Meaning of "plus" ($+$) index

Question

So I came across a notation I can't remember seeing, or at least not in such context. I have looked around and asked a few people unsuccessfully. It is from https://arxiv.org/pdf/1805.11572.pdf and the line, or at least the part of the line that I don't know about $$ \lambda\cdot\mathbb{E} \left[ (||\nabla_x\Psi_\Theta(X)||-1)^2_+\right], $$ where I don't know what the $+$ index would refer to. Would somebody have seen that notation?

Answer 1

As @copper.hat notes, a common notation is$$(x)_+:=\max\{0,\,x\}=\frac{x+|x|}{2},\,(x)_-:=\min\{0,\,x\}=\frac{x-|x|}{2}.$$The corollaries$$(x)_++(x)_-=x,\,(x)_+-(x)_-=|x|$$motivates this notation. Further, $(x)_+$ is common in machine learning as a rectifier.