Automatic differentiation in string diagrams

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• Mario Alvarez Picallo, Huawei Research
• Friday 02 July 2021, 14:00-15:00
• https://bham-ac-uk.zoom.us/j/4040590387?pwd=dlJpN0tyUVJQQWxyUzc3SisvcHJtUT09.

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.

This talk is included in these lists:

• Computer Science Departmental Series
• Computer Science Distinguished Seminars
• Theoretical computer science seminar
• computer sience
• https://bham-ac-uk.zoom.us/j/4040590387?pwd=dlJpN0tyUVJQQWxyUzc3SisvcHJtUT09

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