I have not seen this v show up anywhere else in the paper, and then it pops up here. What would it be? Full paper here
$$\min\left[1, \frac{\sqrt{v}}{\|\mathbf{W}_i,\cdot\|_2} \right]$$
Can I assume this is an Euclidian norm operation on the row $i$? Why is the two in subscript?
The original notation from the paper is
The paper explains it perfectly:
"...where $\nu \in \mathbb{R}^+$ is a regularization parameter...", that is, a scalar parameter that governs the "smoothness" of a function. It is basically the length of the weight vector; the smaller that length, the simpler and smoother the function.
The "2" in $\| \cdot \|_2$ means the squared norm, i.e., $\sqrt{x_1^2 + x_2^2 + \ldots}$. If it had be an "3", then $\sqrt[3]{x_1^3 + x_2^3 + \ldots }$