4 papers
Non-Euclidean dual gradient ascent for entropically regularized linear and semidefinite programming
Yuhang Cai, Michael Lindsey
We present an optimization framework that exhibits dimension-independent convergence on a broad class of semidefinite programs (SDPs). Our approach first regularizes the primal pro…
Toward optimal-scaling DFT: stochastic Hartree theory in the thermodynamic and complete basis set limits at arbitrary temperature
Yuhang Cai, Michael Lindsey
We present the first mathematical analysis of stochastic density functional theory (DFT) in the context of the Hartree approximation. We motivate our analysis via the notion of nea…
Implicit Bias of Gradient Descent for Non-Homogeneous Deep Networks
Yuhang Cai, Kangjie Zhou, Jingfeng Wu +3
We establish the asymptotic implicit bias of gradient descent (GD) for generic non-homogeneous deep networks under exponential loss. Specifically, we characterize three key propert…
Large Stepsize Gradient Descent for Non-Homogeneous Two-Layer Networks: Margin Improvement and Fast Optimization
Yuhang Cai, Jingfeng Wu, Song Mei +2
The typical training of neural networks using large stepsize gradient descent (GD) under the logistic loss often involves two distinct phases, where the empirical risk oscillates i…