点击链接入会：

https://meeting.tencent.com/dm/9XjN6YpGAXsy 

#腾讯会议：442-449-509

Abstract:

Under the data manifold hypothesis, high-dimensional data concentrate near a low-dimensional submanifold. We study Riemannian optimization and sampling when this submanifold is given only implicitly through the data distribution and standard geometric operations are unavailable.

Our key idea is a link function that connects the data distribution to the geometric quantities needed for optimization and sampling: in the small-noise regime, its gradient and Hessian recover the projection onto the manifold and the projection onto its tangent space, respectively. This construction is directly connected to the score function in diffusion models, allowing us to leverage well-studied parameterizations, efficient training procedures, and even pretrained score networks from the diffusion-model literature to perform optimization and sampling on the data manifold.

BiZebang Shen is currently a research scientist at ETH Zürich, hosted by Prof. Niao He. Prior to this role, he was a postdoctoral researcher at ETH Zürich from 2022 to 2024, working under the guidance of Prof. Niao He, and at the University of Pennsylvania from 2019 to 2022, working under the guidance of Professors Alejandro Ribeiro and Hamed Hassani. He earned his bachelor’s degree and Ph.D. from Zhejiang University in China in 2014 and 2019, respectively.

His current research interests lie at the intersection of stochastic processes and differential geometry. His two main research directions are (1) understanding and improving diffusion models under the data manifold hypothesis and (2) understanding the implicit selection among minima and developing active strategies for selecting minima in non-convex optimization.

He is also interested in various machine-learning topics, including the efficient training of large-scale machine-learning models, neural-network-based numerical PDE solvers, trustworthy machine learning, and statistical perspectives on machine learning.

组织者：户将