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This is a clone of the "Differentiation for Hackers" handbook, written by Mike J. Innes. All the purpose of this clone is to render the notebooks with Documenter.jl and host them on GitHub Pages. The notebooks rendered by Documenter.jl are available here. Along with some cosmetic changes in order to make the original texts fit with Documenter.jl's syntax, I also made minor corrections and improvements like fixing the implementations of the quotient rule, adding simplification rule for symbolic representation of exponentiation, etc. Except that, all the contents should be identical and all the credit goes to him.

Differentiation for Hackers

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The goal of this handbook is to demystify algorithmic differentiation, the tool that underlies modern machine learning. It begins with a calculus-101 style understanding and gradually extends this to build toy implementations of systems similar to PyTorch and TensorFlow. I have tried to clarify the relationships between every kind of differentiation I can think of – including forward and reverse, symbolic, numeric, tracing and source transformation. Where typical real-word ADs are mired in implementation details, these implementations are designed to be coherent enough that the real, fundamental differences – of which there are surprisingly few – become obvious.

The intro notebook is recommended to start with, but otherwise notebooks do not have a fixed order.

  • Intro – explains the basics, beginning with a simple symbolic differentiation routine.
  • Back & Forth – discusses the difference between forward and reverse mode AD.
  • Forward – discusses forward-mode AD and its relationship to symbolic and numerical differentiation.
  • Tracing – discusses tracing-based implementations of reverse mode, as used by TensorFlow and PyTorch.
  • Reverse – discusses a more powerful reverse mode based on source transformation (not complete).

If you want to run the notebooks locally, they can be built by running the src/notebooks.jl script using Julia. They should appear inside a /notebooks folder. Alternatively, you can run through the scripts in Juno.