(For the rest of the book, we'll use the notation exp(x) to mean e x .) The sigmoid has a number of advantages; it takes a real-valued number and maps it into the range [0, 1], which is just what we want for a probability. Because it is nearly linear around 0 but flattens toward the ends, it tends to squash outlier values toward 0 or 1. And it's differentiable, which as we'll see in Section 5.8 will be handy for learning.