The December 15th Galois Tech Talk will be delivered by John Launchbury. He will present Conal Elliott’s 2009 ICFP paper entitled Beautiful Differentiation for those of us who were not able to attend this wonderful talk in-person.
- Date: Tuesday, 10:30am, 15 Dec 2009
- Time: 10:30am – 11:30am
- Location: Galois, Inc.421 SW 6th Ave. Suite 300(3rd floor of the Commonwealth Building)Portland, OR 97204
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.Bio: John Launchbury is the founder and Chief Scientist of Galois, Inc.
Galois has been holding weekly technical seminars for several years on topics from functional programming, formal methods, compiler and language design, to cryptography, and operating system construction, with talks by many figures from the programming language and formal methods communities. The talks are open and free. An RSVP is not required, but feel free to contact the organizer with questions and comments.