What is the meaning of the l2-norm when dealing with scalar values? I'm assuming it would be the same thing as taking the absolute value.
For context: I am trying to implement the clustering method presented in the following paper: https://arxiv.org/abs/1909.11832 where I stumbled across the following loss function:
$$ L_{E,G}(\phi(t),\theta(t)) = ||x-\hat{x}||_2^2+\lambda||C_\psi(\hat{x}_a)||_2^2 $$
where E and G are neural networks parameterized by $\phi$ and $\theta$, respectively. These are set up as an autoencoder. C is another neural network parameterized by $\psi$ with a role similar to a discriminator which only outputs values in the interval $[0,1]$. The overall structure presented in the paper is the following: 
The loss for network C is defined as $$ L_C(\psi(t)) = ||C_\psi(\hat{x}_a)-\alpha||_2^2+||C_\psi(\gamma x+(1-\gamma)\hat{x})||_2^2 $$
My current implementation does not result in the expected results and I am now wondering whether the reason could be that I have misunderstood what the l2-norm in the loss functions above is supposed to do.
