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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.

Wed 22 Jan
Times are displayed in time zone: (GMT-06:00) Saskatchewan, Central America change

15:35 - 16:40: Research Papers - Automatic Differentiation / Kleene Algebra at Ile de France II (IDF II)
Chair(s): Lars BirkedalAarhus University
POPL-2020-Research-Papers15:35 - 15:56
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POPL-2020-Research-Papers15:56 - 16:18
Aloïs BrunelDeepomatic, Damiano MazzaCNRS, Michele PaganiIRIF - Université de Paris
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POPL-2020-Research-Papers16:18 - 16:40
Steffen SmolkaCornell University, Nate FosterCornell University, Justin HsuUniversity of Wisconsin-Madison, USA, Tobias KappéUniversity College London, Dexter KozenCornell University, Alexandra SilvaUniversity College London
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