使用空洞卷积识别minist数据集

识别 MNIST 数据集可以使用空洞卷积（Dilated Convolution）来提高准确率。空洞卷积是卷积神经网络中的一种技术，它可以通过在卷积核中引入空洞来增加感受野，从而能够更好地学习图像中的全局信息。

以下是使用 PyTorch 实现空洞卷积识别 MNIST 数据集的示例代码：

import torch
import torch.nn as nn
import torch.optim as optim
from torchvision import datasets, transforms

# 定义网络结构
class Net(nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.conv1 = nn.Conv2d(1, 10, kernel_size=5)
        self.conv2 = nn.Conv2d(10, 20, kernel_size=5)
        self.conv2_drop = nn.Dropout2d()
        self.fc1 = nn.Linear(320, 50)
        self.fc2 = nn.Linear(50, 10)

    def forward(self, x):
        x = nn.functional.relu(nn.functional.max_pool2d(self.conv1(x), 2))
        x = nn.functional.relu(nn.functional.max_pool2d(self.conv2_drop(self.conv2(x)), 2, dilation=2))
        x = x.view(-1, 320)
        x = nn.functional.relu(self.fc1(x))
        x = nn.functional.dropout(x, training=self.training)
        x = self.fc2(x)
        return nn.functional.log_softmax(x, dim=1)

# 加载数据集
train_dataset = datasets.MNIST('./data', train=True, download=True, transform=transforms.Compose([
    transforms.ToTensor(),
    transforms.Normalize((0.1307,), (0.3081,))
]))
test_dataset = datasets.MNIST('./data', train=False, transform=transforms.Compose([
    transforms.ToTensor(),
    transforms.Normalize((0.1307,), (0.3081,))
]))

train_loader = torch.utils.data.DataLoader(train_dataset, batch_size=64, shuffle=True)
test_loader = torch.utils.data.DataLoader(test_dataset, batch_size=1000, shuffle=True)

# 训练模型
model = Net()
optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.5)

def train(epoch):
    model.train()
    for batch_idx, (data, target) in enumerate(train_loader):
        optimizer.zero_grad()
        output = model(data)
        loss = nn.functional.nll_loss(output, target)
        loss.backward()
        optimizer.step()
        if batch_idx % 100 == 0:
            print('Train Epoch: {} [{}/{} ({:.0f}%)]\tLoss: {:.6f}'.format(
                epoch, batch_idx * len(data), len(train_loader.dataset),
                100. * batch_idx / len(train_loader), loss.item()))

def test():
    model.eval()
    test_loss = 0
    correct = 0
    with torch.no_grad():
        for data, target in test_loader:
            output = model(data)
            test_loss += nn.functional.nll_loss(output, target, reduction='sum').item()
            pred = output.argmax(dim=1, keepdim=True)
            correct += pred.eq(target.view_as(pred)).sum().item()

    test_loss /= len(test_loader.dataset)
    print('\nTest set: Average loss: {:.4f}, Accuracy: {}/{} ({:.0f}%)\n'.format(
        test_loss, correct, len(test_loader.dataset),
        100. * correct / len(test_loader.dataset)))

for epoch in range(1, 11):
    train(epoch)
    test()

在这个示例代码中，我们定义了一个包含两个卷积层和两个全连接层的神经网络，其中第二个卷积层使用了空洞卷积，并且在最大池化层中的 dilation 参数设置为 2。我们使用 SGD 作为优化器，并且在每个 epoch 完成后进行测试。