Two 3x3 convolution kernels instead of a 5x5 convolution kernel

In AlexNet, 11 × 11 11\times11 is used to increase the receptive field$11\times 11$、$5\times 5$ and$3\times 3$ Three convolution kernels. And VGG16 illustrates two$3\times 3$ convolution kernel and a$5\times$The receptive field of the convolution kernel of$5\; is$ the same, so that two3 × 3 3\times3can be used$3\times 3$ convolution kernel instead of a$5\times$Convolution kernel of$5$ . Similarly, you can use three$3\times 3$ convolution kernel instead of a$7\times$Convolution kernel of$7$ , using four$3\times 3$ convolution kernel instead of a$9\times$The convolution kernel of$9$ , and so on.

1 Why two $3\times 3$ convolution kernel and a$5\times 5$ convolution kernels have the same receptive field

1.1 Illustrate with pictures

As shown below:

1.2 Calculation instructions

Suppose the feature map is $28\times 2\; to8$ , assuming that the step length of the volume is$step=1$，$padding=0$：

1. Use a layer of $5\times 5$ convolution kernel, by$(28-5)/1+1=24\; is$ available, the output feature map is$24\ast 24$ of
2. Use two layers $3\times 3$ convolution kernel
   1. The first layer, by $(28-3)/1+1=26\; is$ available, the output feature map is$26\times 26$ of
   2. The second layer, by $(26-3)/1+1=24\; is$ available, the output feature map is$24\times 24$ of

You can see that the final result is the same.

2 The benefits of using small convolution instead of winder

1. Under the conditions of ensuring the same receptive field, the depth of the network is improved, and the effect of the network is improved to a certain extent (from this point, it also illustrates the great role of ResNet)
2. Under the condition of ensuring the same receptive field, the amount of calculation and the amount of parameters are reduced