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SemanDiff SIGNED

Semantically correct automatic differentiation

Total Cost €


EC-Contrib. €






Project "SemanDiff" data sheet

The following table provides information about the project.


Organization address
postcode: 3584 CS

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Netherlands [NL]
 Total cost 187˙572 €
 EC max contribution 187˙572 € (100%)
 Programme 1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
 Code Call H2020-MSCA-IF-2019
 Funding Scheme MSCA-IF-EF-RI
 Starting year 2020
 Duration (year-month-day) from 2020-03-15   to  2022-03-14


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITEIT UTRECHT NL (UTRECHT) coordinator 187˙572.00


 Project objective

Many recent advances in machine learning and computational statistics rely on algorithms that calculate derivatives. This use of derivatives has motivated the creation of domain specific modelling languages in which each program can be differentiated automatically, by the compiler. This technique is known as automatic differentiation (AD). AD is typically implemented through source-code-transformations, either directly or indirectly via operator overloading. These transformations become intricate in languages with expressive language features like algebraic data types and higher-order functions. Meanwhile, traditional calculus and differential geometry do not suffice to prove their correctness or even give them meaning, as ordinary differential geometry cannot support higher-order functions. Indeed, such formal correctness proofs have never been published.

This project will use the mathematical foundations of diffeological spaces, a conservative extension of traditional differential geometry to higher-order types, to give precisely such correctness proofs. In particular, it will give appropriate source-code transformations for both the forward mode and reverse mode techniques of AD on a language with specified semantics in diffeological spaces. Next, it will prove that these source-code transformations correctly implement the canonical semantic notion of differentiation, as given by the diffeological spaces semantics. It will perform this analysis for a higher-order language with tuples and variant types. These formal descriptions and correctness proofs of AD for expressive languages will be accompanied by closely matching implementations, built on top of the Accelerate framework for purely functional GPU programming.

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The information about "SEMANDIFF" are provided by the European Opendata Portal: CORDIS opendata.

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