Alvarez-Picallo, M;
Ghica, D;
Sprunger, D;
Zanasi, F;
(2023)
Functorial String Diagrams for Reverse-Mode Automatic Differentiation.
In:
31st EACSL Annual Conference on Computer Science Logic (CSL 2023).
(pp. 6:1-6:20).
Schloss Dagstuhl -- Leibniz-Zentrum für Informatik: Dagstuhl, Germany.
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Abstract
We formulate a reverse-mode automatic differentiation (RAD) algorithm for (applied) simply typed lambda calculus in the style of Pearlmutter and Siskind [27], using the graphical formalism of string diagrams. Thanks to string diagram rewriting, we are able to formally prove for the first time the soundness of such an algorithm. Our approach requires developing a calculus of string diagrams with hierarchical features in the spirit of functorial boxes, in order to model closed monoidal (and cartesian closed) structure. To give an efficient yet principled implementation of the RAD algorithm, we use foliations of our hierarchical string diagrams.
| Type: | Proceedings paper |
|---|---|
| Title: | Functorial String Diagrams for Reverse-Mode Automatic Differentiation |
| Event: | 31st EACSL Annual Conference on Computer Science Logic (CSL 2023) |
| ISBN-13: | 9783959772648 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4230/LIPIcs.CSL.2023.6 |
| Publisher version: | https://doi.org/10.4230/LIPIcs.CSL.2023.6 |
| Language: | English |
| Additional information: | © Mario Alvarez-Picallo, Dan Ghica, David Sprunger, and Fabio Zanasi; licensed under Creative Commons License CC-BY 4.0 31st EACSL Annual Conference on Computer Science Logic (CSL 2023) |
| Keywords: | String diagrams, automatic differentiation, 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/10166255 |
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