However, z can't be the output of the classifier, since it's a vector of real-valued numbers, while what we need for classification is a vector of probabilities. There is a convenient function for normalizing a vector of real values, by which we mean normalizing converting it to a vector that encodes a probability distribution (all the numbers lie between 0 and 1 and sum to 1): the softmax function that we saw on page 91 of softmax Chapter 5. For a vector z of dimensionality d, the softmax is defined as: