differentiation libraries like tensor flow and PI torch can handle this quite gracefully and and really you don't have to worry about it too much at all and it also isn't particularly computationally expensive but we will talk a bit more about a ways to mitigate this in a few slides okay so now how does this approach compared to the black box out of potations that we mentioned before so let's bring up the general form that we talked about before where you have some neural network that's taking a training data point or training data set and a