b'Jianfeng Lu'

research

∙ 06/13/2022

Convergence for score-based generative modeling with polynomial complexity

Score-based generative modeling (SGM) is a highly successful approach fo...

Holden Lee, et al. ∙

research

∙ 05/31/2022

Vector-wise Joint Diagonalization of Almost Commuting Matrices

This work aims to numerically construct exactly commuting matrices close...

Bowen Li, et al. ∙

research

∙ 05/05/2022

Neural Network Based Variational Methods for Solving Quadratic Porous Medium Equations in High Dimensions

In this paper, we propose and study neural network based methods for sol...

Jianfeng Lu, et al. ∙

research

∙ 05/04/2022

Asymptotic analysis of diabatic surface hopping algorithm in the adiabatic and non-adiabatic limits

Surface hopping algorithms, as an important class of quantum dynamics si...

Zhenning Cai, et al. ∙

research

∙ 01/31/2022

Single Time-scale Actor-critic Method to Solve the Linear Quadratic Regulator with Convergence Guarantees

We propose a single time-scale actor-critic algorithm to solve the linea...

Mo Zhou, et al. ∙

research

∙ 01/25/2022

A Regularity Theory for Static Schrödinger Equations on ℝ^d in Spectral Barron Spaces

Spectral Barron spaces have received considerable interest recently as i...

Ziang Chen, et al. ∙

research

∙ 11/25/2021

Low-rank approximation for multiscale PDEs

Historically, analysis for multiscale PDEs is largely unified while nume...

Ke Chen, et al. ∙

research

∙ 10/13/2021

Machine Learning For Elliptic PDEs: Fast Rate Generalization Bound, Neural Scaling Law and Minimax Optimality

In this paper, we study the statistical limits of deep learning techniqu...

Yiping Lu, et al. ∙

research

∙ 09/03/2021

Optimal artificial boundary conditions based on second-order correctors for three dimensional random elliptic media

We are interested in numerical algorithms for computing the electrical f...

Jianfeng Lu, et al. ∙

research

∙ 06/14/2021

On the Representation of Solutions to Elliptic PDEs in Barron Spaces

Numerical solutions to high-dimensional partial differential equations (...

Ziang Chen, et al. ∙

research

∙ 05/04/2021

A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schrödinger Eigenvalue Problems

This paper analyzes the generalization error of two-layer neural network...

Jianfeng Lu, et al. ∙

research

∙ 03/10/2021

Incorporating Orientations into End-to-end Driving Model for Steering Control

In this paper, we present a novel end-to-end deep neural network model f...

Peng Wan, et al. ∙

research

∙ 03/01/2021

Structure-preserving numerical schemes for Lindblad equations

We study a family of structure-preserving deterministic numerical scheme...

Yu Cao, et al. ∙

research

∙ 02/22/2021

Actor-Critic Method for High Dimensional Static Hamilton–Jacobi–Bellman Partial Differential Equations based on Neural Networks

We propose a novel numerical method for high dimensional Hamilton–Jacobi...

Mo Zhou, et al. ∙

research

∙ 01/05/2021

A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations

This paper concerns the a priori generalization analysis of the Deep Rit...

Jianfeng Lu, et al. ∙

research

∙ 01/05/2021

On the global convergence of randomized coordinate gradient descent for non-convex optimization

In this work, we analyze the global convergence property of coordinate g...

Ziang Chen, et al. ∙

research

∙ 12/21/2020

Complexity of zigzag sampling algorithm for strongly log-concave distributions

We study the computational complexity of zigzag sampling algorithm for s...

Jianfeng Lu, et al. ∙

research

∙ 12/15/2020

Neural Collapse with Cross-Entropy Loss

We consider the variational problem of cross-entropy loss with n feature...

Jianfeng Lu, et al. ∙

research

∙ 12/03/2020

SMDS-Net: Model Guided Spectral-Spatial Network for Hyperspectral Image Denoising

Deep learning (DL) based hyperspectral images (HSIs) denoising approache...

Fengchao Xiong, et al. ∙

research

∙ 11/01/2020

Manifold Learning and Nonlinear Homogenization

We describe an efficient domain decomposition-based framework for nonlin...

Shi Chen, et al. ∙

research

∙ 10/28/2020

Fast localization of eigenfunctions via smoothed potentials

We study the problem of predicting highly localized low-lying eigenfunct...

Jianfeng Lu, et al. ∙

research

∙ 10/22/2020

Global optimality of softmax policy gradient with single hidden layer neural networks in the mean-field regime

We study the problem of policy optimization for infinite-horizon discoun...

Andrea Agazzi, et al. ∙

research

∙ 10/22/2020

Random Coordinate Underdamped Langevin Monte Carlo

The Underdamped Langevin Monte Carlo (ULMC) is a popular Markov chain Mo...

Zhiyan Ding, et al. ∙

research

∙ 10/03/2020

Random Coordinate Langevin Monte Carlo

Langevin Monte Carlo (LMC) is a popular Markov chain Monte Carlo samplin...

Zhiyan Ding, et al. ∙

research

∙ 09/30/2020

Efficient sampling from the Bingham distribution

We give a algorithm for exact sampling from the Bingham distribution p(x...

