We can simplify this equation further. Assume this is a hard classification task, meaning that only one class is the correct one, and that there is one output unit in y for each class. If the true class is i, then y is a vector where y i = 1 and y j = 0 ∀ j = i. A vector like this, with one value=1 and the rest 0, is called a one-hot vector. The terms in the sum in Eq. 7.24 will be 0 except for the term corresponding to the true class, i.e.: