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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

Time series augmentation is critical for training robust deep learning models, particularly in domains where labelled data is scarce and expensive to obtain. However, existing augmentation libraries for time series, mainly written in…

Machine Learning · Computer Science 2026-01-07 Wadie Skaf , Felix Kern , Aryamaan Basu Roy , Tejas Pradhan , Roman Kalkreuth , Holger Hoos

Automatic differentiation (AD) is an essential primitive for machine learning programming systems. Tangent is a new library that performs AD using source code transformation (SCT) in Python. It takes numeric functions written in a syntactic…

Mathematical Software · Computer Science 2017-11-09 Bart van Merriënboer , Alexander B. Wiltschko , Dan Moldovan

As computational challenges in optimization and statistical inference grow ever harder, algorithms that utilize derivatives are becoming increasingly more important. The implementation of the derivatives that make these algorithms so…

Mathematical Software · Computer Science 2015-09-25 Bob Carpenter , Matthew D. Hoffman , Marcus Brubaker , Daniel Lee , Peter Li , Michael Betancourt

RooFit is a toolkit for statistical modeling and fitting used by most experiments in particle physics. Just as data sets from next-generation experiments grow, processing requirements for physics analysis become more computationally…

Mathematical Software · Computer Science 2023-04-07 Garima Singh , Jonas Rembser , Lorenzo Moneta , David Lange , Vassil Vassilev

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

Derivative computation is a key component of optimization, sensitivity analysis, uncertainty quantification, and nonlinear solvers. Automatic differentiation (AD) is a powerful technique for evaluating such derivatives, and in recent years,…

Mathematical Software · Computer Science 2025-07-18 Kim Liegeois , Brian Kelley , Eric Phipps , Sivasankaran Rajamanickam , Vassil Vassilev

In this work we present useful techniques and possible enhancements when applying an Algorithmic Differentiation (AD) tool to the linear algebra library Eigen using our in-house AD by overloading (AD-O) tool dco/c++ as a case study. After…

Mathematical Software · Computer Science 2020-06-23 Patrick Peltzer , Johannes Lotz , Uwe Naumann

Fuzzing is a popular bug detection technique achieved by testing software executables with random inputs. This technique can also be extended to libraries by constructing executables that call library APIs, known as fuzz drivers. Automated…

Software Engineering · Computer Science 2023-12-20 Yehong Zhang , Jun Wu , Hui Xu

A C++ library for sensitivity analysis of optimisation problems involving ordinary differential equations (ODEs) enabled by automatic differentiation (AD) and SIMD (Single Instruction, Multiple data) vectorization is presented. The discrete…

Numerical Analysis · Mathematics 2024-10-04 Rui Martins , Evgeny Lakshtanov

A large class of non-smooth practical optimization problems can be written as minimization of a sum of smooth and partly smooth functions. We examine such structured problems which also depend on a parameter vector and study the problem of…

Optimization and Control · Mathematics 2024-10-28 Sheheryar Mehmood , Peter Ochs

Automating C-to-Rust migration is critical for improving software security without sacrificing performance. Traditional rule-based methods struggle with diverse C idioms, often producing rigid and unidiomatic Rust code. Large Language…

Software Engineering · Computer Science 2026-04-06 Jia Feng , Wenjie Gan , Cuiyun Gao , Chaozheng Wang , Feng Luo , Xin Xia , Ge Li , Kui Liu

Rust's novel type system has proved an attractive target for verification and program analysis tools, due to the rich guarantees it provides for controlling aliasing and mutability. However, fully understanding, extracting and exploiting…

Programming Languages · Computer Science 2025-08-27 Zachary Grannan , Aurel Bílý , Jonáš Fiala , Jasper Geer , Markus de Medeiros , Peter Müller , Alexander J. Summers

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

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

Robustness is a key concern for Rust library development because Rust promises no risks of undefined behaviors if developers use safe APIs only. Fuzzing is a practical approach for examining the robustness of programs. However, existing…

Software Engineering · Computer Science 2021-10-25 Jianfeng Jiang , Hui Xu , Yangfan Zhou

Automatic differentiation is involved for long in applied mathematics as an alternative to finite difference to improve the accuracy of numerical computation of derivatives. Each time a numerical minimization is involved, automatic…

Computational Finance · Quantitative Finance 2017-06-08 Sébastien Geeraert , Charles-Albert Lehalle , Barak Pearlmutter , Olivier Pironneau , Adil Reghai

Algorithmic differentiation (AD) has become increasingly capable and straightforward to use. However, AD is inefficient when applied directly to solvers, a feature of most engineering analyses. We can leverage implicit differentiation to…

Optimization and Control · Mathematics 2023-06-28 Andrew Ning , Taylor McDonnell

Rust is a modern programming language that guarantees memory safety and the absence of data races with a strong type system. We present RustyDL, a program logic for Rust, as a foundation for an auto-interactive, deductive verification tool…

Programming Languages · Computer Science 2026-02-26 Daniel Drodt , Reiner Hähnle

We present a technique for applying (forward and) reverse-mode automatic differentiation (AD) on a non-recursive second-order functional array language that supports nested parallelism and is primarily aimed at efficient GPU execution. The…

Programming Languages · Computer Science 2022-02-22 Robert Schenck , Ola Rønning , Troels Henriksen , Cosmin E. Oancea