A Step-by-step Introduction to the Implementation of Automatic Differentiation

Automatic differentiation is a key component in deep learning. This topic is well studied and excellent surveys such as Baydin et al. (2018) have been available to clearly describe the basic concepts. Further, sophisticated implementations of automatic differentiation are now an important part of popular deep learning frameworks. However, it is difficult, if not impossible, to directly teach students the implementation of existing systems due to the complexity. On the other hand, if the teaching stops at the basic concept, students fail to sense the realization of an implementation. For example, we often mention the computational graph in teaching automatic differentiation, but students wonder how to implement and use it. In this document, we partially fill the gap by giving a step by step introduction of implementing a simple automatic differentiation system. We streamline the mathematical concepts and the implementation. Further, we give the motivation behind each implementation detail, so the whole setting becomes very natural.