ConvNet + FCN示例中的FCN尺寸

Question

所以我在pytorch中定义的神经网络如下（取自https://pytorch.org/tutorials/beginner/blitz/neural_networks_tutorial.html）

class Net(nn.Module):

    def __init__(self):
        super(Net, self).__init__()
        # 1 input image channel, 6 output channels, 3x3 square convolution
        # kernel
        self.conv1 = nn.Conv2d(1, 6, 3)
        self.conv2 = nn.Conv2d(6, 16, 3)
        # an affine operation: y = Wx + b
        self.fc1 = nn.Linear(16 * 6 * 6, 120)  # 6*6 from image dimension
        self.fc2 = nn.Linear(120, 84)
        self.fc3 = nn.Linear(84, 10)

    def forward(self, x):
        # Max pooling over a (2, 2) window
        x = F.max_pool2d(F.relu(self.conv1(x)), (2, 2))
        # If the size is a square you can only specify a single number
        x = F.max_pool2d(F.relu(self.conv2(x)), 2)
        x = x.view(-1, self.num_flat_features(x))
        x = F.relu(self.fc1(x))
        x = F.relu(self.fc2(x))
        x = self.fc3(x)
        return x

    def num_flat_features(self, x):
        size = x.size()[1:]  # all dimensions except the batch dimension
        num_features = 1
        for s in size:
            num_features *= s
        return num_features

假设我要在1 * 32 * 32张量上应用NN，self.fc1怎么变成16 * 6 *6。我理解16，不确定我们如何得到6。

Answer 1

首先，您的卷积是没有填充的3x3内核，这意味着数据在通过时会在空间尺寸的每一侧损失1。如果您对原因感到困惑，那么看照片最好：

蓝色是您的输入数据，绿色是结果数据（每个通道一个）。

让我们一步一步看看会发生什么：

Input->    1x32x32
conv1->    6x30x30 (lost 2 on each spatial dimension)
max_pool-> 6x15x15 (halves the spatial dimensions)
conv2->    16x13x13
max_pool-> 16x6x6 (13 doesn't divide evenly)

就在那里！