# 深度学习笔记 —— 卷积层

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

def corr2d(X, K):
"""计算二维互相关运算"""
h, w = K.shape
Y = torch.zeros((X.shape[0] - h + 1, X.shape[1] - w + 1))
for i in range(Y.shape[0]):
for j in range(Y.shape[1]):
Y[i, j] = (X[i: i + h, j: j + w] * K).sum()
return Y

X = torch.tensor([[0.0, 1.0, 2.0], [3.0, 4.0, 5.0], [6.0, 7.0, 8.0]])
K = torch.tensor([[0.0, 1.0], [2.0, 3.0]])
print(corr2d(X, K))

# 实现二维卷积层
class Conv2D(nn.Module):
def __init__(self, kernel_size):
super().__init__()
self.weight = nn.Parameter(torch.rand(kernel_size))
self.bias = nn.Parameter(torch.zeros(1))

def forward(self, x):
return corr2d(x, self.weight) + self.bias

# 简单应用：检测图像中不同颜色的边缘
X = torch.ones((6, 8))
X[:, 2: 6] = 0
print(X)
K = torch.tensor([[1.0, -1.0]])
Y = corr2d(X, K)
print(Y)

# 学习由X生成Y的卷积核
conv2d = nn.Conv2d(1, 1, kernel_size=(1, 2), bias=False)
# 两个1分别表示批量大小数和通道数
X = X.reshape((1, 1, 6, 8))
Y = Y.reshape((1, 1, 6, 7))

for i in range(10):
Y_hat = conv2d(X)
l = (Y_hat - Y) ** 2