1. 1x1卷积核-> 3x3卷积核

假设我们有一个1x1的卷积核，需要通过填充变为一个3x3的卷积核,实现的是像素之间无关联
$$\begin{array}{c}\left[\begin{array}{c}4\end{array}\right]\to \left[\begin{array}{ccc}0& 0& 0\\ & & \\ 0& 4& 0\\ & & \\ 0& 0& 0\end{array}\right]\end{array}$$

2. 输入x --> 3x3卷积核，无变化

我们希望有一个x，用3x3的卷积核表示后依然不变，那么首先是3x3的卷积核本身移动过程中不会改变像素值，像素之间不融合，其次是空间中不融合，假设我们有一个卷积定义如下
$$\begin{array}{c}con2d(2,2,3,padding="same")\end{array}$$
可得： 输出通道为2，输入通道为2，卷积核大小为3，padding=“same”表示卷积核图像不变
卷积权重大小为(2,2,3,3)

• 可以把(2,2,3,3)简单拆分成两个部分，第一个为(2,3,3)的卷积核矩阵，实现的是卷积滑动操作，(2,2)表示的将输入通道数2转换成输出通道数2，那么一个2x2的矩阵，怎样才能够实现通道分离呢？一般就是对角矩阵，那么可以简单看做如下：
  $$\begin{array}{c}\left[\begin{array}{cc}a& b\\ & \\ b& a\end{array}\right];a\to \left[\begin{array}{ccc}0& 0& 0\\ & & \\ 0& 1& 0\\ & & \\ 0& 0& 0\end{array}\right];b\to \left[\begin{array}{ccc}0& 0& 0\\ & & \\ 0& 0& 0\\ & & \\ 0& 0& 0\end{array}\right]\end{array}$$
• 这样就实现了通道上的分离和像素上的分离。

3. 代码

#!/usr/bin/env python
# -*- coding:utf-8 -*-
# @FileName  :confusion_conv2d.py
# @Time      :2024/12/9 8:23
# @Author    :Jason Zhang
import torch
from torch import nn
import torch.nn.functional as Fif __name__ == "__main__":run_code = 0in_channels = 2out_channels = 2kernel_size = 3w = 9h = 9x = torch.ones(1, in_channels, w, h)  # input image size# 1. pytorch method 1.1 x --> image = 1,2,9,9 1.2 kernel --> conv2d -->2,2,3,3 --> 2,2,3,3 --> kernel_size =3x3# 1.3 compute . if we have out_chanel for the 2 ,and# each channel has 2 kernel with 3x3, total 2x2--> 4 counts for 3x3conv_2d = nn.Conv2d(in_channels=in_channels, out_channels=out_channels, kernel_size=kernel_size, padding="same")print(f"conv_2d.weight.shape={conv_2d.weight.shape}")print(f"conv_2d.weight={conv_2d.weight}")conv_2d_pointwise = nn.Conv2d(in_channels=in_channels, out_channels=out_channels, kernel_size=1)result1 = conv_2d(x) + conv_2d_pointwise(x) + xprint(f"result1.shape=\n{result1.shape}")print(f"result1=\n{result1}")zeros = torch.unsqueeze(torch.zeros(kernel_size, kernel_size), 0)starts = torch.unsqueeze(F.pad(torch.ones(1, 1), (1, 1, 1, 1)), 0)print(f"zeros=\n{zeros}")print(f"zeros.shape={zeros.shape}")print(f"starts=\n{starts}")print(f"starts.shape=\n{starts.shape}")starts_zeros = torch.unsqueeze(torch.cat((starts, zeros), 0), 0)zeros_starts = torch.unsqueeze(torch.cat((zeros, starts), 0), 0)print(f"start_zeros=\n{starts_zeros}")print(f"start_zeros.shape=\n{starts_zeros.shape}")print(f"zeros_starts=\n{zeros_starts}")print(f"zeros_starts.shape=\n{zeros_starts.shape}")identity_weight = torch.cat((starts_zeros, zeros_starts), 0)identity_bias = torch.zeros(out_channels)print(f"identity=\n{identity_weight}")print(f"identity.shape=\n{identity_weight.shape}")test_conv2d = nn.Conv2d(in_channels=in_channels, out_channels=out_channels, kernel_size=kernel_size, padding="same")test_conv2d_weight = test_conv2d.weighttest_conv2d_bias = test_conv2d.biasprint(test_conv2d_weight.shape)print(test_conv2d_bias.shape)test_conv2d.weight = nn.Parameter(identity_weight)test_conv2d.bias = nn.Parameter(identity_bias)input_x = torch.randint(1, 10, (1, 2, 9, 9), dtype=torch.float)out_y = test_conv2d(input_x)print(f"input_x=\n{input_x}")print(f"out_y=\n{out_y}")check_out = torch.allclose(input_x, out_y)print(f"input_x is {check_out} same for out_y")point_wise = nn.Conv2d(in_channels=in_channels, out_channels=out_channels, kernel_size=1, padding="same")point_wise_weight = F.pad(point_wise.weight, (1, 1, 1, 1, 0, 0, 0, 0))point_wise_bias = point_wise.biasprint(f"point_wise=\n{point_wise_weight}")print(f"point_wise.shape=\n{point_wise_weight.shape}")point_wise_conv = nn.Conv2d(in_channels=in_channels, out_channels=out_channels, kernel_size=kernel_size,padding="same")point_wise_conv.weight = nn.Parameter(point_wise_weight)point_wise_conv.bias = nn.Parameter(point_wise_bias)point_wise_out = point_wise(input_x)print(f"point_wise_out=\n{point_wise_out}")point_3_wise_out = point_wise_conv(input_x)check_3 = torch.allclose(point_wise_out, point_3_wise_out)print(f"check_3 is {check_3} same for point_3_wise_out")