---

一、CNN基础流程图

卷积：对数据升维
下采样：对数据降维

二、CNN的两个阶段

特征提取阶段：通过卷积和下采样对图像数据进行升维和降维，从而实现特征提取
分类器：将特征提取阶段输出的数据展平成一维，再通过全连接层进行分类

三、卷积的基本知识

卷积后数据维度会变（比如信道数增加、宽度和高度减小）

3.1 单信道的卷积

然后通过滑动卷积框，多次进行卷积计算，直到卷积框移动到Input最下最右，此时就将输出矩阵的信息补充完整了

3.2 三信道的卷积

3.3 N信道卷积

3.4 输入N信道-输出M信道卷积

原理：采用M个卷积核对Input进行卷积，这样就得到了M层的输出

PyTorch代码实现卷积：

import torch

in_channels, out_channels = 5, 10  # 输入信道数、输出信道数
w, h = 100, 100  # 输入图片尺寸
kernel_size = (3, 3)  # 卷积核大小3*3
batch_size = 1  # 每次参与模型更新的数据数量
input = torch.randn(batch_size, in_channels, w, h)  # torch.randn 随机产生输入数据
conv_layer = torch.nn.Conv2d(in_channels, out_channels, kernel_size=kernel_size)  # 定义卷积层（输入信道数，输出信道数，卷积核大小）
output = conv_layer(input)  # 进行卷积操作
# 输出输入、输出和卷积层权重的形状
print(input.shape)
print(output.shape)
print(conv_layer.weight.shape)

输出：

torch.Size([1, 5, 100, 100])
torch.Size([1, 10, 98, 98])
torch.Size([10, 5, 3, 3])

3.5 卷积层的常见参数

3.5.1 Padding

Padding：在输入数据的四周进行扩展的数量，比如Padding = （1，1）代表在输入数据的四周一圈扩展并填充0
一般地：
当卷积核大小为3×3时：Padding=（1，1）
当卷积核大小为5×5时：Padding=（2，2）
…
当卷积核大小为n×n时：Padding=（m，m），其中 m =（n-1）/2，n为奇数

Padding默认填充0

Padding的意义：

• 为了不丢弃原图信息
• 为了保持feature map 的大小与原图一致
• 为了让更深层的layer的input依旧保持有足够大的信息量
• 为了实现上述目的，且不做多余的事情，padding出来的pixel的值都是0，不存在噪音问题。

PyTorch代码体会Padding：

import torch

input = [3, 4, 6, 5, 7,
         2, 4, 6, 8, 2,
         1, 6, 7, 8, 4,
         9, 7, 4, 6, 2,
         3, 7, 5, 4, 1]
input = torch.Tensor(input).view(1, 1, 5, 5)
conv_layer = torch.nn.Conv2d(1, 1, kernel_size=(3, 3), padding=(1, 1), bias=False)
kernel = torch.Tensor([1, 2, 3, 4, 5, 6, 7, 8, 9]).view(1, 1, 3, 3)
conv_layer.weight.data = kernel.data
output = conv_layer(input)
print(output)

输出：

tensor([[[[ 91., 168., 224., 215., 127.],
          [114., 211., 295., 262., 149.],
          [192., 259., 282., 214., 122.],
          [194., 251., 253., 169.,  86.],
          [ 96., 112., 110.,  68.,  31.]]]], grad_fn=<ThnnConv2DBackward>)

3.5.2 Stride

Stride：卷积核滑动的步长，为一个元组。如Stride =（2，2）分别表示宽和高方向上的滑动步长

PyTorch代码体会Stride：

import torch

input = [3, 4, 6, 5, 7,
         2, 4, 6, 8, 2,
         1, 6, 7, 8, 4,
         9, 7, 4, 6, 2,
         3, 7, 5, 4, 1]
input = torch.Tensor(input).view(1, 1, 5, 5)
conv_layer = torch.nn.Conv2d(1, 1, kernel_size=(3, 3), stride=(2, 2), bias=False)
kernel = torch.Tensor([1, 2, 3, 4, 5, 6, 7, 8, 9]).view(1, 1, 3, 3)
conv_layer.weight.data = kernel.data
output = conv_layer(input)
print(output)

