eprintid: 10132859 rev_number: 23 eprint_status: archive userid: 608 dir: disk0/10/13/28/59 datestamp: 2021-08-13 08:54:34 lastmod: 2022-11-30 17:31:26 status_changed: 2021-08-13 08:54:34 type: working_paper metadata_visibility: show creators_name: Alvarez-Picallo, M creators_name: Ghica, DR creators_name: Sprunger, D creators_name: Zanasi, F title: Functorial String Diagrams for Reverse-Mode Automatic Differentiation ispublished: pub divisions: UCL divisions: B04 divisions: C05 divisions: F48 keywords: string diagrams, automatic differentiation, graph rewriting, hierarchical hypergraphs note: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. 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. date: 2021-07-28 date_type: published publisher: ArXiv official_url: https://doi.org/10.48550/arXiv.2107.13433 oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 1881801 lyricists_name: Zanasi, Fabio lyricists_id: FZANA74 actors_name: Zanasi, Fabio actors_id: FZANA74 actors_role: owner full_text_status: public publication: arXiv.org place_of_pub: Ithaca, NY, USA pages: 28 citation: Alvarez-Picallo, M; Ghica, DR; Sprunger, D; Zanasi, F; (2021) Functorial String Diagrams for Reverse-Mode Automatic Differentiation. ArXiv: Ithaca, NY, USA. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10132859/1/2107.13433.pdf