{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/efficient-chad","title":"Efficient CHAD","arxiv_id":"2307.05738","date":"2023-07-07","proceeding":null,"authors":["Tom Smeding","Matthijs Vákár"],"abstract":"We show how the basic Combinatory Homomorphic Automatic Differentiation (CHAD) algorithm can be optimised, using well-known methods, to yield a simple, composable, and generally applicable reverse-mode automatic differentiation (AD) technique that has the correct computational complexity that we would expect of reverse-mode AD. Specifically, we show that the standard optimisations of sparse vectors and state-passing style code (as well as defunctionalisation/closure conversion, for higher-order languages) give us a purely functional algorithm that is most of the way to the correct complexity, with (functional) mutable updates taking care of the final log-factors. We provide an Agda formalisation of our complexity proof. Finally, we discuss how the techniques apply to differentiating parallel functional array programs: the key observations are 1) that all required mutability is (commutative, associative) accumulation, which lets us preserve task-parallelism and 2) that we can write down data-parallel derivatives for most data-parallel array primitives.","url_abs":"https://arxiv.org/abs/2307.05738v3","url_pdf":"https://arxiv.org/pdf/2307.05738v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"efficient-chad","repo_url":"https://github.com/tomsmeding/efficient-chad-agda","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}