优化和理论计算机科学。
