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DOI: 10.4230/LIPIcs.CSL.2020.18
URN: urn:nbn:de:0030-drops-116611
URL: https://drops.dagstuhl.de/opus/volltexte/2020/11661/
Cockett, Robin ; Cruttwell, Geoffrey ; Gallagher, Jonathan ; Lemay, Jean-Simon Pacaud ; MacAdam, Benjamin ; Plotkin, Gordon ; Pronk, Dorette
Reverse Derivative Categories
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Abstract
The reverse derivative is a fundamental operation in machine learning and automatic differentiation [Martín Abadi et al., 2015; Griewank, 2012]. This paper gives a direct axiomatization of a category with a reverse derivative operation, in a similar style to that given by [Blute et al., 2009] for a forward derivative. Intriguingly, a category with a reverse derivative also has a forward derivative, but the converse is not true. In fact, we show explicitly what a forward derivative is missing: a reverse derivative is equivalent to a forward derivative with a dagger structure on its subcategory of linear maps. Furthermore, we show that these linear maps form an additively enriched category with dagger biproducts.
BibTeX - Entry
@InProceedings{cockett_et_al:LIPIcs:2020:11661,
author = {Robin Cockett and Geoffrey Cruttwell and Jonathan Gallagher and Jean-Simon Pacaud Lemay and Benjamin MacAdam and Gordon Plotkin and Dorette Pronk},
title = {{Reverse Derivative Categories}},
booktitle = {28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
pages = {18:1--18:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-132-0},
ISSN = {1868-8969},
year = {2020},
volume = {152},
editor = {Maribel Fern{\'a}ndez and Anca Muscholl},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/11661},
URN = {urn:nbn:de:0030-drops-116611},
doi = {10.4230/LIPIcs.CSL.2020.18},
annote = {Keywords: Reverse Derivatives, Cartesian Reverse Differential Categories, Categorical Semantics, Cartesian Differential Categories, Dagger Categories, Automati}
}
| Keywords: | Reverse Derivatives, Cartesian Reverse Differential Categories, Categorical Semantics, Cartesian Differential Categories, Dagger Categories, Automati | |
| Seminar: | 28th EACSL Annual Conference on Computer Science Logic (CSL 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 06.01.2020 |
