48 citations · 80 across the 4 of their papers we have counts for
4 papers
Understanding Edge-of-Stability Training Dynamics with a Minimalist Example
Xingyu Zhu, Zixuan Wang, Xiang Wang +2
Recently, researchers observed that gradient descent for deep neural networks operates in an ``edge-of-stability'' (EoS) regime: the sharpness (maximum eigenvalue of the Hessian) i…
Convergence of Gradient Algorithms for Nonconvex C^{1+alpha} Cost Functions
Zixuan Wang, Shanjian Tang
This paper is concerned with convergence of stochastic gradient algorithms with momentum terms in the nonconvex setting. A class of stochastic momentum methods, including stochasti…
Sparse Grid Discontinuous Galerkin Methods for High-Dimensional Elliptic Equations
Zixuan Wang, Qi Tang, Wei Guo +1
This paper constitutes our initial effort in developing sparse grid discontinuous Galerkin (DG) methods for high-dimensional partial differential equations (PDEs). Over the past fe…
A New Discontinuous Galerkin Finite Element Method for Directly Solving the Hamilton-Jacobi Equations
Yingda Cheng, Zixuan Wang
In this paper, we improve upon the discontinuous Galerkin (DG) method for Hamilton-Jacobi (HJ) equation with convex Hamiltonians in (Y. Cheng and C.-W. Shu, J. Comput. Phys. 223:39…