Structured and Balanced Multi-Component and Multi-Layer Neural Networks

TL;DR

This paper introduces a balanced multi-component, multi-layer neural network (MMNN) that improves approximation accuracy and training efficiency for complex functions by combining component-wise approximation with layered decomposition.

Contribution

It presents a novel MMNN structure that reduces parameters and enhances training efficiency compared to traditional fully connected networks.

Findings

Effective approximation of highly oscillatory functions

Automatic adaptation to localized features

Significant reduction in training parameters

Abstract

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.