105 citations · 533 across the 41 of their papers we have counts for
42 papers
Can Specific THz Fields Induce Collective Base-Flipping in DNA? A Stochastic Averaging and Resonant Enhancement Investigation Based on a New Mesoscopic Model
Wang Sang Koon, Houman Owhadi, Molei Tao +1
We study the metastability, internal frequencies, activation mechanism, energy transfer, and the collective base-flipping in a mesoscopic DNA via resonance with specific electric f…
Extragradient Type Methods for Riemannian Variational Inequality Problems
Zihao Hu, Guanghui Wang, Xi Wang +3
Riemannian convex optimization and minimax optimization have recently drawn considerable attention. Their appeal lies in their capacity to adeptly manage the non-convexity of the o…
Deep Momentum Multi-Marginal Schrödinger Bridge
Tianrong Chen, Guan-Horng Liu, Molei Tao +1
It is a crucial challenge to reconstruct population dynamics using unlabeled samples from distributions at coarse time intervals. Recent approaches such as flow-based models or Sch…
Essential barrier height and a probabilistic approach in characterizing potential landscape
Yao Li, Molei Tao, Shirou Wang
This paper proposes a probabilistic approach to investigate the shape of landscapes of multi-dimensional potential functions. Under a suitable coupling scheme, two copies of the ov…
Data-driven discovery of non-Newtonian astronomy via learning non-Euclidean Hamiltonian
Oswin So, Gongjie Li, Evangelos A. Theodorou +1
Incorporating the Hamiltonian structure of physical dynamics into deep learning models provides a powerful way to improve the interpretability and prediction accuracy. While previo…
Low Spin-Axis Variations of Circumbinary Planets
Renyi Chen, Gongjie Li, Molei Tao
Having a massive moon has been considered as a primary mechanism for stabilized planetary obliquity, an example of which being our Earth. This is, however, not always consistent wi…
NySALT: Nyström-type inference-based schemes adaptive to large time-stepping
Xingjie Li, Fei Lu, Molei Tao +1
Large time-stepping is important for efficient long-time simulations of deterministic and stochastic Hamiltonian dynamical systems. Conventional structure-preserving integrators, w…
Alternating Mirror Descent for Constrained Min-Max Games
Andre Wibisono, Molei Tao, Georgios Piliouras
In this paper we study two-player bilinear zero-sum games with constrained strategy spaces. An instance of natural occurrences of such constraints is when mixed strategies are used…
gDDIM: Generalized denoising diffusion implicit models
Qinsheng Zhang, Molei Tao, Yongxin Chen
Our goal is to extend the denoising diffusion implicit model (DDIM) to general diffusion models~(DMs) besides isotropic diffusions. Instead of constructing a non-Markov noising pro…
Momentum Stiefel Optimizer, with Applications to Suitably-Orthogonal Attention, and Optimal Transport
Lingkai Kong, Yuqing Wang, Molei Tao
The problem of optimization on Stiefel manifold, i.e., minimizing functions of (not necessarily square) matrices that satisfy orthogonality constraints, has been extensively studie…
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…
Hessian-Free High-Resolution Nesterov Acceleration for Sampling
Ruilin Li, Hongyuan Zha, Molei Tao
Nesterov's Accelerated Gradient (NAG) for optimization has better performance than its continuous time limit (noiseless kinetic Langevin) when a finite step-size is employed \citep…
Improving Sampling Accuracy of Stochastic Gradient MCMC Methods via Non-uniform Subsampling of Gradients
Ruilin Li, Xin Wang, Hongyuan Zha +1
Many Markov Chain Monte Carlo (MCMC) methods leverage gradient information of the potential function of target distribution to explore sample space efficiently. However, computing…
Why Do Deep Residual Networks Generalize Better than Deep Feedforward Networks? -- A Neural Tangent Kernel Perspective
Kaixuan Huang, Yuqing Wang, Molei Tao +1
Deep residual networks (ResNets) have demonstrated better generalization performance than deep feedforward networks (FFNets). However, the theory behind such a phenomenon is still…
Stochasticity of Deterministic Gradient Descent: Large Learning Rate for Multiscale Objective Function
Lingkai Kong, Molei Tao
This article suggests that deterministic Gradient Descent, which does not use any stochastic gradient approximation, can still exhibit stochastic behaviors. In particular, it shows…
Variational Optimization on Lie Groups, with Examples of Leading (Generalized) Eigenvalue Problems
Molei Tao, Tomoki Ohsawa
The article considers smooth optimization of functions on Lie groups. By generalizing NAG variational principle in vector space (Wibisono et al., 2016) to Lie groups, continuous Li…
Space-Time Phononic Crystals with Anomalous Topological Edge States
Mourad Oudich, Yuanchen Deng, Molei Tao +1
It is well known that an interface created by two topologically distinct structures could host nontrivial edge states that are immune to defects. In this letter, we introduce a one…