使用多层感知机完成MNIST手写字体识别

# -*-coding = utf-8
import torch
import torch.nn.functional as F
from torch.utils.data import DataLoader
from torchvision import datasets
from torchvision import transforms


class Net(torch.nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.l1 = torch.nn.Linear(784, 256)
        self.l2 = torch.nn.Linear(256, 128)
        self.l3 = torch.nn.Linear(128, 10)

    def forward(self, x):
        x = x.view(-1, 784)
        x = F.relu(self.l1(x))
        x = F.relu(self.l2(x))
        return self.l3(x)
    # because we use cross-entropy as loss
    # so we needn't to do softmax and binary entropy


def train(epochs):
    running_loss = 0.0
    for index, (x, y) in enumerate(train_loader):
        optimizer.zero_grad()
        y_pred = model(x)
        loss = criterion(y_pred, y)
        loss.backward()
        optimizer.step()

        running_loss = running_loss + loss.item()
    print(f"epoch:{epochs}\nloss:{running_loss}")


def test():
    correct = 0
    tot = 0
    # because we don't need to calculate the gradient in test,
    # so we use this structure
    with torch.no_grad():
        for data in test_loader:
            image, label = data
            output = model(image)
            tot += label.size(0)
            _, pred = torch.max(output, dim=1)
            correct = correct + (label == pred).sum().item()

    print(f"Accuracy:{correct / tot * 100}%")


if __name__ == "__main__":
    model = Net()
    criterion = torch.nn.CrossEntropyLoss()
    optimizer = torch.optim.SGD(params=model.parameters(), lr=0.01, momentum=0.5)
    # momentum is a advanced tricky which speak "冲量"
    batch_size = 64
    transform = transforms.Compose([
        transforms.ToTensor(),
        transforms.Normalize((0.1307,), (0.3081,))
        # why use these two numbers?
    ])
    train_dataset = datasets.MNIST(root=r"dataset\mnist/",
                                   download=True,
                                   train=True,
                                   transform=transform)
# if the atrribute train is true, the data will be splited into train and test
    train_loader = DataLoader(dataset=train_dataset,
                              batch_size=batch_size,
                              shuffle=True)
    test_dataset = datasets.MNIST(root=r"dataset\mnist",
                                  train=False,
                                  download=True,
                                  transform=transform)
    test_loader = DataLoader(dataset=test_dataset,
                             batch_size=batch_size,
                             shuffle=False)
    for index in range(50):
        train(index)
        test()

• 神经网络的计算偏爱小数，在喂数据的时候可以进行一些线性变换，转化为$(0,1)$内的小数。(更不容易过拟合）
• 使用transforms把变换的类型进行封装。
• 使用全连接网络，只能提取一些比较简单的特征，大概在准确率95%左右就会过拟合。

构建简单CNN网络

# -*-coding = utf-8
import torch
import torch.nn.functional as F
from torch.utils.data import DataLoader
from torchvision import datasets
from torchvision import transforms

device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
# define a graphic card

class Net(torch.nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.conv1 = torch.nn.Conv2d(1, 5, (5, 5))
        self.conv2 = torch.nn.Conv2d(5, 10, (5, 5))
        self.pool = torch.nn.MaxPool2d((2, 2))
        self.linear = torch.nn.Linear(160, 10)

    def forward(self, x):
        batch_size = x.size(0)
        x = F.relu(self.pool(self.conv1(x)))
        x = F.relu(self.pool(self.conv2(x)))
        x = x.view(batch_size, -1)
        return self.linear(x)
    # because we use cross-entropy as loss
    # so we needn't to do softmax and binary entropy


def train(epochs):
    running_loss = 0.0
    for index, (x, y) in enumerate(train_loader):
        # x,y = x.to(device),y.to(device)
        # graphic card
        optimizer.zero_grad()
        y_pred = model(x)
        loss = criterion(y_pred, y)
        loss.backward()
        optimizer.step()

        running_loss = running_loss + loss.item()
    print(f"epoch:{epochs}\nloss:{running_loss}")


def test():
    correct = 0
    tot = 0
    # because we don't need to calculate the gradient in test,
    # so we use this structure
    with torch.no_grad():
        for data in test_loader:
            image, label = data
            # image, label = image.to(device),label.to(device)
            output = model(image)
            tot += label.size(0)
            _, pred = torch.max(output, dim=1)
            correct = correct + (label == pred).sum().item()

    print(f"Accuracy:{correct / tot * 100}%")


