How does Pytorch build the computation graph
Here is example pytorch code from the website:
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

In the forward function, we simply apply a series of transformations to x, but never explicitly define which objects are part of that transformation. Yet when computing the gradient and updating the weights, Pytorch 'magically' knows which weights to update and how the gradient should be calculated.
How does this process work? Is there code analysis going on, or something else that I am missing?

Yes, there is implicit analysis on forward pass. Examine the result tensor, there is thingie like grad_fn= &lt;CatBackward&gt;, that's a link, allowing you to unroll the whole computation graph. And it is built during real forward computation process, no matter how you defined your network module, object oriented with 'nn' or 'functional' way.
You can exploit this graph for net analysis, as torchviz do here: https://github.com/szagoruyko/pytorchviz/blob/master/torchviz/dot.py
