论文标题
从特征提取视图中对CNN的近似分析
Approximation analysis of CNNs from a feature extraction view
论文作者
论文摘要
基于深层神经网络的深度学习在许多实际应用中非常成功，但是由于网络架构和结构，它缺乏足够的理论理解。在本文中，我们通过深层多通道卷积神经网络（CNN）为线性特征提取的分析，该分析证明了深度学习对传统线性转换的力量，例如傅立叶，小波，冗余词典编码方法。此外，我们提供了一个精确的结构，呈现如何使用多通道CNN有效地进行线性特征提取。它可以应用于降低基本维度，以近似高维函数。还研究了通过通道实施的此类深网的功能近似值，然后还研究了完全连接的层。将线性特征分解为多分辨率卷积的谐波分析在我们的工作中起着至关重要的作用。然而，构建了矩阵的专用矢量化，它桥梁1d CNN和2D CNN，使我们能够进行相应的2D分析。
Deep learning based on deep neural networks has been very successful in many practical applications, but it lacks enough theoretical understanding due to the network architectures and structures. In this paper we establish some analysis for linear feature extraction by a deep multi-channel convolutional neural networks (CNNs), which demonstrates the power of deep learning over traditional linear transformations, like Fourier, wavelets, redundant dictionary coding methods. Moreover, we give an exact construction presenting how linear features extraction can be conducted efficiently with multi-channel CNNs. It can be applied to lower the essential dimension for approximating a high dimensional function. Rates of function approximation by such deep networks implemented with channels and followed by fully-connected layers are investigated as well. Harmonic analysis for factorizing linear features into multi-resolution convolutions plays an essential role in our work. Nevertheless, a dedicate vectorization of matrices is constructed, which bridges 1D CNN and 2D CNN and allows us to have corresponding 2D analysis.
