Help understanding equation with $\nabla_\hat{x}$ I have the following defined: $\hat{x} \leftarrow \epsilon x + (1-\epsilon)\tilde{x}$ and then this: $\lambda(||\nabla_\hat{x}D_w(\hat{x})||_2-1)^2$ Now this is something I have to implement into a computer program, and I think I've got most of it, with the exception of $\nabla_\hat{x}$ All of the different x are vectors Could someone please help me understand what it means? Thank you in advance! **Edit for clarifications:** * I'm implementing a Wasserstein GAN from the following paper: (< Section 4, page 4, equation 3 contains the equation in question * $D_w$ is a neural network ( The discriminator in a GAN ) * The second equation is something the authors of the paper have called _Gradient Penalty_ and is supposed to be added to the calculated loss used to train the algorithm.

In Linear Algebra the operator in question is called the Del operator, $\
abla$ , and is defined such that:

$\
abla = \frac{\partial}{\partial x}\mathbf{i} + \frac{\partial}{\partial y}\mathbf{j} + \frac{\partial}{\partial z}\mathbf{k}$.

The subscript used in your equation is $\hat{x}$, but what is the vector in question. From what I can understand you have del acting on this function $D_{w}(\hat{x})$ but the subscript might be restricting or changing what coordinate system Del is acting in.

I hope this helps.