convolutional neural Network (ii): convolutional neural network BP algorithm for CNN

This document references: http://www.cnblogs.com/tornadomeet/p/3468450.html

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Generally speaking, the output of a multi-class neural network is generally in softmax form, that is, the activation function of the output layer does not use sigmoid or Tanh functions. Then the output of the last layer of the neural network is

The following is how the error from the pooling layer to the convolution layer is transmitted in reverse, and as with the multilayer neural network, the error propagation can be achieved through the connection between the layer and the layer, only the calculation formula becomes,

The coefficients are assigned according to the method of pooling, and if it is mean-pooling, the error of the pooling layer is averaged to its 4 inputs, and if it is max-pooling the error is transmitted all the way to its input.

next look at how to calculate the error of the convolution layer back propagation to the pooling, the pooling layer of the 1 feature map and m convolution layer feature map of the connection, then the pooling layer error terms are calculated as follows,

In the above formula, the * number is the convolution operation, the kernel function k is rotated 180 degrees and then the error term is related to the operation, and then summed.

Finally, we study how to calculate the partial derivative of the kernel function connected with the convolution layer after obtaining the error terms of each layer, and the formula is as follows.

The partial derivative of the kernel function can be obtained when the error item of the convolution layer is rotated 180 degrees and its input layer is related.

The partial derivative of the offset item is obtained by adding all the elements in the error term.

convolutional neural Network (ii): convolutional neural network BP algorithm for CNN