Alvarez-Picallo, M;
Ghica, DR;
Sprunger, D;
Zanasi, F;
(2021)
Functorial String Diagrams for Reverse-Mode Automatic Differentiation.
ArXiv: Ithaca, NY, USA.
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Abstract
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.
| Type: | Working / discussion paper |
|---|---|
| Title: | Functorial String Diagrams for Reverse-Mode Automatic Differentiation |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://doi.org/10.48550/arXiv.2107.13433 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | string diagrams, automatic differentiation, graph rewriting, hierarchical hypergraphs |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10132859 |
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