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In this paper we introduce DiffSharp, an automatic differentiation (AD) library designed with machine learning in mind. AD is a family of techniques that evaluate derivatives at machine precision with only a small constant factor of overhead, by systematically applying the chain rule of calculus at the elementary operator level. DiffSharp aims to make an extensive array of AD techniques available, in convenient form, to the machine learning community. These including arbitrary nesting of forward/reverse AD operations, AD with linear algebra primitives, and a functional API that emphasizes the use of higher-order functions and composition. The library exposes this functionality through an API that provides gradients, Hessians, Jacobians, directional derivatives, and matrix-free Hessian- and Jacobian-vector products. Bearing the performance requirements of the latest machine learning techniques in mind, the underlying computations are run through a high-performance BLAS/LAPACK backend, using OpenBLAS by default. GPU support is currently being implemented.
Automatic differentiation is a set of techniques to efficiently and accurately compute the derivative of a function represented by a computer program. Existing C++ libraries for automatic differentiation (e.g. Adept, Stan Math Library), however, exhi
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 complicated, executes
Derivatives play a critical role in computational statistics, examples being Bayesian inference using Hamiltonian Monte Carlo sampling and the training of neural networks. Automatic differentiation is a powerful tool to automate the calculation of de
Automatic and adaptive approximation, optimization, or integration of functions in a cone with guarantee of accuracy is a relatively new paradigm. Our purpose is to create an open-source MATLAB package, Guaranteed Automatic Integration Library (GAIL)
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 techniques underlyi