Softmax regression model uses the simplest two layer neural network, i.e. it only contains input layer and output layer, so that it's regression ability is limited. To achieve better recognition effect, we consider adding several hidden layers \[[10](#References)\] between the input layer and the output layer.
Convolutional layer is the core of Convolutional Neural Networks. The parameters in this layer are composed of a set of filters, or kernels. In forward step, each kernel moves horizontally and vertically, and compute dot product of the kernel and input on corresponding positions, then add bias and apply activation function. The result is two dimensional activation map. For example, some kernel may recognize corners, and some may recognize circles. These convolution kernels may respond strongly to the corresponding features.
Fig. 4 is a dynamic graph for a convolutional layer, where depths are not shown for simplicity. Input is $W_1=5,H_1=5,D_1=3$. In fact, this is a common representation for colored images. The width and height of a colored image corresponds to $W_1$ and $H_1$, and the 3 color channels for RGB corresponds to $D_1$. The parameters of convolutional layers are $K=2,F=3,S=2,P=1$. $K$ is the number of kernels. Here, $Filter W_0$ and $Filter W_1$ are two convolution kernels. $F$ is kernel size. $W0$ and $W1$ are both $3\times3$ matrix in all depths. $S$ is stride. Kernels moves leftwards or downwards by 2 units each time. $P$ is padding, which is the extension for the input.
Pooling layer is a sampling method. The main functionality is to reduce computation by reducing network parameters. It also prevents over-fitting to some extent. Usually, a pooling layer is added after a convolutional layer. Pooling layer includes max pooling, average pooling, etc. Max pooling uses rectangles to divide input layer into several parts, and compute maximum value in each part as output (Fig. 5.)
