Automatic differentiation in ML: Where we are and where we should be going (1810.11530v2)

Abstract: We review the current state of automatic differentiation (AD) for array programming in ML, including the different approaches such as operator overloading (OO) and source transformation (ST) used for AD, graph-based intermediate representations for programs, and source languages. Based on these insights, we introduce a new graph-based intermediate representation (IR) which specifically aims to efficiently support fully-general AD for array programming. Unlike existing dataflow programming representations in ML frameworks, our IR naturally supports function calls, higher-order functions and recursion, making ML models easier to implement. The ability to represent closures allows us to perform AD using ST without a tape, making the resulting derivative (adjoint) program amenable to ahead-of-time optimization using tools from functional language compilers, and enabling higher-order derivatives. Lastly, we introduce a proof of concept compiler toolchain called Myia which uses a subset of Python as a front end.