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Universality of deep convolutional neural networks
Applied and Computational Harmonic Analysis ( IF 2.5 ) Pub Date : 2019-06-13 , DOI: 10.1016/j.acha.2019.06.004
Ding-Xuan Zhou

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.



中文翻译:

深卷积神经网络的普遍性

深度学习已被广​​泛应用,并在语音识别,计算机视觉和许多其他领域取得了突破。深度神经网络架构和计算问题已经在机器学习中得到了很好的研究。但是,缺乏了解网络架构(例如深度卷积神经网络)生成的深度学习方法的逼近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,它可以用于将任意连续函数近似为任意精度。这回答了学习理论中的一个开放性问题。我们的定量估算值,根据要计算的自由参数的数量,给出了严格的估算,验证了深层CNN在处理大规模数据方面的效率。我们的研究还证明了卷积在深层CNN中的作用。

更新日期:2019-06-13
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