输出：

tensor([[[[211., 262.],
          [251., 169.]]]], grad_fn=<ThnnConv2DBackward>)

3.5.3 下采样（MaxPooling）

最常用的下采样方法是最大池化（Max Pooling）
如下图所示，MaxPooling=（2，2），即将输入数据分成四个（2，2）无交集的区域，然后选取每个区域的最大值作为输出数据

由MaxPooling的计算特性可知，MaxPooling不会对信道的数量产生影响

PyTorch代码体会MaxPooling：

import torch

input = [3, 4, 6, 5,
         2, 4, 6, 8,
         1, 6, 7, 5,
         9, 7, 4, 6]
input = torch.Tensor(input).view(1, 1, 4, 4)
max_pooling_layer = torch.nn.MaxPool2d(kernel_size=(2, 2))
output = max_pooling_layer(input)
print(output)

输出：

tensor([[[[4., 8.],
          [9., 7.]]]])

四、实现一个简单的CNN

4.1 网络结构图

4.2 PyTorch代码-CPU

构建网络模型：

class Net(torch.nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.conv1 = torch.nn.Conv2d(1, 10, kernel_size=(5, 5))
        self.conv2 = torch.nn.Conv2d(10, 20, kernel_size=(5, 5))
        self.pooling = torch.nn.MaxPool2d((2, 2))
        self.fc = torch.nn.Linear(320, 10)

    def forward(self, x):
        batch_size = x.size(0)
        x = torch.relu(self.pooling(self.conv1(x)))
        x = torch.relu(self.pooling(self.conv2(x)))
        x = x.view(batch_size, -1)
        x = self.fc(x)
        return x

完整代码：

import torch
from torchvision import transforms
from torchvision import datasets
from torch.utils.data import DataLoader
import torch.optim as optim


class Net(torch.nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.conv1 = torch.nn.Conv2d(1, 10, kernel_size=(5, 5))
        self.conv2 = torch.nn.Conv2d(10, 20, kernel_size=(5, 5))
        self.pooling = torch.nn.MaxPool2d((2, 2))
        self.fc = torch.nn.Linear(320, 10)

    def forward(self, x):
        batch_size = x.size(0)
        x = torch.relu(self.pooling(self.conv1(x)))
        x = torch.relu(self.pooling(self.conv2(x)))
        x = x.view(batch_size, -1)
        x = self.fc(x)
        return x


# 单次训练函数
def train(epoch, criterion):
    running_loss = 0.0
    for batch_idx, data in enumerate(train_loader, 0):
        inputs, target = data
        optimizer.zero_grad()
        outputs = model(inputs)
        loss = criterion(outputs, target)
        loss.backward()
        optimizer.step()
        running_loss += loss.item()
        if batch_idx % 300 == 299:
            print('[%d, %5d] loss: %.3f' % (epoch + 1, batch_idx + 1, running_loss / 300))
            running_loss = 0.0


# 单次测试函数
def ttt():
    correct = 0.0
    total = 0.0
    with torch.no_grad():
        for data in test_loader:
            images, labels = data
            outputs = model(images)
            _, predicted = torch.max(outputs.data, dim=1)
            total += labels.size(0)
            correct += (predicted == labels).sum().item()
    print('Accuracy on test set: %d %% [%d/%d]' % (100 * correct / total, correct, total))


if __name__ == '__main__':
    batch_size = 64
    transform = transforms.Compose([transforms.ToTensor(), transforms.Normalize((0.1307,), (0.3081,))])
    train_dataset = datasets.MNIST(root='../dataset/', train=True, download=True, transform=transform)

    train_loader = DataLoader(train_dataset, shuffle=True, batch_size=batch_size)

    test_dataset = datasets.MNIST(root='../dataset/', train=False, download=True, transform=transform)
    test_loader = DataLoader(test_dataset, shuffle=False, batch_size=batch_size)

