Universality of deep convolutional neural networks
Universality of deep convolutional neural networks
复制标题
深度卷积神经网络的通用性
DOI：
10.1016/j.acha.2019.06.004
复制
发表时间：
2020-03-01
影响因子：
2.5
通讯作者：
Zhou, Ding-Xuan
中科院分区：
文献类型：
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作者：
Zhou, Ding-Xuan
深度学习已经在语音识别、计算机视觉等许多领域得到了广泛的应用和突破。深度神经网络架构和计算问题在机器学习中已经得到了很好的研究。但是，缺乏理解深度卷积神经网络等网络架构生成的深度学习方法的近似或泛化能力的理论基础。在这里，我们证明了深度卷积神经网络（CNN）是通用的，这意味着当神经网络的深度足够大时，它可以用来以任意精度逼近任何连续函数。这回答了学习理论中的一个开放性问题。我们的定量估计，严格按照要计算的自由参数的数量给出，验证了深度CNN在处理高维数据时的效率。我们的研究还证明了卷积在深度CNN中的作用。(C)2019爱思唯尔公司All rights reserved.
Deep learning has been widely applied and brought breakthroughs in speech recognition, computer vision, and many other domains. Deep neural network architectures and computational issues have been well studied in machine learning. But there lacks a theoretical foundation for understanding the approximation or generalization ability of deep learning methods generated by the network architectures such as deep convolutional neural networks. Here we show that a deep convolutional neural network (CNN) is universal, meaning that it can be used to approximate any continuous function to an arbitrary accuracy when the depth of the neural network is large enough. This answers an open question in learning theory. Our quantitative estimate, given tightly in terms of the number of free parameters to be computed, verifies the efficiency of deep CNNs in dealing with large dimensional data. Our study also demonstrates the role of convolutions in deep CNNs. (C) 2019 Elsevier Inc. All rights reserved.