Title: A Theory of Feature Learning in Kernel Models

Speaker: Ruan Feng, Assistant Professor, Northwestern University

Host: Huikang Liu, Associate Professor, Antai College of Economics and Management, Shanghai Jiao Tong University

Time: 14:00–15:30, Wednesday, March 18, 2026

Venue: Room 308, Haoran Building, Antai College, Xuhui Campus, Shanghai Jiao Tong University

Brief introduction of the content: 

We study feature learning in a compositional variant of kernel ridge regression in which the predictor is applied to a learnable linear transformation of the input. When the response depends on the input only through a low-dimensional predictive subspace, we show that all global minimizers of the population objective for the linear transformation annihilate directions orthogonal to this subspace, and in certain regimes, exactly identify the subspace. Moreover, we show that global minimizers of the finite-sample objective inherit the exact same low-dimensional structure with high probability, even without any explicit penalization on the linear transformation.

Speaker's profile:

Feng Ruan is an Assistant Professor in the Department of Statistics and Data Science at Northwestern University. His research lies at the interface of machine learning, statistics, and optimization. Broadly speaking, he has two main research interests. The first is representation learning, where he studies how learning systems automatically discover low-dimensional predictive structures in data, with a particular focus on feature learning in kernel and compositional models. The second is nonsmooth optimization, where he develops variational and algorithmic foundations for nonsmooth and nonconvex problems arising in modern statistical learning.