if __name__ == "__main__":
    model = Net()
    # model.to(device=device)
    # if need train on graphic card
    criterion = torch.nn.CrossEntropyLoss()
    optimizer = torch.optim.SGD(params=model.parameters(), lr=0.01, momentum=0.5)
    batch_size = 64
    transform = transforms.Compose([
        transforms.ToTensor(),
        transforms.Normalize((0.1307,), (0.3081,))
        # why use these two numbers?
    ])
    train_dataset = datasets.MNIST(root=r"dataset\mnist/",
                                   download=True,
                                   train=True,
                                   transform=transform)
    train_loader = DataLoader(dataset=train_dataset,
                              batch_size=batch_size,
                              shuffle=True)
    test_dataset = datasets.MNIST(root=r"dataset\mnist",
                                  train=False,
                                  download=True,
                                  transform=transform)
    test_loader = DataLoader(dataset=test_dataset,
                             batch_size=batch_size,
                             shuffle=False)
    for index in range(10):
        train(index)
        test()

• 事实上只需要修改MyModel对类的定义即可
• 关于显卡上的使用也是比较简单的

使用Inception Model

# -*-coding = utf-8
import torch
import torch.nn.functional as F
from torch.utils.data import DataLoader
from torchvision import datasets
from torchvision import transforms

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


# define a graphic card

class Inception(torch.nn.Module):
    def __init__(self, in_channels):
        super(Inception, self).__init__()
        # these are different branches in the picture
        self.branch1x1 = torch.nn.Conv2d(in_channels, 16, kernel_size=1)

        self.branch5x5_1 = torch.nn.Conv2d(in_channels, 16, kernel_size=1)
        self.branch5x5_2 = torch.nn.Conv2d(16, 24, kernel_size=5, padding=2)

        self.branch3x3_1 = torch.nn.Conv2d(in_channels, 16, kernel_size=1)
        self.branch3x3_2 = torch.nn.Conv2d(16, 24, kernel_size=3, padding=1)
        self.branch3x3_3 = torch.nn.Conv2d(24, 24, kernel_size=3, padding=1)

        self.branch_pool = torch.nn.Conv2d(in_channels, 24, kernel_size=1)

    def forward(self, x):
        branch1x1 = self.branch1x1(x)

        branch5x5 = self.branch5x5_1(x)
        branch5x5 = self.branch5x5_2(branch5x5)

        branch3x3 = self.branch3x3_1(x)
        branch3x3 = self.branch3x3_2(branch3x3)
        branch3x3 = self.branch3x3_3(branch3x3)

        pool = F.avg_pool2d(x, kernel_size=3, stride=1, padding=1)
        pool = self.branch_pool(pool)
        out = [branch1x1, branch3x3, branch5x5, pool]
        return torch.cat(out, dim=1)
        # cat the channels


class Net(torch.nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.Conv1 = torch.nn.Conv2d(1, 10, kernel_size=5)
        self.Conv2 = torch.nn.Conv2d(88, 20, kernel_size=5)
        self.incep1 = Inception(in_channels=10)
        self.incep2 = Inception(in_channels=20)
        self.mp = torch.nn.MaxPool2d(2)
        self.fc = torch.nn.Linear(1408, 10)

    def forward(self, x):
        in_size = x.size(0)
        x = F.relu(self.mp(self.Conv1(x)))
        x = self.incep1(x)
        x = F.relu(self.mp(self.Conv2(x)))
        x = self.incep2(x)
        x = x.view(in_size, -1)
        x = self.fc(x)
        return x
        # show the structure of the model

    # because we use cross-entropy as loss
    # so we needn't to do softmax and binary entropy


def train(epochs):
    running_loss = 0.0
    for index, (x, y) in enumerate(train_loader):
        # x,y = x.to(device),y.to(device)
        # graphic card
        optimizer.zero_grad()
        y_pred = model(x)
        loss = criterion(y_pred, y)
        loss.backward()
        optimizer.step()

        running_loss = running_loss + loss.item()
    print(f"epoch:{epochs}\nloss:{running_loss}")


def test():
    correct = 0
    tot = 0
    # because we don't need to calculate the gradient in test,
    # so we use this structure
    with torch.no_grad():
        for data in test_loader:
            image, label = data
            # image, label = image.to(device),label.to(device)
            output = model(image)
            tot += label.size(0)
            _, pred = torch.max(output, dim=1)
            correct = correct + (label == pred).sum().item()

    print(f"Accuracy:{correct / tot * 100}%")


