机器学习与数据科学博士生系列论坛（第九十二期）—— When Random Tensors Meet Random Matrices
报告人：向彦瑾（国产自慰
）
时间：2025-10-16 16:00-17:00
地点：腾讯会议：331-2528-5257
摘要：
Although random matrix models have been extensively studied and well understood in the literature, the understanding of random tensor models is still in its infancy and the ideas from random matrix analysis do not easily extend to higher-order tensors. Indeed, the resolvent notion which is at the heart of random matrices does not generalize to tensors.
In this talk we provide an exact expression of the asymptotic singular value and alignments $\langle x^{(i)},u^{(i)} \rangle$, when the tensor dimensions $n_i \to \infty$ with $\frac{n_i}{\sum^d_{j=1}n_j} \to c_i \in (0,1)$, where the tuple $(\lambda_*, u^{(1)}_*, \cdots, u^{(d)}_*)$ is associated to a local optimum of the ML problem verifying some technical conditions. We conjecture that when the SNR $\beta$ is large enough, there is a unique local optimum verifying some assumptions and for which our results characterize the corresponding alignments. We further conjecture that $(\lambda_*, u^{(1)}_*, \cdots, u^{(d)}_*)$ coincides with the global maximum above some $\beta_c$ that needs to be characterized.
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。
