Convolution operation and Grouped Convolution

原创已于 2023-08-25 17:08:43 修改 · 866 阅读

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#深度学习 #pytorch #神经网络

于 2023-07-31 19:15:57 首次发布

文章解释了在卷积神经网络中，滤波器（filter）由一个或多个内核（kernel）组成，其大小和数量取决于输入和输出特征图的维度。输出通道的数量不直接由输入通道决定，而是由权重矩阵的设置（如卷积层的输出通道数）。随着网络深度增加，通道数快速增加，导致计算复杂度提高，为此提出了分组卷积来降低复杂性。

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.

$H_{out} = \lfloor \frac{H_{in} + 2p - H_k}{s} + 1 \rfloor$

$W_{out} = \lfloor \frac{W_{in} + 2p - W_k}{s} + 1 \rfloor$

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.

$filters=C_{out}$

$kernels\ of \ filter = C_{in}$

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])

check this video for more details.