AD in Fortran, Part 1: Design

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 the reach and convenience of AD while allowing abstraction of concepts of interest to scientific-computing practice, such as root finding, optimization, and finding equilibria of continuous games. Multiple different subprograms for these tasks can share common interfaces, regardless of whether and how they use AD internally. A programmer can maximize a function F by calling a library maximizer, XSTAR=ARGMAX(F,X0), which internally constructs derivatives of F by AD, without having to learn how to use any particular AD tool. We illustrate the utility of these extensions by example: programs become much more concise and closer to traditional mathematical notation. A companion paper describes how these extensions can be implemented by a program that generates input to existing Fortran-based AD tools

DiffSharp: Automatic Differentiation Library

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

DiffSharp: An AD Library for .NET Languages

DiffSharp is an algorithmic differentiation or automatic differentiation (AD) library for the .NET ecosystem, which is targeted by the C# and F# languages, among others. The library has been designed with machine learning applications in mind, allowing very succinct implementations of models and optimization routines. DiffSharp is implemented in F# and exposes forward and reverse AD operators as general nestable higher-order functions, usable by any .NET language. It provides high-performance linear algebra primitives---scalars, vectors, and matrices, with a generalization to tensors underway---that are fully supported by all the AD operators, and which use a BLAS/LAPACK backend via the highly optimized OpenBLAS library. DiffSharp currently uses operator overloading, but we are developing a transformation-based version of the library using F#'s "code quotation" metaprogramming facility. Work on a CUDA-based GPU backend is also underway

DiffSharp: An AD Library for .NET Languages

DiffSharp is an algorithmic differentiation or automatic differentiation (AD) library for the .NET ecosystem, which is targeted by the C# and F# languages, among others. The library has been designed with machine learning applications in mind, allowing very succinct implementations of models and optimization routines. DiffSharp is implemented in F# and exposes forward and reverse AD operators as general nestable higher-order functions, usable by any .NET language. It provides high-performance linear algebra primitives---scalars, vectors, and matrices, with a generalization to tensors underway---that are fully supported by all the AD operators, and which use a BLAS/LAPACK backend via the highly optimized OpenBLAS library. DiffSharp currently uses operator overloading, but we are developing a transformation-based version of the library using F#'s "code quotation" metaprogramming facility. Work on a CUDA-based GPU backend is also underway

Automatic Differentiation of Algorithms for Machine Learning

Automatic differentiation---the mechanical transformation of numeric computer programs to calculate derivatives efficiently and accurately---dates to the origin of the computer age. Reverse mode automatic differentiation both antedates and generalizes the method of backwards propagation of errors used in machine learning. Despite this, practitioners in a variety of fields, including machine learning, have been little influenced by automatic differentiation, and make scant use of available tools. Here we review the technique of automatic differentiation, describe its two main modes, and explain how it can benefit machine learning practitioners. To reach the widest possible audience our treatment assumes only elementary differential calculus, and does not assume any knowledge of linear algebra.Comment: 7 pages, 1 figur