52 citations · 103 across the 12 of their papers we have counts for
13 papers
Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width
Yanming Lai, Defeng Sun, Yang Wang
In contrast to most studies on neural network approximation theory that characterize results through a single parameter, such as the total number of network parameters, \cite{shen2…
Beyond the Prompt in Large Language Models: Comprehension, In-Context Learning, and Chain-of-Thought
Yuling Jiao, Yanming Lai, Huazhen Lin +3
Large Language Models (LLMs) have demonstrated remarkable proficiency across diverse tasks, exhibiting emergent properties such as semantic prompt comprehension, In-Context Learnin…
Standard Transformers Achieve the Minimax Rate in Nonparametric Regression with Targets
Yanming Lai, Defeng Sun
The tremendous success of Transformer models in fields such as large language models and computer vision necessitates a rigorous theoretical investigation. To the best of our knowl…
Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective
Yuling Jiao, Yanming Lai, Yang Wang +1
The Transformer model is widely used in various application areas of machine learning, such as natural language processing. This paper investigates the approximation of the Hölder…
Approximation Bounds for Transformer Networks with Application to Regression
Yuling Jiao, Yanming Lai, Defeng Sun +2
We explore the approximation capabilities of Transformer networks for Hölder and Sobolev functions, and apply these results to address nonparametric regression estimation with depe…
Error Analysis of Three-Layer Neural Network Trained with PGD for Deep Ritz Method
Yuling Jiao, Yanming Lai, Yang Wang
Machine learning is a rapidly advancing field with diverse applications across various domains. One prominent area of research is the utilization of deep learning techniques for so…
Convergence Analysis of Flow Matching in Latent Space with Transformers
Yuling Jiao, Yanming Lai, Yang Wang +1
We present theoretical convergence guarantees for ODE-based generative models, specifically flow matching. We use a pre-trained autoencoder network to map high-dimensional original…
Convergence Analysis of the Deep Galerkin Method for Weak Solutions
Yuling Jiao, Yanming Lai, Yang Wang +2
This paper analyzes the convergence rate of a deep Galerkin method for the weak solution (DGMW) of second-order elliptic partial differential equations on with Diric…
Analysis of Deep Ritz Methods for Laplace Equations with Dirichlet Boundary Conditions
Chenguang Duan, Yuling Jiao, Yanming Lai +3
Deep Ritz methods (DRM) have been proven numerically to be efficient in solving partial differential equations. In this paper, we present a convergence rate in norm for dee…
A rate of convergence of Physics Informed Neural Networks for the linear second order elliptic PDEs
Yuling Jiao, Yanming Lai, Dingwei Li +4
In recent years, physical informed neural networks (PINNs) have been shown to be a powerful tool for solving PDEs empirically. However, numerical analysis of PINNs is still missing…
Error Analysis of Deep Ritz Methods for Elliptic Equations
Yuling Jiao, Yanming Lai, Yisu Lo +2
Using deep neural networks to solve PDEs has attracted a lot of attentions recently. However, why the deep learning method works is falling far behind its empirical success. In thi…
Convergence Rate Analysis for Deep Ritz Method
Chenguang Duan, Yuling Jiao, Yanming Lai +2
Using deep neural networks to solve PDEs has attracted a lot of attentions recently. However, why the deep learning method works is falling far behind its empirical success. In thi…
Deep Neural Networks with ReLU-Sine-Exponential Activations Break Curse of Dimensionality in Approximation on Hölder Class
Yuling Jiao, Yanming Lai, Xiliang Lu +3
In this paper, we construct neural networks with ReLU, sine and as activation functions. For general continuous defined on with continuity modulus ,…