Related papers: Automatic Differentiation: a look through Tensor a…
Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…
Automatic differentiation is a technique which allows a programmer to define a numerical computation via compositions of a broad range of numeric and computational primitives and have the underlying system support the computation of partial…
Computing derivatives of tensor expressions, also known as tensor calculus, is a fundamental task in machine learning. A key concern is the efficiency of evaluating the expressions and their derivatives that hinges on the representation of…
A computational revolution unleashed the power of artificial neural networks. At the heart of that revolution is automatic differentiation, which calculates the derivative of a performance measure relative to a large number of parameters.…
We describe an algorithm for the automated deduction of many $d_2$ differentials in the Adams spectral sequence. We discuss our implementation and the results of the computation.
En este trabajo se presenta una propuesta para realizar Diferenciaci\'on Autom\'atica Anidada utilizando cualquier biblioteca de Diferenciaci\'on Autom\'atica que permita sobrecarga de operadores. Para calcular las derivadas anidadas en una…
We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed…
This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and…
In this review we present hyper-dual numbers as a tool for the automatic differentiation of computer programs via operator overloading. We start with a motivational introduction into the ideas of algorithmic differentiation. Then we…
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…
Two of the most important areas in computational finance: Greeks and, respectively, calibration, are based on efficient and accurate computation of a large number of sensitivities. This paper gives an overview of adjoint and automatic…
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…
We present a system for the automatic differentiation of a higher-order functional array-processing language. The core functional language underlying this system simultaneously supports both source-to-source automatic differentiation and…
We discuss the role of automatic differentiation tools in optimization software. We emphasize issues that are important to large-scale optimization and that have proved useful in the installation of nonlinear solvers in the NEOS Server. Our…
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) 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…
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…
We present the classical coordinate-free formalism for forward and backward mode ad in the real and complex setting. We show how to formally derive the forward and backward formulae for a number of matrix functions starting from basic…
Kjolstad et. al. proposed a tensor algebra compiler. It takes expressions that define a tensor element-wise, such as $f_{ij}(a,b,c,d) = \exp\left[-\sum_{k=0}^4 \left((a_{ik}+b_{jk})^2\, c_{ii} + d_{i+k}^3 \right) \right]$, and generates the…