2026-07-22T20:50:05Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17467 2024-03-06T11:00:03Z ddc:004 open_access

Functorial String Diagrams for Reverse-Mode Automatic Differentiation Alvarez-Picallo, Mario Ghica, Dan Sprunger, David Zanasi, Fabio string diagrams automatic differentiation hierarchical hypergraphs We formulate a reverse-mode automatic differentiation (RAD) algorithm for (applied) simply typed lambda calculus in the style of Pearlmutter and Siskind [Barak A. Pearlmutter and Jeffrey Mark Siskind, 2008], 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Mario Alvarez-Picallo and Dan Ghica and David Sprunger and Fabio Zanasi 2023 Is Part Of LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2023.6 urn:nbn:de:0030-drops-174674 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.6 eng https://creativecommons.org/licenses/by/4.0/legalcode