arxiv:2107.13433

Functorial String Diagrams for Reverse-Mode Automatic Differentiation

Published on Jul 28, 2021

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Abstract

An enhanced calculus of hierarchical string diagrams for monoidal and cartesian closed categories is used to develop and prove the soundness of an automatic differentiation algorithm for simply typed lambda calculus, with a principled implementation using hierarchical hypergraphs called hypernets.

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We enhance the calculus of string diagrams for monoidal categories with hierarchical features in order to capture closed monoidal (and cartesian closed) structure. Using this new syntax we formulate an automatic differentiation algorithm for (applied) simply typed lambda calculus in the style of [Pearlmutter and Siskind 2008] and we prove for the first time its soundness. To give an efficient yet principled implementation of the AD algorithm we define a sound and complete representation of hierarchical string diagrams as a class of hierarchical hypergraphs we call hypernets.

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