Why using negative integers (as dimensions?) in tensor shapes rather than natural numbers?

Question

Consider the following paragraph from A.1 MULTI-MNIST AND CLEVR of A IMPLEMENTATION DETAILS from the research paper titled GENERATING MULTIPLE OBJECTS AT SPATIALLY DISTINCT LOCATIONS by Tobias Hinz et al.

In the global pathway of the generator we first obtain the layout encoding. For this we create a tensor of shape (10, 16, 16) (CLEVR: (13, 16, 16)) that contains the one-hot labels at the location of the bounding boxes and is zero everywhere else. We then apply three convolutional layers, each followed by batch normalization and a leaky ReLU activation. We reshape the output to shape (1, 64) and concatenate it with the noise tensor of shape (1, 100) (sampled from a random normal distribution) to form a tensor of shape (1, 164). This tensor is then fed into a dense layer, followed by batch normalization and a ReLU activation and the output is reshaped to (−1, 4, 4). We then apply two upsampling blocks to obtain a tensor of shape (−1, 16, 16).

The paragraph is saying that a tensor of shape (1, 164) is reshaped to (-1, 4, 4). What is the reason behind using negative number -1? Is it representing axis? Can't we represent it with $a \times x \times y$, where $a, x, y$ are natural number s and dimensions of the tensor?

$\dfrac{164}{4 \times 4}$ is not a natural number, so what is the shape of the reshaped tensor using only the natural numbers?

Answer 1

It definitely is. If you check the code (line 145) you'll see that in the forward definition of the Stage1 Generator they do:

class STAGE1_G(nn.Module):
    def __init__(self):
...
    def forward(self, text_embedding, noise):
    c_code, mu, logvar = self.ca_net(text_embedding)
    z_c_code = torch.cat((noise, c_code), 1)
    h_code = self.fc(z_c_code)

    h_code = h_code.view(-1, self.gf_dim, 4, 4)

Where self.gf_dim is a parameter defined in the configuration file of the gan (most likely number of feature maps, but check cause they didn't write documentation about the config settings)