Differentiate Everything with a Reversible Programming Language

This paper considers the source-to-source automatic differentiation (AD) in a reversible language. We start by reviewing the limitations of traditional AD frameworks. To solve the issues in these frameworks, we developed a reversible eDSL NiLang in Julia that can differentiate a general program while being compatible with Julia's ecosystem. It empowers users the flexibility to tradeoff time, space, and energy so that one can use it to obtain gradients and Hessians ranging for elementary mathematical functions, sparse matrix operations, and linear algebra that are widely used in scientific programming. We demonstrate that a source-to-source AD framework can achieve the state-of-the-art performance by showing and benchmarking several examples. Finally, we will discuss the challenges that we face towards rigorous reversible programming, mainly from the instruction and hardware perspective.