    # 声明模型
    model = Net()
    # 定义损失函数
    criterion = torch.nn.CrossEntropyLoss()
    # 定义优化器
    optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.5)

    for epoch in range(10):
        train(epoch, criterion)
        ttt()

输出：

[1,   300] loss: 0.564
[1,   600] loss: 0.191
[1,   900] loss: 0.141
Accuracy on test set: 96 %
[2,   300] loss: 0.110
[2,   600] loss: 0.092
[2,   900] loss: 0.088
Accuracy on test set: 97 %
[3,   300] loss: 0.079
[3,   600] loss: 0.072
[3,   900] loss: 0.069
Accuracy on test set: 98 %
[4,   300] loss: 0.064
[4,   600] loss: 0.056
[4,   900] loss: 0.063
Accuracy on test set: 98 %
[5,   300] loss: 0.052
[5,   600] loss: 0.053
[5,   900] loss: 0.055
Accuracy on test set: 98 %
[6,   300] loss: 0.048
[6,   600] loss: 0.050
[6,   900] loss: 0.045
Accuracy on test set: 98 %
[7,   300] loss: 0.048
[7,   600] loss: 0.042
[7,   900] loss: 0.041
Accuracy on test set: 98 %
[8,   300] loss: 0.039
[8,   600] loss: 0.042
[8,   900] loss: 0.040
Accuracy on test set: 98 %
[9,   300] loss: 0.039
[9,   600] loss: 0.034
[9,   900] loss: 0.039
Accuracy on test set: 98 %
[10,   300] loss: 0.034
[10,   600] loss: 0.036
[10,   900] loss: 0.035
Accuracy on test set: 98 %

4.3 PyTorch代码-GPU

import torch
from torchvision import transforms
from torchvision import datasets
from torch.utils.data import DataLoader
import torch.optim as optim


class Net(torch.nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.conv1 = torch.nn.Conv2d(1, 10, kernel_size=(5, 5))
        self.conv2 = torch.nn.Conv2d(10, 20, kernel_size=(5, 5))
        self.pooling = torch.nn.MaxPool2d((2, 2))
        self.fc = torch.nn.Linear(320, 10)

    def forward(self, x):
        batch_size = x.size(0)
        x = torch.relu(self.pooling(self.conv1(x)))
        x = torch.relu(self.pooling(self.conv2(x)))
        x = x.view(batch_size, -1)
        x = self.fc(x)
        return x


# 单次训练函数
def train(epoch, criterion):
    running_loss = 0.0
    for batch_idx, data in enumerate(train_loader, 0):
        inputs, target = data
        # 将inputs, target转移到Gpu或者Cpu上
        inputs, target = inputs.to(device), target.to(device)
        optimizer.zero_grad()
        outputs = model(inputs)
        loss = criterion(outputs, target)
        loss.backward()
        optimizer.step()
        running_loss += loss.item()
        if batch_idx % 300 == 299:
            print('[%d, %5d] loss: %.3f' % (epoch + 1, batch_idx + 1, running_loss / 300))
            running_loss = 0.0


# 单次测试函数
def ttt():
    correct = 0.0
    total = 0.0
    with torch.no_grad():
        for data in test_loader:
            images, labels = data
            # 将images, labels转移到Gpu或者Cpu上
            images, labels = images.to(device), labels.to(device)
            outputs = model(images)
            _, predicted = torch.max(outputs.data, dim=1)
            total += labels.size(0)
            correct += (predicted == labels).sum().item()
    print('Accuracy on test set: %d %% [%d/%d]' % (100 * correct / total, correct, total))


if __name__ == '__main__':
    batch_size = 64
    transform = transforms.Compose([transforms.ToTensor(), transforms.Normalize((0.1307,), (0.3081,))])
    train_dataset = datasets.MNIST(root='../dataset/', train=True, download=True, transform=transform)

    train_loader = DataLoader(train_dataset, shuffle=True, batch_size=batch_size)

    test_dataset = datasets.MNIST(root='../dataset/', train=False, download=True, transform=transform)
    test_loader = DataLoader(test_dataset, shuffle=False, batch_size=batch_size)

    device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")

