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Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the mathematical notion of derivative is not always entirely clear—discrepancies can arise, sometimes inadvertently. In order to study automatic differentiation in such programming contexts, we define a small but expressive programming language that includes a construct for reverse-mode differentiation. We give operational and denotational semantics for this language. The operational semantics employs popular implementation techniques, while the denotational semantics employs notions of differentiation familiar from real analysis. We establish that these semantics coincide.

Conference Day
Wed 22 Jan

Displayed time zone: Saskatchewan, Central America change

15:35 - 16:40
Automatic Differentiation / Kleene AlgebraResearch Papers at Ile de France II (IDF II)
Chair(s): Lars BirkedalAarhus University
15:35
21m
Talk
A Simple Differentiable Programming Language
Research Papers
Link to publication DOI Media Attached
15:56
21m
Talk
Backpropagation in the Simply Typed Lambda-calculus with Linear Negation
Research Papers
Aloïs BrunelDeepomatic, Damiano MazzaCNRS, Michele PaganiIRIF - Université de Paris
Link to publication DOI Media Attached File Attached
16:18
21m
Talk
Guarded Kleene Algebra with Tests: Verification of Uninterpreted Programs in Nearly Linear TimeDistinguished Paper
Research Papers
Steffen SmolkaCornell University, Nate FosterCornell University, Justin HsuUniversity of Wisconsin-Madison, USA, Tobias KappéUniversity College London, Dexter KozenCornell University, Alexandra SilvaUniversity College London
Link to publication DOI Media Attached