2022/10/14 by Jianfei Li, Feng Han, Li, Jianfei +3 · 1 citation
Computer Science · Engineering · Mathematics · #Activation function #Algorithm #Artificial Intelligence (cs.AI) #Artificial intelligence #Artificial neural network #Computer science #Convolutional neural network #Deep learning #Dimension (graph theory) #FOS: Computer and information sciences #FOS: Mathematics #Feature extraction #Function approximation #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Machine Learning (cs.LG) #Mathematics #Neural Networks and Applications #Pattern recognition (psychology) #Sparse and Compressive Sensing Techniques #Wavelet
paper · pdf · doi:10.48550/arxiv.2210.09041
openalex publication_date 2022/10/14 · openalex created_date 2022/10/20 · openalex updated_date 2026/07/28
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.