Convolution operation and Grouped Convolution

filter is not the kernel,but the kernels.that's mean a filter include one or two or more kernels.that's depend the input feature map and the output feature maps. for example, if we have an image, the shape of image is (32,32), has 3 channels,that's RGB.so the input feature maps is (1,3,32,32).the format of input feature maps is (batch_size,in_channels,H_in,W_in),the output feature maps is(batch_size,out_channels,H_out,W_out),there is a formulation for out_H,out_W.

p is padding,default is 0. s is stride,default is 1.

so, we get the the Height and Width of output feature map,but how about the output channels?how do we get the output channels from the input channels.Or,In other words,what's the convolution operation?

first,i'll give the conclusion and explain it later.

so the weight size is (filters, kernels of filter,H_k,W_k),the format of weight vector is (C_out,C_in,H_k,W_k)

that's mean we have C_out filters, and each filter has C_in kernels.if you don't understand, look through this link,it will tell you the specific operations.

as we go deeper into the convolution this dimension of channels increases very rapidly thus increases complexity. The spatial dimensions(means height and weight) have some degree of effect on the complexity but in deeper layers, they are not really the cause of concern. Thus in bigger neural networks, the filter groups will dominate.so,the grouped convolution was proposed,you can access to this link for more details.

you can try this code for validation.

import torch.nn as nn
import torch

# 假设输入特征图的大小为 (batch_size, in_channels, H, W)
batch_size = 1
in_channels = 4
out_channels = 2
H = 6
W = 6

# 定义1x1卷积层，输入通道数为in_channels，输出通道数为out_channels
conv = nn.Conv2d(in_channels, out_channels, kernel_size=1, stride=1, padding=0)

# 对输入特征图进行1x1卷积操作
x = torch.randn(batch_size, in_channels, H, W)
y = conv(x)

# 输入特征图的大小为 (batch_size, in_channels, H, W)
print(x.shape)  # torch.Size([1, 4, 6, 6])
# 输出特征图的大小为 (batch_size, out_channels, H, W)
print(y.size())   # torch.Size([1, 2, 6, 6])
# 获取卷积核的尺寸 (out_channels, in_channels // groups, *kernel_size)
weight_size = conv.weight.size()
print('卷积核的尺寸为：', weight_size)  # torch.Size([2, 4, 1, 1])