深度ReLU神经网络的万有一致性  

Universal consistency of deep ReLU neural networks

作　　者：刘霞 王迪 Xia LIU;Di WANG(School of Science,Xi'an University of Technology,Xi'an 710048,China;School of Management,Xi'an Jiaotong University,Xi'an 710049,China)

机构地区：[1]西安理工大学理学院,西安710048 [2]西安交通大学管理学院,西安710049

出　　处：《中国科学：信息科学》2024年第3期638-652,共15页Scientia Sinica(Informationis)

基　　金：国家自然科学基金(批准号:12371514,12271431,12171388);陕西数理基础科学研究项目(批准号:22JSQ023)资助。

摘　　要：随着数据量爆炸式增长、计算资源愈加丰富,浅层神经网络并不总能满足时代需求,从而导致深度神经网络的出现.深度神经网络的迅猛发展主要体现在应用领域,其理论研究相对匮乏.基于此,本文聚焦研究深度ReLU神经网络的万有一致性,具体内容包括:首先,是否存在一个具有统一结构的深度神经网络(即深度、宽度、激活函数等均已确定)使得该深度神经网络可以学习更多特征,并具有万有逼近性;其次,针对已确定的深度神经网络模型,证明其是强万有一致的;最后,从实验的角度验证理论结果的合理性.With the explosive growth of data and richer computing resources,shallow neural networks can not always meet the requirements of the times,resulting in the emergence of deep neural networks.The rapid development of deep neural networks is mainly re ected in applications,and the theoretical research is relatively scarce.This paper focuses on the universal consistency of deep ReLU neural networks.The contents include:rstly,whether there is a deep neural network with a uni ed structure(i.e.,the depth,width,and activation function have been determined)that can learn more features and has universal approximation;secondly,the determined deep neural network model has the property of universal consistency;nally,we verify the theoretical results from the perspective of experiments.

关 键 词：深度神经网络 万有一致性 深度学习 ReLU 函数 逼近性 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]