What are the parameters and use of self.fc_mu() and self.fc_sigma()?

1

I am looking through some example code, and am not new to Machine Learning, but I saw:

self.fc_mu = nn.Linear(hidden_size, hidden_size)
self.fc_sigma = nn.Linear(hidden_size, hidden_size)

I understand that self.fc1(),self.fc2()… are referring to the fully connected layers one and two which are both Linear in my example, but what is self.fc_mu referring to, and what does it return? Also, what are the parameters of self.fc_mu(), and self.fc_sigma() which I saw used many times? Thank you in advance, I am just struggling to figure this out.

2

self.fc_mu and self.fc_sigma are just the attribute names for both linear layers.
Their meaning depends on the context. In this case they might be used to apply the “reparametrization trick”.

4

In the context that I am currently in, this is the code:

class Discriminator(nn.Module):
def init(self, input_size=2, output_size=1, hidden_size=128):
super().init()
self.fc1 = nn.Linear(input_size, hidden_size)
self.fc2 = nn.Linear(hidden_size, hidden_size)
self.fc_mu = nn.Linear(hidden_size, hidden_size)
self.fc_sigma = nn.Linear(hidden_size, hidden_size)
self.fc3 = nn.Linear(hidden_size, output_size)

    for m in self.modules():
        if isinstance(m, nn.Linear):
            nn.init.kaiming_normal_(m.weight)
            nn.init.constant_(m.bias, 0.0)
            
def forward(self, x):
    x = F.leaky_relu(self.fc1(x), negative_slope=2e-1)
    x = F.leaky_relu(self.fc2(x), negative_slope=2e-1)
    mu = self.fc_mu(x)
    sigma = torch.sigmoid(self.fc_sigma(x))
    x = torch.sigmoid(F.leaky_relu(self.fc3(mu + sigma * torch.randn_like(sigma)), negative_slope=2e-1))
    return x, mu, sigma

What would this entail? And what is the reparametrization trick entailing?