105 citations · 533 across the 41 of their papers we have counts for
8 papers · 1 filter
The Mirror Langevin Algorithm Converges with Vanishing Bias
Ruilin Li, Molei Tao, Santosh S. Vempala +1
The technique of modifying the geometry of a problem from Euclidean to Hessian metric has proved to be quite effective in optimization, and has been the subject of study for sampli…
Large Learning Rate Tames Homogeneity: Convergence and Balancing Effect
Yuqing Wang, Minshuo Chen, Tuo Zhao +1
Recent empirical advances show that training deep models with large learning rate often improves generalization performance. However, theoretical justifications on the benefits of…
Parametric resonance for enhancing the rate of metastable transition
Ying Chao, Molei Tao
This work is devoted to quantifying how periodic perturbation can change the rate of metastable transition in stochastic mechanical systems with weak noises. A closed-form explicit…
Sqrt(d) Dimension Dependence of Langevin Monte Carlo
Ruilin Li, Hongyuan Zha, Molei Tao
This article considers the popular MCMC method of unadjusted Langevin Monte Carlo (LMC) and provides a non-asymptotic analysis of its sampling error in 2-Wasserstein distance. The…
Variational Symplectic Accelerated Optimization on Lie Groups
Taeyoung Lee, Molei Tao, Melvin Leok
There has been significant interest in generalizations of the Nesterov accelerated gradient descent algorithm due to its improved performance guarantee compared to the standard gra…
GRIT: a package for structure-preserving simulations of gravitationally interacting rigid-bodies
Renyi Chen, Gongjie Li, Molei Tao
Spin-orbit coupling of planetary systems plays an important role in the dynamics and habitability of planets. However, symplectic integrators that can accurately simulate not only…
Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Maps
Renyi Chen, Molei Tao
We consider the learning and prediction of nonlinear time series generated by a latent symplectic map. A special case is (not necessarily separable) Hamiltonian systems, whose solu…
Accurate and Efficient Simulations of Hamiltonian Mechanical Systems with Discontinuous Potentials
Molei Tao, Shi Jin
This article considers Hamiltonian mechanical systems with potential functions admitting jump discontinuities. The focus is on accurate and efficient numerical approximations of th…