English
Related papers

Related papers: A Brief Introduction to Automatic Differentiation …

200 papers

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 proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidden fields. We analyze the source of errors in the framework…

Numerical Analysis · Mathematics 2024-12-20 Kailai Xu , Eric Darve

The deep learning community has devised a diverse set of methods to make gradient optimization, using large datasets, of large and highly complex models with deeply cascaded nonlinearities, practical. Taken as a whole, these methods…

Machine Learning · Computer Science 2016-11-14 Atılım Güneş Baydin , Barak A. Pearlmutter , Jeffrey Mark Siskind

Deep learning has seen tremendous success over the past decade in computer vision, machine translation, and gameplay. This success rests in crucial ways on gradient-descent optimization and the ability to learn parameters of a neural…

Machine Learning · Computer Science 2019-08-30 Fei Wang , Daniel Zheng , James Decker , Xilun Wu , Grégory M. Essertel , Tiark Rompf

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

We develop nested automatic differentiation (AD) algorithms for exact inference and learning in integer latent variable models. Recently, Winner, Sujono, and Sheldon showed how to reduce marginalization in a class of integer latent variable…

Machine Learning · Statistics 2018-06-11 Daniel Sheldon , Kevin Winner , Debora Sujono

Automatic differentiation (AD) has driven recent advances in machine learning, including deep neural networks and Hamiltonian Markov Chain Monte Carlo methods. Partially observed nonlinear stochastic dynamical systems have proved resistant…

Methodology · Statistics 2024-07-04 Kevin Tan , Giles Hooker , Edward L. Ionides

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

Many engineering problems involve learning hidden dynamics from indirect observations, where the physical processes are described by systems of partial differential equations (PDE). Gradient-based optimization methods are considered…

Numerical Analysis · Mathematics 2019-12-17 Kailai Xu , Dongzhuo Li , Eric Darve , Jerry M. Harris

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

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

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

Modelers use automatic differentiation (AD) of computation graphs to implement complex Deep Learning models without defining gradient computations. Stochastic AD extends AD to stochastic computation graphs with sampling steps, which arise…

Machine Learning · Statistics 2021-10-27 Emile van Krieken , Jakub M. Tomczak , Annette ten Teije

Algorithmic differentiation (AD) tools allow to obtain gradient information of a continuously differentiable objective function in a computationally cheap way using the so-called backward mode. It is common practice to use the same tools…

Optimization and Control · Mathematics 2024-12-02 Lukas Baumgärtner , Franz Bethke

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

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

For a real function, automatic differentiation is such a standard algorithm used to efficiently compute its gradient, that it is integrated in various neural network frameworks. However, despite the recent advances in using complex…

Machine Learning · Computer Science 2021-01-19 Chu Guo , Dario Poletti

Agent-based models (ABMs) simulate complex systems by capturing the bottom-up interactions of individual agents comprising the system. Many complex systems of interest, such as epidemics or financial markets, involve thousands or even…

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