  Automatic differentiation---the mechanical transformation of numeric computer
programs to calculate derivatives efficiently and accurately---dates to the
origin of the computer age. Reverse mode automatic differentiation both
antedates and generalizes the method of backwards propagation of errors used in
machine learning. Despite this, practitioners in a variety of fields, including
machine learning, have been little influenced by automatic differentiation, and
make scant use of available tools. Here we review the technique of automatic
differentiation, describe its two main modes, and explain how it can benefit
machine learning practitioners. To reach the widest possible audience our
treatment assumes only elementary differential calculus, and does not assume
any knowledge of linear algebra.
