Convolutional Layer


### Share the same parameters across different locations (assume input stationary)
In practice usually zero pad the border
parameter 가 fully connected 나 locally connected 보다 훨씬 작아서
There are weight variables which are same as the size of filter including all that channels 
Using small filter is better

[CNN Stride](https://texonom.com/cnn-stride-b84e6cf4abd347289dc8dbe6ffc1097d)

1x1 is also valid because we can reduce or increase the Output Channel of feature map with different scaling
채널별 필터 총합이 최종필터
**Commonly number of filters K is powers of 2**
K가 늘면 지수적으로 연관 픽셀이 늘어나는게 아니라 선형적으로 가까운 거리로  늘어남
![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F2b27a771-bf6c-4c73-bb6c-6dc888a9d56e%2FUntitled.png?table=block&id=04353e66-16fb-48a3-a472-44bf24a7fe77&cache=v2)
### Multiple small sized filter layer’s parameters have much smaller than one large sized filter layer (also more nonlinearity, less compute)
so we use mostly 3x3 after [VGG](https://texonom.com/vgg-c59b523e5e894bf2842474c9022dceec) ([ALexNet](https://texonom.com/alexnet-e33d746e06a540d4b8900be7ccede18c) used 11x11 or 7x7 convolution layer) 
1x1 으로 더 줄일 수 있는데 그게 [CNN bottleneck layer](https://texonom.com/cnn-bottleneck-layer-c67427171be5400db198dd6e7ef644ce) 


### total parameter
$$filter \; size ^2 +1\;for\;bias$$