    # 声明模型
    model = Net()
    # 将模型转移道Gpu或者Cpu上
    model.to(device)
    # 定义损失函数
    criterion = torch.nn.CrossEntropyLoss()
    # 定义优化器
    optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.5)

    for epoch in range(10):
        train(epoch, criterion)
        ttt()

输出：

[1,   300] loss: 0.666
[1,   600] loss: 0.206
[1,   900] loss: 0.148
Accuracy on test set: 96 % [9652/10000]
[2,   300] loss: 0.117
[2,   600] loss: 0.109
[2,   900] loss: 0.097
Accuracy on test set: 97 % [9749/10000]
[3,   300] loss: 0.080
[3,   600] loss: 0.082
[3,   900] loss: 0.077
Accuracy on test set: 98 % [9804/10000]
[4,   300] loss: 0.067
[4,   600] loss: 0.070
[4,   900] loss: 0.062
Accuracy on test set: 98 % [9814/10000]
[5,   300] loss: 0.056
[5,   600] loss: 0.060
[5,   900] loss: 0.059
Accuracy on test set: 98 % [9845/10000]
[6,   300] loss: 0.053
[6,   600] loss: 0.047
[6,   900] loss: 0.054
Accuracy on test set: 98 % [9855/10000]
[7,   300] loss: 0.047
[7,   600] loss: 0.048
[7,   900] loss: 0.044
Accuracy on test set: 98 % [9845/10000]
[8,   300] loss: 0.044
[8,   600] loss: 0.041
[8,   900] loss: 0.042
Accuracy on test set: 98 % [9883/10000]
[9,   300] loss: 0.040
[9,   600] loss: 0.039
[9,   900] loss: 0.041
Accuracy on test set: 98 % [9867/10000]
[10,   300] loss: 0.038
[10,   600] loss: 0.036
[10,   900] loss: 0.038
Accuracy on test set: 98 % [9872/10000]

4.4 课后作业（尝试更复杂的CNN）

PyTorch-GPU代码实现：

除了上图所示的改变外，我还做了以下2点改变：

• 为了获得更多的特征。增加了每个层的信道数量
• 为了获得更多的特征，并考虑到计算量开销，采取了卷积核大小逐层递减的策略，第一层卷积核大小设置为（9，9），第二层卷积核大小设置为（7，7），第三层卷积核大小设置为（5，5），为了保证足够多的特征数量，每一层都采用了padding

import torch
from torchvision import transforms
from torchvision import datasets
from torch.utils.data import DataLoader
import torch.optim as optim


class Net(torch.nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.conv1 = torch.nn.Conv2d(1, 20, padding=(4, 4), kernel_size=(9, 9))
        self.conv2 = torch.nn.Conv2d(20, 40, padding=(3, 3), kernel_size=(7, 7))
        self.conv3 = torch.nn.Conv2d(40, 60, padding=(2, 2), kernel_size=(5, 5))
        self.pooling = torch.nn.MaxPool2d((2, 2))
        self.fc1 = torch.nn.Linear(540, 256)
        self.fc2 = torch.nn.Linear(256, 10)

    def forward(self, x):
        batch_size = x.size(0)
        x = torch.relu(self.pooling(self.conv1(x)))
        x = torch.relu(self.pooling(self.conv2(x)))
        x = torch.relu(self.pooling(self.conv3(x)))
        x = x.view(batch_size, -1)
        x = torch.relu(self.fc1(x))
        x = self.fc2(x)
        return x


