相关论文: Confusion of Tagged Perturbations in Forward Autom…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

Federated learning (FL) is a general framework for learning across an axis of group partitioned data (heterogeneous clients) while preserving data privacy, under the orchestration of a central server. FL methods often compute gradients of…

In scientific computation, it is often necessary to calculate higher-order derivatives of a function. Currently, two primary methods for higher-order automatic differentiation exist: symbolic differentiation and algorithmic automatic…

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…

Automatic Differentiation (AD) is instrumental for science and industry. It is a tool to evaluate the derivative of a function specified through a computer program. The range of AD application domain spans from Machine Learning to Robotics…

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…

Where dual-numbers forward-mode automatic differentiation (AD) pairs each scalar value with its tangent value, dual-numbers reverse-mode AD attempts to achieve reverse AD using a similarly simple idea: by pairing each scalar value with a…

Automatic differentiation (AD) has been a topic of interest for researchers in many disciplines, with increased popularity since its application to machine learning and neural networks. Although many researchers appreciate and know how to…