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Reverse AD at Higher Types: Pure, Principled and Denotationally Correct

We show how to define forward- and reverse-mode automatic differentiation source-code transformations or on a standard higher-order functional language. The transformations generate purely functional code, and they are principled in the sense that their definition arises from a categorical universal...

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Detalles Bibliográficos
Autor principal: Vákár, Matthijs
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7984537/
http://dx.doi.org/10.1007/978-3-030-72019-3_22
Descripción
Sumario:We show how to define forward- and reverse-mode automatic differentiation source-code transformations or on a standard higher-order functional language. The transformations generate purely functional code, and they are principled in the sense that their definition arises from a categorical universal property. We give a semantic proof of correctness of the transformations. In their most elegant formulation, the transformations generate code with linear types. However, we demonstrate how the transformations can be implemented in a standard functional language without sacrificing correctness. To do so, we make use of abstract data types to represent the required linear types, e.g. through the use of a basic module system.