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Found 16 papers, 1 papers with code
A Mean Field Analysis Of Deep ResNet And Beyond: Towards Provably Optimization Via Overparameterization From Depth
Specifically, we propose a \textbf{new continuum limit} of deep residual networks, which enjoys a good landscape in the sense that \textbf{every local minimizer is global}.
Score-based generative models break the curse of dimensionality in learning a family of sub-Gaussian probability distributions
While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited.
Optimal Deep Neural Network Approximation for Korobov Functions with respect to Sobolev Norms
This paper establishes the nearly optimal rate of approximation for deep neural networks (DNNs) when applied to Korobov functions, effectively overcoming the curse of dimensionality.
Two-Scale Gradient Descent Ascent Dynamics Finds Mixed Nash Equilibria of Continuous Games: A Mean-Field Perspective
Finding the mixed Nash equilibria (MNE) of a two-player zero sum continuous game is an important and challenging problem in machine learning.
Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equations
Deep operator network (DeepONet) has demonstrated great success in various learning tasks, including learning solution operators of partial differential equations.
Birth-death dynamics for sampling: Global convergence, approximations and their asymptotics
Motivated by the challenge of sampling Gibbs measures with nonconvex potentials, we study a continuum birth-death dynamics.
A Regularity Theory for Static Schrödinger Equations on $\mathbb{R}^d$ in Spectral Barron Spaces
Spectral Barron spaces have received considerable interest recently as it is the natural function space for approximation theory of two-layer neural networks with a dimension-free convergence rate.
On the Representation of Solutions to Elliptic PDEs in Barron Spaces
Numerical solutions to high-dimensional partial differential equations (PDEs) based on neural networks have seen exciting developments.
A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schrödinger Eigenvalue Problems
We prove that the convergence rate of the generalization error is independent of the dimension $d$, under the a priori assumption that the ground state lies in a spectral Barron space.
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 Ritz Method (DRM) [W. E and B. Yu, 2017], a popular neural-network-based method for solving high dimensional partial differential equations.
A Universal Approximation Theorem of Deep Neural Networks for Expressing Probability Distributions
In particular, the size of neural network can grow exponentially in $d$ when $1$-Wasserstein distance is used as the discrepancy, whereas for both MMD and KSD the size of neural network only depends on $d$ at most polynomially.
A Mean-field Analysis of Deep ResNet and Beyond: Towards Provable Optimization Via Overparameterization From Depth
Specifically, we propose a new continuum limit of deep residual networks, which enjoys a good landscape in the sense that every local minimizer is global.
A Mean-field Analysis of Deep ResNet and Beyond:Towards Provable Optimization Via Overparameterization From Depth
Specifically, we propose a \textbf{new continuum limit} of deep residual networks, which enjoys a good landscape in the sense that \textbf{every local minimizer is global}.
Accelerating Langevin Sampling with Birth-death
A fundamental problem in Bayesian inference and statistical machine learning is to efficiently sample from multimodal distributions.
Uniform-in-Time Weak Error Analysis for Stochastic Gradient Descent Algorithms via Diffusion Approximation
Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon.
Scaling limit of the Stein variational gradient descent: the mean field regime
We study an interacting particle system in $\mathbf{R}^d$ motivated by Stein variational gradient descent [Q. Liu and D. Wang, NIPS 2016], a deterministic algorithm for sampling from a given probability density with unknown normalization.
