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Automatic differentiation (AD) is a range of algorithms to compute the numeric value of a function's (partial) derivative, where the function is typically given as a computer program or abstract syntax tree. AD has become immensely popular…

Programming Languages · Computer Science 2023-05-16 Tom Schrijvers , Birthe van den Berg , Fabrizio Riguzzi

Automatic differentiation (AD) is an ensemble of techniques that allow to evaluate accurate numerical derivatives of a mathematical function expressed in a computer programming language. In this paper we use AD for stating and solving solid…

Numerical Analysis · Mathematics 2020-01-22 Andrea Vigliotti , Ferdinando Auricchio

We present a system for the automatic differentiation of a higher-order functional array-processing language. The core functional language underlying this system simultaneously supports both source-to-source automatic differentiation and…

Mathematical Software · Computer Science 2018-06-07 Amir Shaikhha , Andrew Fitzgibbon , Dimitrios Vytiniotis , Simon Peyton Jones , Christoph Koch

Algorithmic differentiation (AD) is a set of techniques that provide partial derivatives of computer-implemented functions. Such a function can be supplied to state-of-the-art AD tools via its source code, or via an intermediate…

Mathematical Software · Computer Science 2023-07-10 Max Aehle , Johannes Blühdorn , Max Sagebaum , Nicolas R. Gauger

Automatic differentiation, also known as backpropagation, AD, autodiff, or algorithmic differentiation, is a popular technique for computing derivatives of computer programs accurately and efficiently. Sometimes, however, the derivatives…

Numerical Analysis · Mathematics 2023-05-15 Jan Hückelheim , Harshitha Menon , William Moses , Bruce Christianson , Paul Hovland , Laurent Hascoët

We present semantic correctness proofs of automatic differentiation (AD). We consider a forward-mode AD method on a higher-order language with algebraic data types and we characterise it as the unique structure-preserving macro given a…

Programming Languages · Computer Science 2026-05-07 Mathieu Huot , Sam Staton , Matthijs Vákár

In mathematics and computer algebra, automatic differentiation (AD) is a set of techniques to evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no matter how…

Mathematical Software · Computer Science 2021-02-03 Vassil Vassilev , Aleksandr Efremov , Oksana Shadura

Tools for algorithmic differentiation (AD) provide accurate derivatives of computer-implemented functions for use in, e. g., optimization and machine learning (ML). However, they often require the source code of the function to be available…

Mathematical Software · Computer Science 2022-12-29 Max Aehle , Johannes Blühdorn , Max Sagebaum , Nicolas R. Gauger

We show that Automatic Differentiation (AD) operators can be provided in a dynamic language without sacrificing numeric performance. To achieve this, general forward and reverse AD functions are added to a simple high-level dynamic…

Programming Languages · Computer Science 2016-11-11 Jeffrey Mark Siskind , Barak A. Pearlmutter

Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD), also called algorithmic differentiation or simply "autodiff", is a family of techniques similar to but more…

Symbolic Computation · Computer Science 2018-07-18 Atilim Gunes Baydin , Barak A. Pearlmutter , Alexey Andreyevich Radul , Jeffrey Mark Siskind

Automatic differentiation (AD), a technique for constructing new programs which compute the derivative of an original program, has become ubiquitous throughout scientific computing and deep learning due to the improved performance afforded…

Machine Learning · Computer Science 2023-01-10 Gaurav Arya , Moritz Schauer , Frank Schäfer , Chris Rackauckas

Automatic differentiation (AD) in reverse mode (RAD) is a central component of deep learning and other uses of large-scale optimization. Commonly used RAD algorithms such as backpropagation, however, are complex and stateful, hindering deep…

Programming Languages · Computer Science 2018-10-03 Conal Elliott

Automatic differentiation (AD) is an important family of algorithms which enables derivative based optimization. We show that AD can be simply implemented with effects and handlers by doing so in the Frank language. By considering how our…

Programming Languages · Computer Science 2021-01-21 Jesse Sigal

Algorithmic differentiation (AD) allows exact computation of derivatives given only an implementation of an objective function. Although many AD tools are available, a proper and efficient implementation of AD methods is not…

Mathematical Software · Computer Science 2018-07-27 Filip Šrajer , Zuzana Kukelova , Andrew Fitzgibbon

Algorithmic Differentiation (AD) can be used to automate the generation of derivatives in arbitrary software projects. This will generate maintainable derivatives, that are always consistent with the computation of the software. If a domain…

Mathematical Software · Computer Science 2018-03-13 Max Sagebaum , Nicolas R. Gauger

We present semantic correctness proofs of Automatic Differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a…

Programming Languages · Computer Science 2020-04-02 Mathieu Huot , Sam Staton , Matthijs Vákár

Automatic differentiation (AD) is a set of techniques that systematically applies the chain rule to compute the gradients of functions without requiring human intervention. Although the fundamentals of this technology were established…

Machine Learning · Computer Science 2025-09-03 Afif Boudaoud , Alexandru Calotoiu , Marcin Copik , Torsten Hoefler

Automatic differentiation (AD) is conventionally understood as a family of distinct algorithms, rooted in two "modes" -- forward and reverse -- which are typically presented (and implemented) separately. Can there be only one? Following up…

Programming Languages · Computer Science 2022-12-07 Alexey Radul , Adam Paszke , Roy Frostig , Matthew Johnson , Dougal Maclaurin

Automatic differentiation (AD) aims to compute derivatives of user-defined functions, but in Turing-complete languages, this simple specification does not fully capture AD's behavior: AD sometimes disagrees with the true derivative of a…

Programming Languages · Computer Science 2021-12-07 Alexander K. Lew , Mathieu Huot , Vikash K. Mansinghka

Machine learning and neural network models in particular have been improving the state of the art performance on many artificial intelligence related tasks. Neural network models are typically implemented using frameworks that perform…

Machine Learning · Computer Science 2021-10-18 Davan Harrison
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