Deep neural networks have become the cornerstone of modern machine learning, yet their multi-layer structure, nonlinearities, and intricate optimization processes pose considerable theoretical challenges. In the first part of the talk, I will review recent advances in random matrix analysis that shed new light on these complex ML models. Starting with the foundational case of linear regression, I ...

主讲人学术背景：刘永强，中国科学技术大学几何与物理研究中心特任教授。研究领域为代数几何和代数拓扑，主要研究方向是代数簇奇异点的拓扑及Hodge理论。已在Adv. Math，Crelle和Math. Ann等国际数学杂志上发表多篇论文。 讲座题目：Kahler weighted right-angled Artin group 讲座摘要：It is a question of Serre to characterize finitely presented groups that can serve as the fundamental group of a compact Kahler manif...

随着循证医学的发展，医学研究及其日常的临床应用日趋方法化、规范化。同时，创新试验设计 （innovative trial design）、系统综述和元分析（systematic reviews and meta-analysis）越来越多的应用到前沿医学科研当中。主讲人结合其在英国从事医学科研研究的经历，着重介绍医学相关的统计分析方法和研究发展方向。 嘉宾介绍：黄超，统计学学者，英国赫尔大学准教授（Reader in Statistics）。南开大学统计学本硕，英国曼彻斯特大...

Deep neural networks have become the cornerstone of modern machine learning, yet their multi-layer structure, nonlinearities, and intricate optimization processes pose considerable theoretical challenges. In the first part of the talk, I will review recent advances in random matrix analysis that shed new light on these complex ML models. Starting with the foundational case of linear regression, I ...

In this talk, I will present our recent work on the optimality of Approximate Message Passing (AMP) algorithms for spiked matrix models with rotationally invariant noise. We introduce a new AMP algorithm that employs a matrix denoiser—acting on the eigenvalues of the observed matrix—and an iterate denoiser—applied to the AMP iterates. The resulting dynamics admit a simple state-evolution character...

The rise of data-driven sciences and the recent surge of generative AI have contributed to an overwhelming flood of data, making it increasingly critical to amplify both experts' and casual users' capabilities to interact with data. In this talk, I will present our work on this challenge, spanning two stages of human-data interaction: data preparation and data analysis. For data preparation, in th...