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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

Rewriting logic is a natural and expressive framework for the specification of concurrent systems and logics. The Maude specification language provides an implementation of this formalism that allows executing, verifying, and analyzing the…

Logic in Computer Science · Computer Science 2024-02-02 Steven Eker , Narciso Martí-Oliet , José Meseguer , Rubén Rubio , Alberto Verdejo

This paper presents a novel optimization for differentiable programming named coarsening optimization. It offers a systematic way to synergize symbolic differentiation and algorithmic differentiation (AD). Through it, the granularity of the…

Dual numbers are a well-established tool for computing derivatives and constitute the basis of forward-mode automatic differentiation. While the theoretical framework for computing derivatives of arbitrary order is well understood,…

Numerical Analysis · Mathematics 2026-02-06 F. Peñuñuri , K. B. Cantún-Avila , R. Peón-Escalante

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

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

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

Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…

Optimization and Control · Mathematics 2019-06-28 Jacob H. Seidman , Mahyar Fazlyab , Victor M. Preciado , George J. Pappas

We propose extensions to Fortran which integrate forward and reverse Automatic Differentiation (AD) directly into the programming model. Irrespective of implementation technology, embedding AD constructs directly into the language extends…

Programming Languages · Computer Science 2012-03-09 Alexey Radul , Barak A. Pearlmutter , Jeffrey Mark Siskind

We present semantic correctness proofs of forward-mode Automatic Differentiation (AD) for languages with sources of partiality such as partial operations, lazy conditionals on real parameters, iteration, and term and type recursion. We…

Programming Languages · Computer Science 2024-05-28 Matthijs Vákár

We show how the basic Combinatory Homomorphic Automatic Differentiation (CHAD) algorithm can be optimised, using well-known methods, to yield a simple, composable, and generally applicable reverse-mode automatic differentiation (AD)…

Programming Languages · Computer Science 2023-11-15 Tom Smeding , Matthijs Vákár

We introduce Combinatory Homomorphic Automatic Differentiation (CHAD), a principled, pure, provably correct define-then-run method for performing forward- and reverse-mode automatic differentiation (AD) on programming languages with…

Programming Languages · Computer Science 2026-05-05 Matthijs Vákár , Tom Smeding

Building on the observation that reverse-mode automatic differentiation (AD) -- a generalisation of backpropagation -- can naturally be expressed as pullbacks of differential 1-forms, we design a simple higher-order programming language…

Programming Languages · Computer Science 2020-02-20 Carol Mak , Luke Ong

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

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) 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

Classical reverse-mode automatic differentiation (AD) imposes only a small constant-factor overhead in operation count over the original computation, but has storage requirements that grow, in the worst case, in proportion to the time…

Programming Languages · Computer Science 2018-07-18 Jeffrey Mark Siskind , Barak A. Pearlmutter

Large Language Models (LLMs) have demonstrated impressive capabilities in understanding and generating codes. Due to these capabilities, many recent methods are proposed to automatically refine the codes with LLMs. However, we should…

Software Engineering · Computer Science 2024-10-31 Minju Seo , Jinheon Baek , Sung Ju Hwang

We review the current state of automatic differentiation (AD) for array programming in machine learning (ML), including the different approaches such as operator overloading (OO) and source transformation (ST) used for AD, graph-based…

Machine Learning · Computer Science 2019-01-04 Bart van Merriënboer , Olivier Breuleux , Arnaud Bergeron , Pascal Lamblin

Context: Large Language Model (LLM) agents are becoming widely used for various Requirements Engineering (RE) tasks. Research on improving their accuracy mainly focuses on prompt engineering, model fine-tuning, and retrieval augmented…

Software Engineering · Computer Science 2025-11-20 Marc Oriol , Quim Motger , Jordi Marco , Xavier Franch