How to calculate dimensions of first linear layer of a CNN
Currently, I am working with a CNN where there is a fully connected layer attached to it and I am working with a 3 channel image of size 32x32. I am wondering on if there is a consistent formula I can use to calculate the input dimensions of the first linear layer with the input from the last conv/maxpooling layer. I want to be able to calculate the dimensions of the first linear layer given only information of the last conv2d layer and maxpool later. In other words, I would like to be able to calculate that value without having to use information of the previous layers before (so I don't have to manually calculate weight dimensions of a very deep network)
I also want to understand the calculation of acceptable dimensions, like what would be the reasoning of those calculations?
For some reason these calculations work and Pytorch accepted these dimensions:
val = int((32*32)/4)
self.fc1 = nn.Linear(val, 200)

and this also worked
self.fc1 = nn.Linear(64*4*4, 200)

Why do those values work, and is there a limitation in the calculation of those methods? I feel like this would break if I were to change stride distance or kernel size, for example.
Here is the general model architecture I was working with:
# define the CNN architecture
class Net(nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        # convolutional layer
        self.conv1 = nn.Conv2d(in_channels=3, out_channels=16, kernel_size=3, padding=1)
        # max pooling layer
        self.pool = nn.MaxPool2d(2, 2)  


        self.conv2 = nn.Conv2d(in_channels=16, out_channels=32,kernel_size=3)
        self.pool2 = nn.MaxPool2d(2,2)

        self.conv3 = nn.Conv2d(in_channels=32, out_channels=64, kernel_size=3)
        self.pool3 = nn.MaxPool2d(2,2)
        
        self.dropout = nn.Dropout(0.25)

        # H*W/4
        val = int((32*32)/4)
        #self.fc1 = nn.Linear(64*4*4, 200)
        ################################################
        self.fc1 = nn.Linear(val, 200)  # dimensions of the layer I wish to calculate
        ###############################################
        self.fc2 = nn.Linear(200,100)
        self.fc3 = nn.Linear(100,10)


    def forward(self, x):
        # add sequence of convolutional and max pooling layers
        x = self.pool(F.relu(self.conv1(x)))
        x = self.pool2(F.relu(self.conv2(x)))
        x = self.pool3(F.relu(self.conv3(x)))
        #print(x.shape)
        x = torch.flatten(x, 1) # flatten all dimensions except batch
        
        x = F.relu(self.fc1(x))
        x = self.dropout(x)
        x = F.relu(self.fc2(x))
        x = self.dropout(x)
        x = self.fc3(x)

        return x

# create a complete CNN
model = Net()
print(model)

Can anyone tell me how to calculate the dimensions of the first linear layer and explain the reasoning?

Given the input spatial dimension w, a 2d convolution layer will output a tensor with the following size on this dimension:
int((w + 2*p - d*(k - 1) - 1)/s + 1)

The exact same is true for nn.MaxPool2d. For reference, you can look it up here, on the PyTorch documentation.
The convolution part of your model is made up of three (Conv2d + MaxPool2d) blocks. You can easily infer the spatial dimension size of the output with this helper function:
def conv_shape(x, k=1, p=0, s=1, d=1):
    return int((x + 2*p - d*(k - 1) - 1)/s + 1)

Calling it recursively, you get the resulting spatial dimension:
&gt;&gt;&gt; w = conv_shape(conv_shape(32, k=3, p=1), k=2, s=2)
&gt;&gt;&gt; w = conv_shape(conv_shape(w, k=3), k=2, s=2)
&gt;&gt;&gt; w = conv_shape(conv_shape(w, k=3), k=2, s=2)

&gt;&gt;&gt; w
2

Since your convolutions have squared kernels and identical strides, paddings (horizontal equals vertical), the above calculations hold true for the width and the height dimensions of the tensor. Lastly, looking at the last convolution layer conv3, which has 64 filters, the resulting number of elements per batch element before your fully connected layer is: w*w*64, i.e. 256.

However, nothing stops you from calling your layers to find out the output shape!
class Net(nn.Module):
    def __init__(self):
        super().__init__()
        
        self.feature_extractor = nn.Sequential(
            nn.Conv2d(in_channels=3, out_channels=16, kernel_size=3, padding=1),
            nn.ReLU(),
            nn.MaxPool2d(2, 2),
            nn.Conv2d(in_channels=16, out_channels=32, kernel_size=3),
            nn.ReLU(),
            nn.MaxPool2d(2,2),
            nn.Conv2d(in_channels=32, out_channels=64, kernel_size=3),
            nn.ReLU(),
            nn.MaxPool2d(2,2),
            nn.Flatten())

        n_channels = self.feature_extractor(torch.empty(1, 3, 32, 32)).size(-1)

        self.classifier = nn.Sequential(
            nn.Linear(n_channels, 200),
            nn.ReLU(),
            nn.Dropout(0.25),
            nn.Linear(200, 100),
            nn.ReLU(),
            nn.Dropout(0.25),
            nn.Linear(100, 10))

    def forward(self, x):
        features = self.feature_extractor(x)
        out = self.classifier(features)
        return out

model = Net()

