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

• URL: http://arxiv.org/abs/2503.07976v1
• Date: Tue, 11 Mar 2025 02:15:09 GMT
• Title: Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach
• Authors: Qin Fang, Lei Shi, Min Xu, Ding-Xuan Zhou,
• Abstract summary: This paper investigates approximation capabilities of two-dimensional (2D) deep convolutional neural networks (CNNs)<n>We focus on 2D CNNs, comprising multi-channel convolutional layers with zero-padding and ReLU activations, followed by a fully connected layer.<n>We propose a fully constructive approach for building 2D CNNs to approximate Korobov functions and provide rigorous analysis of the complexity of the constructed networks.
• Score: 13.218398833013293
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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.

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