卷积神经网络（李沐老师课程）

卷积神经网络（李沐老师课程）

回顾MLP单层（上述列子需要14GB GPU）

找寻图片上的人在哪里

找寻图片上的人的两个基本原则

从全连接层出发到卷积

卷积层

二维交叉相关

二维卷积层

案列

交叉相关和卷积

代码的实现

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
​
​
"""
验证上述二维互相关运算的输出
"""
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]])
corr = corr2d(x, K)
print(corr)
​
"""
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
​
​
"""
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]])
"""
输出Y中的1代表从白色到黑色的边缘，-1代表从黑色到白色的边缘
"""
y = corr2d(x, k)
print(y)
"""
以上卷积核只能检测垂直边缘
"""
print(corr2d(x.t(), k))
​
"""
学习由X到Y生成的卷积核
"""
conv2d =nn.Conv2d(1,1,kernel_size=(1,2),bias=False)
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
    conv2d.zero_grad()
    l.sum().backward()
    conv2d.weight.data[:]-=3e-2*conv2d.weight.grad
    if (i+1)%2==0:
        print(f"batch {i+1},loss {l.sum():.3f}")
​
"""
所学的卷积核的权重张量
"""
print(conv2d.weight.data.reshape((1, 2)))