2024/06/30 by Hongkai Zhao, Zhang, Shijun, Zhao, Hongkai +4 · 3 citations
Computer Science · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications #Neural and Evolutionary Computing (cs.NE) #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2407.00765
openalex publication_date 2024/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we propose a balanced multi-component and multi-layer neural network (MMNN) structure to accurately and efficiently approximate functions with complex features, in terms of both degrees of freedom and computational cost. The main idea is inspired by a multi-component approach, in which each component can be effectively approximated by a single-layer network, combined with a multi-layer decomposition strategy to capture the complexity of the target function. Although MMNNs can be viewed as a simple modification of fully connected neural networks (FCNNs) or multi-layer perceptrons (MLPs) by introducing balanced multi-component structures, they achieve a significant reduction in training parameters, a much more efficient training process, and improved accuracy compared to FCNNs or MLPs. Extensive numerical experiments demonstrate the effectiveness of MMNNs in approximating highly oscillatory functions and their ability to automatically adapt to localized features.