6 papers
A Priori Error Bounds for Boundary-Adapted PINNs Solving Elliptic Dirichlet Problems
Nathanael Tepakbong, Jun Fan, Xiang Zhou +1
We study the numerical resolution of uniformly elliptic Dirichlet boundary value problems (BVPs) by minimization of the PDE residual over a hypothesis space of Neural Networks made…
Ghost in the Kernel: In-Context Learning with Efficient Transformers via Domain Generalization
Peilin Liu, Ding-Xuan Zhou
Transformer-based large models have demonstrated remarkable generalization abilities across different tasks by leveraging a context-aware attention module for in-context learning.…
Generalization Analysis of Transformers in Distribution Regression
Peilin Liu, Ding-Xuan Zhou
In recent years, models based on the Transformer architecture have seen widespread applications and have become one of the core tools in the field of deep learning. Numerous succes…
Optimal Convergence Rates of Deep Neural Network Classifiers
Zihan Zhang, Lei Shi, Ding-Xuan Zhou
In this paper, we study the binary classification problem on under the Tsybakov noise condition (with exponent ) and the compositional assumption. This…
Super-fast Rates of Convergence for Neural Network Classifiers under the Hard Margin Condition
Nathanael Tepakbong, Xiang Zhou, Ding-Xuan Zhou
We study the classical binary classification problem for hypothesis spaces of Deep Neural Networks (DNNs) under Tsybakov's low-noise condition with exponent , as well as its l…
Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach
Qin Fang, Lei Shi, Min Xu +1
This paper investigates approximation capabilities of two-dimensional (2D) deep convolutional neural networks (CNNs), with Korobov functions serving as a benchmark. We focus on 2D…