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We review the current state of automatic differentiation (AD) for arrayprogramming in machine learning (ML), including the different approaches suchas 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 intermediaterepresentation (IR) which specifically aims to efficiently supportfully-general AD for array programming. Unlike existing dataflow programmingrepresentations in ML frameworks, our IR naturally supports function calls,higher-order functions and recursion, making ML models easier to implement. Theability to represent closures allows us to perform AD using ST without a tape,making the resulting derivative (adjoint) program amenable to ahead-of-timeoptimization using tools from functional language compilers, and enablinghigher-order derivatives. Lastly, we introduce a proof of concept compilertoolchain called Myia which uses a subset of Python as a front end.

Automatic differentiation in ML: Where we are and where we should be going