Beautiful differentiation Export

@inproceedings{citeulike:5867045, abstract = {Automatic differentiation (AD) is a precise, efficient, and convenient method for computing derivatives of functions. Its forward-mode implementation can be quite simple even when extended to compute all of the higher-order derivatives as well. The higher-dimensional case has also been tackled, though with extra complexity. This paper develops an implementation of higher-dimensional, higher-order, forward-mode AD in the extremely general and elegant setting of calculus on manifolds and derives that implementation from a simple and precise specification. In order to motivate and discover the implementation, the paper poses the question "What does AD mean, independently of implementation?" An answer arises in the form of naturality of sampling a function and its derivative. Automatic differentiation flows out of this naturality condition, together with the chain rule. Graduating from first-order to higher-order AD corresponds to sampling all derivatives instead of just one. Next, the setting is expanded to arbitrary vector spaces, in which derivative values are linear maps. The specification of AD adapts to this elegant and very general setting, which even simplifies the development.}, address = {New York, NY, USA}, author = {Elliott, Conal M.}, booktitle = {ICFP '09: Proceedings of the 14th ACM SIGPLAN international conference on Functional programming}, citeulike-article-id = {5867045}, citeulike-linkout-0 = {http://portal.acm.org/citation.cfm?id=1596550.1596579}, citeulike-linkout-1 = {http://dx.doi.org/10.1145/1596550.1596579}, doi = {10.1145/1596550.1596579}, isbn = {978-1-60558-332-7}, keywords = {calculus, haskell, vector\_spaces}, location = {Edinburgh, Scotland}, pages = {191--202}, posted-at = {2009-10-01 17:54:49}, priority = {3}, publisher = {ACM}, title = {Beautiful differentiation}, url = {http://dx.doi.org/10.1145/1596550.1596579}, year = {2009} }

TY - CONF ID - citeulike:5867045 L3 - citeulike-article-id:5867045 N2 - Automatic differentiation (AD) is a precise, efficient, and convenient method for computing derivatives of functions. Its forward-mode implementation can be quite simple even when extended to compute all of the higher-order derivatives as well. The higher-dimensional case has also been tackled, though with extra complexity. This paper develops an implementation of higher-dimensional, higher-order, forward-mode AD in the extremely general and elegant setting of calculus on manifolds and derives that implementation from a simple and precise specification. In order to motivate and discover the implementation, the paper poses the question "What does AD mean, independently of implementation?" An answer arises in the form of naturality of sampling a function and its derivative. Automatic differentiation flows out of this naturality condition, together with the chain rule. Graduating from first-order to higher-order AD corresponds to sampling all derivatives instead of just one. Next, the setting is expanded to arbitrary vector spaces, in which derivative values are linear maps. The specification of AD adapts to this elegant and very general setting, which even simplifies the development. CY - Edinburgh, Scotland SN - 978-1-60558-332-7 AD - New York, NY, USA EP - 202 TI - Beautiful differentiation PB - ACM T2 - ICFP '09: Proceedings of the 14th ACM SIGPLAN international conference on Functional programming SP - 191 KW - calculus KW - haskell KW - vector_spaces AU - Elliott, Conal PY - 2009/// UR - http://dx.doi.org/10.1145/1596550.1596579 ER -