the logistic loss realize that logistic loss when this argument is very small can be approximated by Taylor's theorem and I could see an exponential exponential of a lot of terms added together you only need to keep the smallest one because the rest are exponentially smaller okay so that this line is Taylor's theorem and then this one says if you add a bunch of like e to the minus ten plus e to the minus hundred you only need to care about either minus ten so only the smallest of these terms matter that's why there's a min here and