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.
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15:35 - 16:40: Automatic Differentiation / Kleene AlgebraResearch Papers at Ile de France II (IDF II) Chair(s): Lars BirkedalAarhus University | |||
15:35 - 15:56 Talk | A Simple Differentiable Programming Language Research Papers Link to publication DOI Media Attached | ||
15:56 - 16:18 Talk | Backpropagation in the Simply Typed Lambda-calculus with Linear Negation Research Papers Link to publication DOI Media Attached File Attached | ||
16:18 - 16:40 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 |