Work

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach

Year: 2025

Type: preprint

Abstract: 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 CNNs, comprising multi-channel convolutional layers with zero-padding and ReLU activations, followed by a fully connected layer. We propose a fully constructive approach for building 2D CNNs to approximate Korobov functions and provide a rigorous analysis of the complexity of the constructed networks. Our results demonstrate that 2D CNNs achieve near-optimal approximation rates under the continuous weight selection model, significantly alleviating the curse of dimensionality. This work provides a solid theoretical foundation for 2D CNNs and illustrates their potential for broader applications in function approximation.

Source: arXiv (Cornell University)

Authors: Fang, Qin, Shi, Lei, Xu, Min, Zhou, Ding-Xuan

Institutions: Dalian University, Fudan University, Dalian University of Technology, The University of Sydney

Language: English

Topic: Neural Networks and Applications

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Australian Research Council

Awards: Approximation theory of structured neural networks , G4082439926

OpenAlex ID: W6979248797

Cites:

Cited by:

Related to: