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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

The successes of deep learning, variational inference, and many other fields have been aided by specialized implementations of reverse-mode automatic differentiation (AD) to compute gradients of mega-dimensional objectives. The AD…

Machine Learning · Computer Science 2021-03-16 Deniz Oktay , Nick McGreivy , Joshua Aduol , Alex Beatson , Ryan P. Adams

Differentiation along algorithms, i.e., piggyback propagation of derivatives, is now routinely used to differentiate iterative solvers in differentiable programming. Asymptotics is well understood for many smooth problems but the…

Optimization and Control · Mathematics 2022-06-02 Jérôme Bolte , Edouard Pauwels , Samuel Vaiter

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) 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 consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…

Optimization and Control · Mathematics 2025-09-03 Mootta Prangprakhon , Nimit Nimana

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, 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

Automatic differentiation (AD) is a technique for computing the derivative of a function represented by a program. This technique is considered as the de-facto standard for computing the differentiation in many machine learning and…

Programming Languages · Computer Science 2022-12-21 Amir Shaikhha , Mathieu Huot , Shabnam Ghasemirad , Andrew Fitzgibbon , Simon Peyton Jones , Dimitrios Vytiniotis

We study the problem of efficiently computing the derivative of the fixed-point of a parametric nondifferentiable contraction map. This problem has wide applications in machine learning, including hyperparameter optimization, meta-learning…

Machine Learning · Statistics 2024-06-05 Riccardo Grazzi , Massimiliano Pontil , Saverio Salzo

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

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

This article provides an overview of some of the mathematical principles of Automatic Differentiation (AD). In particular, we summarise different descriptions of the Forward Mode of AD, like the matrix-vector product based approach, the…

Numerical Analysis · Mathematics 2016-07-07 Philipp H. W. Hoffmann

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

This article aims to demonstrate and discuss the applications of automatic differentiation (AD) for finding derivatives in PDE-constrained optimization problems and Jacobians in non-linear finite element analysis. The main idea is to…

Numerical Analysis · Mathematics 2025-06-03 Julian Andrej , Tzanio Kolev , Boyan Lazarov

Motivated by federated learning, we consider the hub-and-spoke model of distributed optimization in which a central authority coordinates the computation of a solution among many agents while limiting communication. We first study some past…

Machine Learning · Computer Science 2020-05-12 Reese Pathak , Martin J. Wainwright

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

We demonstrate that automatic differentiation (AD), which has become commonly available in machine learning frameworks, is an efficient way to explore ideas that lead to algorithmic improvement in multi-scale affine image registration and…

Optimization and Control · Mathematics 2025-08-05 Warin Watson , Cash Cherry , Rachelle Lang

We consider an inertial primal-dual fixed point algorithm (IPDFP) to compute the minimizations of the following Problem (1.1). This is a full splitting approach, in the sense that the nonsmooth functions are processed individually via their…

Optimization and Control · Mathematics 2016-04-20 Meng Wen , Yu-Chao Tang , Jigen Peng

In this paper, we consider the Forward--Backward proximal splitting algorithm to minimize the sum of two proper convex functions, one of which having a Lipschitz continuous gradient and the other being partly smooth relative to an active…

Optimization and Control · Mathematics 2015-03-11 Jingwei Liang , Jalal Fadili , Gabriel Peyré
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