1. 激活函数的改进：将LeNet中的激活函数替换为ReLU。

class LeNet_ReLU(nn.Module): def init(self): super(LeNet_ReLU, self).init() self.conv1 = nn.Conv2d(1, 6, 5) self.pool1 = nn.MaxPool2d(2, 2) self.conv2 = nn.Conv2d(6, 16, 5) self.pool2 = nn.MaxPool2d(2, 2) self.fc1 = nn.Linear(16 * 4 * 4, 120) self.fc2 = nn.Linear(120, 84) self.fc3 = nn.Linear(84, 10)

def forward(self, x):
    x = self.pool1(F.relu(self.conv1(x)))
    x = self.pool2(F.relu(self.conv2(x)))
    x = x.view(-1, 16 * 4 * 4)
    x = F.relu(self.fc1(x))
    x = F.relu(self.fc2(x))
    x = self.fc3(x)
    return x

2. 池化方式：平均池化改为最大池化。

class LeNet_MaxPool(nn.Module): def init(self): super(LeNet_MaxPool, self).init() self.conv1 = nn.Conv2d(1, 6, 5) self.pool1 = nn.MaxPool2d(2, 2) self.conv2 = nn.Conv2d(6, 16, 5) self.pool2 = nn.MaxPool2d(2, 2) self.fc1 = nn.Linear(16 * 4 * 4, 120) self.fc2 = nn.Linear(120, 84) self.fc3 = nn.Linear(84, 10)

def forward(self, x):
    x = self.pool1(F.relu(self.conv1(x)))
    x = self.pool2(F.relu(self.conv2(x)))
    x = x.view(-1, 16 * 4 * 4)
    x = F.relu(self.fc1(x))
    x = F.relu(self.fc2(x))
    x = self.fc3(x)
    return x

3. 卷积核大小：将其中一个55的卷积核修改为77。

class LeNet_7x7(nn.Module): def init(self): super(LeNet_7x7, self).init() self.conv1 = nn.Conv2d(1, 6, 5) self.pool1 = nn.MaxPool2d(2, 2) self.conv2 = nn.Conv2d(6, 16, 7) # 修改为7x7的卷积核 self.pool2 = nn.MaxPool2d(2, 2) self.fc1 = nn.Linear(16 * 4 * 4, 120) self.fc2 = nn.Linear(120, 84) self.fc3 = nn.Linear(84, 10)

def forward(self, x):
    x = self.pool1(F.relu(self.conv1(x)))
    x = self.pool2(F.relu(self.conv2(x)))
    x = x.view(-1, 16 * 4 * 4)
    x = F.relu(self.fc1(x))
    x = F.relu(self.fc2(x))
    x = self.fc3(x)
    return x

4. 正则化方法1：在全连接层后加入Dropout层（中间的全连接层可增加维度）

class LeNet_Dropout(nn.Module): def init(self): super(LeNet_Dropout, self).init() self.conv1 = nn.Conv2d(1, 6, 5) self.pool1 = nn.MaxPool2d(2, 2) self.conv2 = nn.Conv2d(6, 16, 5) self.pool2 = nn.MaxPool2d(2, 2) self.fc1 = nn.Linear(16 * 4 * 4, 240) # 增加全连接层的维度 self.fc2 = nn.Linear(240, 120) # 增加全连接层的维度 self.fc3 = nn.Linear(120, 84) self.fc4 = nn.Linear(84, 10) self.dropout = nn.Dropout(p=0.5) # 加入Dropout层

def forward(self, x):
    x = self.pool1(F.relu(self.conv1(x)))
    x = self.pool2(F.relu(self.conv2(x)))
    x = x.view(-1, 16 * 4 * 4)
    x = F.relu(self.fc1(x))
    x = self.dropout(x)  # 在第一个全连接层后加入Dropout层
    x = F.relu(self.fc2(x))
    x = F.relu(self.fc3(x))
    x = self.fc4(x)
    return x

