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import torch from torch import nn from d2l import torch as d2l # 输入矩阵X和卷积核矩阵K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 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)) """ tensor([[ 0., 0., 1.], [ 0., 4., 6.], [ 4., 12., 9.]]) """ # 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)) """ tensor([[[[ 0., 0., 1.], [ 0., 4., 6.], [ 4., 12., 9.]]]], grad_fn=<SlowConvTranspose2DBackward>) """ # 填充、步幅和多通道 # 当将高和宽两侧的填充数指定为1时,转置卷积的输出中将删除第一和最后的行与列。 tconv = nn.ConvTranspose2d(1, 1, kernel_size=2, padding=1, bias=False) tconv.weight.data = K print(tconv(X)) # tensor([[[[4.]]]], grad_fn=<SlowConvTranspose2DBackward>) # 步幅为2的转置卷积的输出 tconv = nn.ConvTranspose2d(1, 1, kernel_size=2, stride=2, bias=False) tconv.weight.data = K print(tconv(X)) """ tensor([[[[0., 0., 0., 1.], [0., 0., 2., 3.], [0., 2., 0., 3.], [4., 6., 6., 9.]]]] """ 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) print(conv(X).shape) # torch.Size([1, 20, 6, 6]) print(tconv(conv(X)).shape) # torch.Size([1, 10, 16, 16]) print(tconv(conv(X)).shape == X.shape) # True # 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) """ tensor([[27., 37.], [57., 67.]]) """ # 将卷积核K重写为包含大量0的稀疏权重矩阵W。 权重矩阵的形状是4 * 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) print(W) """ 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.]]) """ print(Y == torch.matmul(W, X.reshape(-1)).reshape(2, 2)) """ tensor([[True, True], [True, True]]) """ # 使用矩阵乘法来实现转置卷积 Z = trans_conv(Y, K) print(Z == torch.matmul(W.T, Y.reshape(-1)).reshape(3, 3)) """ tensor([[True, True, True], [True, True, True], [True, True, True]]) """
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