转置卷积¶

In [1]:

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

实现基本的转置卷积运算

In [2]:

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

In [3]:

X = torch.tensor([[0.0, 1.0], [2.0, 3.0]])
K = torch.tensor([[0.0, 1.0], [2.0, 3.0]])
trans_conv(X, K)

Out[3]:

tensor([[ 0.,  0.,  1.],
        [ 0.,  4.,  6.],
        [ 4., 12.,  9.]])

使用高级API获得相同的结果

In [4]:

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
tconv(X)

Out[4]:

tensor([[[[ 0.,  0.,  1.],
          [ 0.,  4.,  6.],
          [ 4., 12.,  9.]]]], grad_fn=<SlowConvTranspose2DBackward>)

填充、步幅和多通道

In [5]:

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

Out[5]:

tensor([[[[4.]]]], grad_fn=<SlowConvTranspose2DBackward>)

In [6]:

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

Out[6]:

tensor([[[[0., 0., 0., 1.],
          [0., 0., 2., 3.],
          [0., 2., 0., 3.],
          [4., 6., 6., 9.]]]], grad_fn=<SlowConvTranspose2DBackward>)

In [7]:

X = torch.rand(size=(1, 10, 16, 16))
conv = nn.Conv2d(10, 20, kernel_size=5, padding=2, stride=3)
tconv = nn.ConvTranspose2d(20, 10, kernel_size=5, padding=2, stride=3)
tconv(conv(X)).shape == X.shape

Out[7]:

True

与矩阵变换的联系

In [8]:

X = torch.arange(9.0).reshape(3, 3)
K = torch.tensor([[1.0, 2.0], [3.0, 4.0]])
Y = d2l.corr2d(X, K)
Y

Out[8]:

tensor([[27., 37.],
        [57., 67.]])

In [9]:

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)
W

Out[9]:

tensor([[1., 2., 0., 3., 4., 0., 0., 0., 0.],
        [0., 1., 2., 0., 3., 4., 0., 0., 0.],
        [0., 0., 0., 1., 2., 0., 3., 4., 0.],
        [0., 0., 0., 0., 1., 2., 0., 3., 4.]])

In [10]:

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

Out[10]:

tensor([[True, True],
        [True, True]])

In [11]:

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

Out[11]:

tensor([[True, True, True],
        [True, True, True],
        [True, True, True]])