University of Birmingham > Talks@bham > Theoretical computer science seminar > Automatic differentiation in string diagrams

Automatic differentiation in string diagrams

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If you have a question about this talk, please contact Dan Ghica.

Reverse-mode automatic differentiation, especially in the presence of complex language features, is notoriously hard to implement correctly, and most implementations focus on differentiating straight-line imperative first-order code. Generalisations exist, however, that can tackle more advanced features; for example, the algorithm described by Pearlmutter and Siskind in their 2008 paper can differentiate higher-order functions written in a pure functional language. We show that AD algorithms can benefit enormously from being translated into the language of string diagrams in two steps: first, we describe a Pearlmutter-Siskind style AD algorithm as a set of rules for transforming hierarchical graphs; rules which can and indeed have been be implemented correctly and efficiently for a non-trivial language. Then, we present a proof of soundness for it by reducing the above rewrite rules to a suitable graphical version of the axioms of cartesian reverse differential categories, expressed as string diagrams.

This talk is part of the Theoretical computer science seminar series.

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