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03/03/2023
Deep Momentum Multi-Marginal Schrödinger Bridge
Reconstructing population dynamics using only samples from distributions...
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09/30/2022
Data-driven discovery of non-Newtonian astronomy via learning non-Euclidean Hamiltonian
Incorporating the Hamiltonian structure of physical dynamics into deep l...
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07/13/2022
NySALT: Nyström-type inference-based schemes adaptive to large time-stepping
Large time-stepping is important for efficient long-time simulations of ...
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06/11/2022
gDDIM: Generalized denoising diffusion implicit models
Our goal is to extend the denoising diffusion implicit model (DDIM) to g...
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06/08/2022
Alternating Mirror Descent for Constrained Min-Max Games
In this paper we study two-player bilinear zero-sum games with constrain...
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05/27/2022
Momentum Stiefel Optimizer, with Applications to Suitably-Orthogonal Attention, and Optimal Transport
The problem of optimization on Stiefel manifold, i.e., minimizing functi...
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10/07/2021
Large Learning Rate Tames Homogeneity: Convergence and Balancing Effect
Recent empirical advances show that training deep models with large lear...
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09/24/2021
The Mirror Langevin Algorithm Converges with Vanishing Bias
The technique of modifying the geometry of a problem from Euclidean to H...
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09/08/2021
Sqrt(d) Dimension Dependence of Langevin Monte Carlo
This article considers the popular MCMC method of unadjusted Langevin Mo...
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03/09/2021
Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Maps
We consider the learning and prediction of nonlinear time series generat...
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06/16/2020
Hessian-Free High-Resolution Nesterov Acceleration for Sampling
We propose an accelerated-gradient-based MCMC method. It relies on a mod...
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06/16/2020
Hessian-Free High-Resolution Nesterov Accelerationfor Sampling
We propose an accelerated-gradient-based MCMC method. It relies on a mod...
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02/20/2020
Improving Sampling Accuracy of Stochastic Gradient MCMC Methods via Non-uniform Subsampling of Gradients
Common Stochastic Gradient MCMC methods approximate gradients by stochas...
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02/14/2020
Why Do Deep Residual Networks Generalize Better than Deep Feedforward Networks? – A Neural Tangent Kernel Perspective
Deep residual networks (ResNets) have demonstrated better generalization...
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02/14/2020
Stochasticity of Deterministic Gradient Descent: Large Learning Rate for Multiscale Objective Function
This article suggests that deterministic Gradient Descent, which does no...
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01/27/2020
Variational Optimization on Lie Groups, with Examples of Leading (Generalized) Eigenvalue Problems
The article considers smooth optimization of functions on Lie groups. By...
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03/25/2019
Dynamic mode decomposition for multiscale nonlinear physics
We present a data-driven method for separating complex, multiscale syste...
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03/25/2019