Rong Ge, et al. ∙

research

∙ 07/29/2020

On explicit L^2-convergence rate estimate for piecewise deterministic Markov processes

We establish L^2-exponential convergence rate for three popular piecewis...

Jianfeng Lu, et al. ∙

research

∙ 07/21/2020

Neural Machine Translation with Error Correction

Neural machine translation (NMT) generates the next target token given a...

Kaitao Song, et al. ∙

research

∙ 06/22/2020

A Proximal-Gradient Algorithm for Crystal Surface Evolution

As a counterpoint to recent numerical methods for crystal surface evolut...

Katy Craig, et al. ∙

research

∙ 06/21/2020

Stable Phase Retrieval from Locally Stable and Conditionally Connected Measurements

This paper is concerned with stable phase retrieval for a family of phas...

Cheng Cheng, et al. ∙

research

∙ 06/13/2020

Numerical analysis for inchworm Monte Carlo method: Sign problem and error growth

We consider the numerical analysis of the inchworm Monte Carlo method, w...

Zhenning Cai, et al. ∙

research

∙ 04/27/2020

LightPAFF: A Two-Stage Distillation Framework for Pre-training and Fine-tuning

While pre-training and fine-tuning, e.g., BERT <cit.>, GPT-2 <cit.>, hav...

Kaitao Song, et al. ∙

research

∙ 04/20/2020

MPNet: Masked and Permuted Pre-training for Language Understanding

BERT adopts masked language modeling (MLM) for pre-training and is one o...

Kaitao Song, et al. ∙

research

∙ 04/19/2020

A Universal Approximation Theorem of Deep Neural Networks for Expressing Distributions

This paper studies the universal approximation property of deep neural n...

Yulong Lu, et al. ∙

research

∙ 04/08/2020

Posterior computation with the Gibbs zig-zag sampler

Markov chain Monte Carlo (MCMC) sampling algorithms have dominated the l...

Matthias Sachs, et al. ∙

research

∙ 03/22/2020

Complexity of randomized algorithms for underdamped Langevin dynamics

We establish an information complexity lower bound of randomized algorit...

Yu Cao, et al. ∙

research

∙ 03/14/2020

Existence and computation of generalized Wannier functions for non-periodic systems in two dimensions and higher

Exponentially-localized Wannier functions (ELWFs) are a basis of the Fer...

Kevin D. Stubbs, et al. ∙

research

∙ 03/11/2020

A Mean-field Analysis of Deep ResNet and Beyond: Towards Provable Optimization Via Overparameterization From Depth

Training deep neural networks with stochastic gradient descent (SGD) can...

Yiping Lu, et al. ∙

research

∙ 03/04/2020

Ensemble Kalman Inversion for nonlinear problems: weights, consistency, and variance bounds

Ensemble Kalman Inversion (EnKI), originally derived from Enseble Kalman...

Zhiyan Ding, et al. ∙

research

∙ 02/07/2020

Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach

We propose a new method to solve eigenvalue problems for linear and semi...

Jiequn Han, et al. ∙

research

∙ 01/09/2020

Deep Network Approximation for Smooth Functions

This paper establishes optimal approximation error characterization of d...

Jianfeng Lu, et al. ∙

research

∙ 01/05/2020

Non-Convex Planar Harmonic Maps

We formulate a novel characterization of a family of invertible maps bet...

Shahar Z. Kovalsky, et al. ∙

research

∙ 12/04/2019

Universal approximation of symmetric and anti-symmetric functions

We consider universal approximations of symmetric and anti-symmetric fun...

Jiequn Han, et al. ∙

research

∙ 11/11/2019

Part-based Multi-stream Model for Vehicle Searching

Due to the enormous requirement in public security and intelligent trans...

Ya Sun, et al. ∙

research

∙ 11/08/2019

Estimating Normalizing Constants for Log-Concave Distributions: Algorithms and Lower Bounds

Estimating the normalizing constant of an unnormalized probability distr...

Rong Ge, et al. ∙

research

∙ 07/03/2019

Fisher information regularization schemes for Wasserstein gradient flows

We propose a variational scheme for computing Wasserstein gradient flows...

Wuchen Li, et al. ∙

research

∙ 05/27/2019

Efficient posterior sampling for high-dimensional imbalanced logistic regression

High-dimensional data are routinely collected in many application areas....

Deborshee Sen, et al. ∙

research

∙ 05/27/2019

Temporal-difference learning for nonlinear value function approximation in the lazy training regime

We discuss the approximation of the value function for infinite-horizon ...

Andrea Agazzi, et al. ∙

research

∙ 05/23/2019

Accelerating Langevin Sampling with Birth-death

A fundamental problem in Bayesian inference and statistical machine lear...

Yulong Lu, et al. ∙

research

∙ 05/17/2019

Tensor Ring Decomposition: Energy Landscape and One-loop Convergence of Alternating Least Squares

In this work, we study the tensor ring decomposition and its associated ...

Ziang Chen, et al. ∙

research

∙ 05/07/2019

Variational training of neural network approximations of solution maps for physical models

A novel solve-training framework is proposed to train neural network in ...

Yingzhou Li, et al. ∙

Jianfeng Lu

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