理解LeNet-5中的最后两个线性变换

Question

我需要帮助理解LeNet-5 CNN：

1. 为什么FC3和FC4有120个和84个参数？
2. 如何选择过滤器6和16？(基于数据集的直觉？)

在我看过的所有地方，我都没有找到#1的答案，包括LeCunn最初的纸。

我遗漏了什么？

我的任务是交换5x5核(f = 5)和3x3核(f = 3)。如果我知道这些值(特别是84,120)来自哪里，我想我就能做到。我能够使用PyTorch实现LeNet-5 .

如果你有什么建议，什么价值观最有效，为什么，我将不胜感激。数据集为Cifar-10。

更新：

我修改了我的代码，正如@Oxbowerce建议的那样，在激活第一个完全连接的网络之前，确保图像大小在未平展之前与视图中的图像大小匹配：

在类LeNet的构造函数中：

self.fc1 = nn.Linear(4 * kernel_size * kernel_size * 16, 120)  # added 4

在前馈网络中：

x = x.view(-1, 4 * self.kernel_size * self.kernel_size * 16) # added 4

这是我的网络课程：

class LeNet(nn.Module):

def __init__(self, activation, kernel_size:int = 5):
    super().__init__()

    self.kernel_size = kernel_size

    self.conv1 = nn.Conv2d(in_channels=3, out_channels=6, kernel_size=kernel_size, stride=1)
    self.pool = nn.MaxPool2d(kernel_size=2, stride=2)
    self.conv2 = nn.Conv2d(in_channels=6, out_channels=16, kernel_size=kernel_size, stride=1)

    self.fc1 = nn.Linear(4 * kernel_size * kernel_size * 16, 120)  # added 4
    self.fc2 = nn.Linear(120, 84) 
    self.fc3 = nn.Linear(84, 10)

    self.activation = activation

def forward(self, x):

    x = self.pool(self.activation(self.conv1(x)))
    x = self.pool(self.activation(self.conv2(x)))

    x = x.view(-1, 4 * self.kernel_size * self.kernel_size * 16) # added 4

    x = self.activation(self.fc1(x))
    x = self.activation(self.fc2(x))
    x = self.fc3(x)

    return x

我用这样的方法来调用火车方法：

model.train(activation=nn.Tanh(), learn_rate=0.001, epochs=10, kernel_size=3)

列车方法：

def train(self, activation:Any, learn_rate:float, epochs:int, momentum:float = 0.0, kernel_size:int = 5) -> None:

    self.activation = activation
    self.learn_rate = learn_rate
    self.epochs = epochs
    self.momentum = momentum

    self.model = LeNet(activation=activation, kernel_size=kernel_size)
    self.model.to(device)

    optimizer = torch.optim.SGD(params=self.model.parameters(), lr=learn_rate, momentum=momentum)

    for epoch in range(1, epochs + 1):
        loss = 0.0
        correct = 0
        total = 0
        predicted = 0

        for batch_id, (images, labels) in enumerate(self.train_loader):
            images, labels = images.to(device), labels.to(device)

            optimizer.zero_grad()
            outputs = self.model(images)
            
            # Calculate accurracy
            predicted = torch.argmax(outputs, 1)
            correct += (predicted == labels).sum().item() # <--- exception
            total += labels.size(0)
            
            loss.backward()
            optimizer.step()

        accuracy = 100 * correct / total
        self.train_accuracy.append(accuracy)
        self.train_error.append(error)
        self.train_loss.append(loss.item())

        self.test()

    for i in self.model.parameters():
        self.params.append(i)

下面是错误的堆栈跟踪：

Error
Traceback (most recent call last):
  File "/usr/lib/python3.9/unittest/case.py", line 59, in testPartExecutor
    yield
  File "/usr/lib/python3.9/unittest/case.py", line 593, in run
    self._callTestMethod(testMethod)
  File "/usr/lib/python3.9/unittest/case.py", line 550, in _callTestMethod
    method()
  File "/home/steve/workspace_psu/cs510nlp/hw2/venv/lib/python3.9/site-packages/nose/case.py", line 198, in runTest
    self.test(*self.arg)
  File "/home/steve/workspace_psu/cs510dl/hw2/test_cs510dl_hw2.py", line 390, in test_part2_relu_cel_k3
    model.train(activation=activation, learn_rate=learn_rate, momentum=momentum, epochs=epochs, kernel_size=kernel_size)
  File "/home/steve/workspace_psu/cs510dl/hw2/cs510dl_hw2.py", line 389, in train
    correct += (predicted == labels).sum().item()
  File "/home/steve/workspace_psu/cs510nlp/hw2/venv/lib/python3.9/site-packages/torch/tensor.py", line 27, in wrapped
    return f(*args, **kwargs)
Exception: The size of tensor a (16) must match the size of tensor b (4) at non-singleton dimension 0

Answer 1

最后两个密集层中神经元数目和滤波器数目的选择有些随意，大多数情况下是通过尝试不同的配置来确定的(使用类似于超参数网格搜索的方法)。还请参见stackexchange上的这个答案。如果你想改变5x5核的大小，你只需要改变第一个完全连接层中的神经元数量，最后两个就不需要改变网络才能“有效”。