if __name__ == "__main__":
    model = Net()
    # model.to(device=device)
    # if need train on graphic card
    criterion = torch.nn.CrossEntropyLoss()
    optimizer = torch.optim.SGD(params=model.parameters(), lr=0.01, momentum=0.5)
    batch_size = 64
    transform = transforms.Compose([
        transforms.ToTensor(),
        transforms.Normalize((0.1307,), (0.3081,))
        # why use these two numbers?
    ])
    train_dataset = datasets.MNIST(root=r"dataset\mnist/",
                                   download=True,
                                   train=True,
                                   transform=transform)
    train_loader = DataLoader(dataset=train_dataset,
                              batch_size=batch_size,
                              shuffle=True)
    test_dataset = datasets.MNIST(root=r"dataset\mnist",
                                  train=False,
                                  download=True,
                                  transform=transform)
    test_loader = DataLoader(dataset=test_dataset,
                             batch_size=batch_size,
                             shuffle=False)
    for index in range(10):
        train(index)
        test()

• 感觉inception模型就是让网络自动选择那种卷积方式最好。
• 通过这个模型，可以达到目前最高的识别率（98.6%）
• 直接堆3x3的卷积网络会遇到梯度消失等各种困难。

Residual 模型（残差神经网络）

• 里面最重要的是residual block，他的输入和输出的channels是一样的，这样的话梯度才能在他们之间传播。

# -*-coding = utf-8
import torch
import torch.nn.functional as F
from torch.utils.data import DataLoader
from torchvision import datasets
from torchvision import transforms

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


# define a graphic card

class ResidualBlock(torch.nn.Module):
    def __init__(self, channels):
        super(ResidualBlock, self).__init__()
        self.Conv1 = torch.nn.Conv2d(channels, channels, kernel_size=3, padding=1)
        self.Conv2 = torch.nn.Conv2d(channels, channels, kernel_size=3, padding=1)

    def forward(self, x):
        y = F.relu(self.Conv1(x))
        y = self.Conv2(y)
        return F.relu(x+y)
    # this is the structure of the residual model


class Net(torch.nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.Conv1 = torch.nn.Conv2d(1, 16, kernel_size=5)
        self.Conv2 = torch.nn.Conv2d(16, 32, kernel_size=5)
        self.mp = torch.nn.MaxPool2d(2)
        self.rb1 = ResidualBlock(16)
        self.rb2 = ResidualBlock(32)
        self.fc = torch.nn.Linear(512, 10)

    def forward(self, x):
        in_size = x.size(0)
        x = F.relu(self.mp(self.Conv1(x)))
        x = self.rb1(x)
        x = F.relu(self.mp(self.Conv2(x)))
        x = self.rb2(x)
        x = x.view(in_size, -1)
        return self.fc(x)

    # because we use cross-entropy as loss
    # so we needn't to do softmax and binary entropy


def train(epochs):
    running_loss = 0.0
    for index, (x, y) in enumerate(train_loader):
        # x,y = x.to(device),y.to(device)
        # graphic card
        optimizer.zero_grad()
        y_pred = model(x)
        loss = criterion(y_pred, y)
        loss.backward()
        optimizer.step()

        running_loss = running_loss + loss.item()
    print(f"epoch:{epochs}\nloss:{running_loss}")


def test():
    correct = 0
    tot = 0
    # because we don't need to calculate the gradient in test,
    # so we use this structure
    with torch.no_grad():
        for data in test_loader:
            image, label = data
            # image, label = image.to(device),label.to(device)
            output = model(image)
            tot += label.size(0)
            _, pred = torch.max(output, dim=1)
            correct = correct + (label == pred).sum().item()

    print(f"Accuracy:{correct / tot * 100}%")


if __name__ == "__main__":
    model = Net()
    # model.to(device=device)
    # if need train on graphic card
    criterion = torch.nn.CrossEntropyLoss()
    optimizer = torch.optim.SGD(params=model.parameters(), lr=0.01, momentum=0.5)
    batch_size = 64
    transform = transforms.Compose([
        transforms.ToTensor(),
        transforms.Normalize((0.1307,), (0.3081,))
        # why use these two numbers?
    ])
    train_dataset = datasets.MNIST(root=r"dataset\mnist/",
                                   download=True,
                                   train=True,
                                   transform=transform)
    train_loader = DataLoader(dataset=train_dataset,
                              batch_size=batch_size,
                              shuffle=True)
    test_dataset = datasets.MNIST(root=r"dataset\mnist",
                                  train=False,
                                  download=True,
                                  transform=transform)
    test_loader = DataLoader(dataset=test_dataset,
                             batch_size=batch_size,
                             shuffle=False)
    for index in range(10):
        train(index)
        test()

• 在残差神经网络中，准确率可以达到99%以上
• 最重要的是残差神经网络的梯度的解决技巧，通过跳跃传播