# 单次训练函数
def train(epoch, criterion):
    running_loss = 0.0
    for batch_idx, data in enumerate(train_loader, 0):
        inputs, target = data
        # 将inputs, target转移到Gpu或者Cpu上
        inputs, target = inputs.to(device), target.to(device)
        optimizer.zero_grad()
        outputs = model(inputs)
        loss = criterion(outputs, target)
        loss.backward()
        optimizer.step()
        running_loss += loss.item()
        if batch_idx % 300 == 299:
            print('[%d, %5d] loss: %.3f' % (epoch + 1, batch_idx + 1, running_loss / 300))
            running_loss = 0.0


# 单次测试函数
def ttt():
    correct = 0.0
    total = 0.0
    with torch.no_grad():
        for data in test_loader:
            images, labels = data
            # 将images, labels转移到Gpu或者Cpu上
            images, labels = images.to(device), labels.to(device)
            outputs = model(images)
            _, predicted = torch.max(outputs.data, dim=1)
            total += labels.size(0)
            correct += (predicted == labels).sum().item()
    print('Accuracy on test set: %d %% [%d/%d]' % (100 * correct / total, correct, total))


if __name__ == '__main__':
    batch_size = 64
    transform = transforms.Compose([transforms.ToTensor(), transforms.Normalize((0.1307,), (0.3081,))])
    train_dataset = datasets.MNIST(root='../dataset/', train=True, download=True, transform=transform)

    train_loader = DataLoader(train_dataset, shuffle=True, batch_size=batch_size)

    test_dataset = datasets.MNIST(root='../dataset/', train=False, download=True, transform=transform)
    test_loader = DataLoader(test_dataset, shuffle=False, batch_size=batch_size)

    device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")

    # 声明模型
    model = Net()
    # 将模型转移道Gpu或者Cpu上
    model.to(device)
    # 定义损失函数
    criterion = torch.nn.CrossEntropyLoss()
    # 定义优化器
    optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.5)

    for epoch in range(10):
        train(epoch, criterion)
        ttt()

输出：

[1,   300] loss: 1.350
[1,   600] loss: 0.215
[1,   900] loss: 0.139
Accuracy on test set: 96 % [9684/10000]
[2,   300] loss: 0.103
[2,   600] loss: 0.090
[2,   900] loss: 0.079
Accuracy on test set: 98 % [9800/10000]
[3,   300] loss: 0.070
[3,   600] loss: 0.064
[3,   900] loss: 0.060
Accuracy on test set: 98 % [9856/10000]
[4,   300] loss: 0.048
[4,   600] loss: 0.053
[4,   900] loss: 0.051
Accuracy on test set: 98 % [9833/10000]
[5,   300] loss: 0.044
[5,   600] loss: 0.040
[5,   900] loss: 0.041
Accuracy on test set: 98 % [9850/10000]
[6,   300] loss: 0.032
[6,   600] loss: 0.039
[6,   900] loss: 0.036
Accuracy on test set: 98 % [9889/10000]
[7,   300] loss: 0.027
[7,   600] loss: 0.033
[7,   900] loss: 0.031
Accuracy on test set: 99 % [9906/10000]
[8,   300] loss: 0.023
[8,   600] loss: 0.028
[8,   900] loss: 0.027
Accuracy on test set: 99 % [9903/10000]
[9,   300] loss: 0.022
[9,   600] loss: 0.025
[9,   900] loss: 0.023
Accuracy on test set: 98 % [9873/10000]
[10,   300] loss: 0.020
[10,   600] loss: 0.019
[10,   900] loss: 0.021
Accuracy on test set: 99 % [9910/10000]

从输出结果可以看出，正确率从之前的98%提升至了99%，说明本节建立的三层CNN模型比之前的两层CNN模型具有更好的特征提取能力和分类能力。