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Introduction to Convolutional Neural Networks

Introduction to Convolutional Neural NetworksJianxin WuLAMDA GroupNational Key Lab for Novel Software TechnologyNanjing University, 1, 2017 Contents1 Introduction22 Tensor and vectorization .. Vector calculus and the chain rule ..43 CNN in a The architecture .. The forward run .. Stochastic gradient descent (SGD) .. Error back propagation ..84 Layer input, output and notations95 The ReLU layer106 The convolution What is convolution? .. Why to convolve? .. Convolution as matrix product .. The Kronecker product .. Backward propagation: update the parameters .. Even higher dimensional indicator matrices .. Backward propagation: prepare supervision signal for the previ-ous layer .. Fully connected layer as a convolution layer.

1 Introduction This is a note that describes how a Convolutional Neural Network (CNN) op-erates from a mathematical perspective. This note is self-contained, and the focus is to make it comprehensible to beginners in the CNN eld. The Convolutional Neural Network (CNN) has shown excellent performance

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