用傅里叶函数网络逼近科罗博夫空间上的函数

IF 6 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Peilin Liu , Yuqing Liu , Xiang Zhou , Ding-Xuan Zhou
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引用次数: 0

摘要

利用深度神经网络从功能数据中学习已变得越来越有用,人们已开发出许多神经网络架构来解决实际领域中提出的高维问题。尽管在实践中取得了令人瞩目的成就,但支撑神经网络从函数数据中学习能力的理论基础在很大程度上仍未得到探索。在本文中,我们研究了由傅立叶神经算子和深度卷积神经网络组成的函数式神经网络(称为傅立叶函数式网络)的逼近能力,并大大减少了参数。我们建立了用傅立叶函数网络逼近定义在周期函数的科罗博夫空间上的非线性连续函数的比率。最后,我们的结果证明了收敛率与维度无关,克服了维度诅咒。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Approximation of functionals on Korobov spaces with Fourier Functional Networks
Learning from functional data with deep neural networks has become increasingly useful, and numerous neural network architectures have been developed to tackle high-dimensional problems raised in practical domains. Despite the impressive practical achievements, theoretical foundations underpinning the ability of neural networks to learn from functional data largely remain unexplored. In this paper, we investigate the approximation capacity of a functional neural network, called Fourier Functional Network, consisting of Fourier neural operators and deep convolutional neural networks with a great reduction in parameters. We establish rates of approximating by Fourier Functional Networks nonlinear continuous functionals defined on Korobov spaces of periodic functions. Finally, our results demonstrate dimension-independent convergence rates, which overcomes the curse of dimension.
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来源期刊
Neural Networks
Neural Networks 工程技术-计算机:人工智能
CiteScore
13.90
自引率
7.70%
发文量
425
审稿时长
67 days
期刊介绍: Neural Networks is a platform that aims to foster an international community of scholars and practitioners interested in neural networks, deep learning, and other approaches to artificial intelligence and machine learning. Our journal invites submissions covering various aspects of neural networks research, from computational neuroscience and cognitive modeling to mathematical analyses and engineering applications. By providing a forum for interdisciplinary discussions between biology and technology, we aim to encourage the development of biologically-inspired artificial intelligence.
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