A brief introduction to the interest of convolutional neural networks

      Convolutional neural network is a magical 、 A profound vocabulary . Now let's uncover it The Painted Veil .“ Convolution ” I think everyone is familiar with it , It is learned in probability theory, and convolution neural network is the operation of mathematical convolution on image pixel matrix . so The charm of Mathematics ！

One 、 Convolution understanding

Convolution is the sum of two variables multiplied in a certain range ;

In the case of discreteness, the number sequence is multiplied and then summed ;

 

In continuous case, it is function multiplication and integration ;

 

Convolution is the operation of two functions , Meet the conditions （ Commutative law , Distributive law , Associative law , The law of combination of number and multiplication , Translation properties , Differential properties , Integral characteristics, etc ） The operator of . in short ： On the original input, a small area and a small area are used for feature extraction , The calculation process of convolution will be explained in detail later .

Two 、 Convolutional neural networks （convolutional neural network,CNN） yes ⼀ Class of powerful neural networks , It is designed for processing image data . Based on convolution neural ⽹ The model of network structure has occupied a dominant position in the field of computer vision .

1、 nature

（1）. Translation invariance ： No matter where it appears in the image , nerve ⽹ The bottom layer of the network should respond similarly to the same image area . This principle is “ Translation invariance ”.

（2）  Locality ： nerve ⽹ The bottom of the network should only explore losing ⼊ Local areas in the image , Without considering the content of the remote area of the image , This is it. “ Locality ” principle .

3、 ... and 、 Compare convolutional neural network and fully connected neural network

On the left ： All connected neural networks （ Plane ）： Input layer , Activation function , Fully connected layer .

Right picture ： Convolutional neural networks （ Three-dimensional ）： Input layer , Convolution layer , Activation function , Pooling layer , Fully connected layer .

Four 、 Cross correlation operation

Suppose you lose ⼊ Shape is nh × nw, The shape of convolution kernel is kh × kw, Then output shape It will be (nh − kh + 1) × (nw − kw + 1).

 

  Detailed calculation process ：

   ×  + 

= 

  Multiply the corresponding elements plus offset b You can get . Subsequent sliding 2 Cycle this step to calculate .

Why slide two grids ？

Sliding grid （stride） The smaller it is , The more features are extracted . Generally do not take 1, Consider time efficiency .

5、 ... and 、 Pooling layer （ Compress image features , Personal understanding （ The feeling of dimensionality reduction ））

  The pool operator is deterministic , We usually calculate all the elements in the pooled window The maximum or average of . These operations are called most ⼤ Pooling layer （maximum pooling） and Average pooling layer （average pooling）.