深度学习笔记 —— 转置卷积

语义分割要做像素级别的预测，但是卷积不断地减小高宽，所以需要另外一种卷积把小的高宽变大。

转置卷积：输入中的单个元素与kernel按元素做乘法但不相加，然后按元素写回到原始的地方。

再谈转置卷积：

换算成卷积之后，卷积是正常卷积，也就是填充为0，步幅为1，与前面填充和步幅是无关的。

如果要做逆变换需要能推出来：n >= sn' + k - 2p - s（刚好整除的情况下取等号）

转置卷积是形状上做逆运算，但元素值不是。转置卷积本质上还是一种卷积。

import torch
from torch import nn
from d2l import torch as d2l


# 实现基本的转置卷积运算
def trans_conv(X, K):
    h, w = K.shape
    Y = torch.zeros((X.shape[0] + h - 1, X.shape[1] + w - 1))
    for i in range(X.shape[0]):
        for j in range(X.shape[1]):
            Y[i: i + h, j: j + w] += X[i, j] * K
    return Y


# 验证上述实现输出
X = torch.tensor([[0.0, 1.0], [2.0, 3.0]])
K = torch.tensor([[0.0, 1.0], [2.0, 3.0]])
print(trans_conv(X, K))


# 使用高级API获得相同的结果
X, K = X.reshape(1, 1, 2, 2), K.reshape(1, 1, 2, 2)
tconv = nn.ConvTranspose2d(1, 1, kernel_size=2, bias=False)
tconv.weight.data = K
print(tconv(X))


# 填充、步幅和多通道
# 填充在输出上面
tconv = nn.ConvTranspose2d(1, 1, kernel_size=2, padding=1, bias=False)
tconv.weight.data = K
print(tconv(X))

tconv = nn.ConvTranspose2d(1, 1, kernel_size=2, stride=2, bias=False)
tconv.weight.data = K
print(tconv(X))

X = torch.rand(size=(1, 10, 16, 16))
conv = nn.Conv2d(1, 1, kernel_size=5, padding=2, stride=3)
tconv = nn.ConvTranspose2d(1, 1, kernel_size=5, padding=2, stride=3)
print(tconv(conv(X)).shape == X.shape)


# 与矩阵变换的联系
X = torch.arange(9.0).reshape(3, 3)
K = torch.tensor([[1.0, 2.0], [3.0, 4.0]])
Y = d2l.corr2d(X, K)
print(Y)


def kernel2matrix(K):
    k, W = torch.zeros(5), torch.zeros((4, 9))
    k[:2], k[3:5] = K[0, :], K[1, :]
    W[0, :5], W[1, 1:6], W[2, 3:8], W[3, 4:] = k, k, k, k
    return W


W = kernel2matrix(K)
print(W)

print(Y == torch.matmul(W, X.reshape(-1)).reshape(2, 2))

Z = trans_conv(Y, K)
print(Z == torch.matmul(W.T, Y.reshape(-1)).reshape(3, 3))