5. 正则化方法2：卷积层后加入BatchNorm层

class LeNet_BatchNorm(nn.Module): def init(self): super(LeNet_BatchNorm, self).init() self.conv1 = nn.Conv2d(1, 6, 5) self.batchnorm1 = nn.BatchNorm2d(6) # 加入BatchNorm层 self.pool1 = nn.MaxPool2d(2, 2) self.conv2 = nn.Conv2d(6, 16, 5) self.batchnorm2 = nn.BatchNorm2d(16) # 加入BatchNorm层 self.pool2 = nn.MaxPool2d(2, 2) self.fc1 = nn.Linear(16 * 4 * 4, 120) self.fc2 = nn.Linear(120, 84) self.fc3 = nn.Linear(84, 10)

def forward(self, x):
    x = self.pool1(F.relu(self.batchnorm1(self.conv1(x))))  # 在卷积层后加入BatchNorm层
    x = self.pool2(F.relu(self.batchnorm2(self.conv2(x))))  # 在卷积层后加入BatchNorm层
    x = x.view(-1, 16 * 4 * 4)
    x = F.relu(self.fc1(x))
    x = F.relu(self.fc2(x))
    x = self.fc3(x)
    return x

6. 将卷积核从55修改为33，但增加网络的层数（注意调整步长）

class LeNet_3x3(nn.Module): def init(self): super(LeNet_3x3, self).init() self.conv1 = nn.Conv2d(1, 6, 3) # 修改为3x3的卷积核 self.conv2 = nn.Conv2d(6, 12, 3) # 修改为3x3的卷积核 self.conv3 = nn.Conv2d(12, 24, 3) # 修改为3x3的卷积核 self.fc1 = nn.Linear(24 * 4 * 4, 240) self.fc2 = nn.Linear(240, 120) self.fc3 = nn.Linear(120, 84) self.fc4 = nn.Linear(84, 10)

def forward(self, x):
    x = F.relu(self.conv1(x))
    x = F.max_pool2d(x, 2)  # 修改池化方式为最大池化
    x = F.relu(self.conv2(x))
    x = F.max_pool2d(x, 2)  # 修改池化方式为最大池化
    x = F.relu(self.conv3(x))
    x = x.view(-1, 24 * 4 * 4)
    x = F.relu(self.fc1(x))
    x = F.relu(self.fc2(x))
    x = F.relu(self.fc3(x))
    x = self.fc4(x)
    return x

7. 残差连接：选择一条跨层的路径（跨一层或跨多层均可），加入残差连接。注意需要用1*1卷积使维度相匹配

class LeNet_Residual(nn.Module): def init(self): super(LeNet_Residual, self).init() self.conv1 = nn.Conv2d(1, 6, 5) self.batchnorm1 = nn.BatchNorm2d(6) self.conv2 = nn.Conv2d(6, 16, 5) self.batchnorm2 = nn.BatchNorm2d(16) self.conv3 = nn.Conv2d(16, 32, 3) # 添加第三个卷积层 self.batchnorm3 = nn.BatchNorm2d(32) # 添加第三个BatchNorm层 self.fc1 = nn.Linear(32 * 3 * 3, 120) # 修改全连接层的输入维度 self.fc2 = nn.Linear(120, 84) self.fc3 = nn.Linear(84, 10) self.conv1x1 = nn.Conv2d(16, 32, 1) # 添加1x1卷积层，使得维度相同

def forward(self, x):
    x = F.relu(self.batchnorm1(self.conv1(x)))
    residual = x  # 保存输入到第二个卷积层前的输出
    x = F.relu(self.batchnorm2(self.conv2(x)))
    x = F.max_pool2d(x, 2)
    residual = self.conv1x1(residual)  # 用1x1卷积层使得维度相同
    x += residual  # 加入残差连接
    residual = x  # 保存输入到第三个卷积层前的输出
    x = F.relu(self.batchnorm3(self.conv3(x)))
    residual = self.conv1x1(residual)  # 用1x1卷积层使得维度相同
    x += residual  # 加入残差连接
    x = x.view(-1, 32 * 3 * 3)
    x = F.relu(self.fc1(x))
    x = F.relu(self.fc2(x))
    x = self.fc3(x)
    return