Automatic differentiation in machine learning: a survey

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 general than backpropagation for efficiently and accurately evaluating derivatives of numeric functions expressed as computer programs. AD is a small but established field with applications in areas including computational fluid dynamics, atmospheric sciences, and engineering design optimization. Until very recently, the fields of machine learning and AD have largely been unaware of each other and, in some cases, have independently discovered each other's results. Despite its relevance, general-purpose AD has been missing from the machine learning toolbox, a situation slowly changing with its ongoing adoption under the names "dynamic computational graphs" and "differentiable programming". We survey the intersection of AD and machine learning, cover applications where AD has direct relevance, and address the main implementation techniques. By precisely defining the main differentiation techniques and their interrelationships, we aim to bring clarity to the usage of the terms "autodiff", "automatic differentiation", and "symbolic differentiation" as these are encountered more and more in machine learning settings.Comment: 43 pages, 5 figure

Automatic differentiation in machine learning: a survey

Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD) is a technique for calculating derivatives of numeric functions expressed as computer programs efficiently and accurately, used in fields such as computational fluid dynamics, nuclear engineering, and atmospheric sciences. Despite its advantages and use in other fields, machine learning practitioners have been little influenced by AD and make scant use of available tools. We survey the intersection of AD and machine learning, cover applications where AD has the potential to make a big impact, and report on some recent developments in the adoption of this technique. We aim to dispel some misconceptions that we contend have impeded the use of AD within the machine learning community

Automatic differentiation in machine learning: a survey

Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD) is a technique for calculating derivatives of numeric functions expressed as computer programs efficiently and accurately, used in fields such as computational fluid dynamics, nuclear engineering, and atmospheric sciences. Despite its advantages and use in other fields, machine learning practitioners have been little influenced by AD and make scant use of available tools. We survey the intersection of AD and machine learning, cover applications where AD has the potential to make a big impact, and report on some recent developments in the adoption of this technique. We aim to dispel some misconceptions that we contend have impeded the use of AD within the machine learning community

Confusion of Tagged Perturbations in Forward Automatic Differentiation of Higher-Order Functions

Forward Automatic Differentiation (AD) is a technique for augmenting programs to both perform their original calculation and also compute its directional derivative. The essence of Forward AD is to attach a derivative value to each number, and propagate these through the computation. When derivatives are nested, the distinct derivative calculations, and their associated attached values, must be distinguished. In dynamic languages this is typically accomplished by creating a unique tag for each application of the derivative operator, tagging the attached values, and overloading the arithmetic operators. We exhibit a subtle bug, present in fielded implementations, in which perturbations are confused despite the tagging machinery

A Flexible and Expressive Substrate for Computation

In this dissertation I propose a shift in the foundations of computation. Modern programming systems are not expressive enough. The traditional image of a single computer that has global effects on a large memory is too restrictive. The propagation paradigm replaces this with computing by networks of local, independent, stateless machines interconnected with stateful storage cells. In so doing, it offers great flexibility and expressive power, and has therefore been much studied, but has not yet been tamed for general-purpose computation. The novel insight that should finally permit computing with general-purpose propagation is that a cell should no

Automatic differentiation in machine learning: a survey

Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD) is a technique for calculating derivatives of numeric functions expressed as computer programs efficiently and accurately, used in fields such as computational fluid dynamics, nuclear engineering, and atmospheric sciences. Despite its advantages and use in other fields, machine learning practitioners have been little influenced by AD and make scant use of available tools. We survey the intersection of AD and machine learning, cover applications where AD has the potential to make a big impact, and report on some recent developments in the adoption of this technique. We aim to dispel some misconceptions that we contend have impeded the use of AD within the machine learning community

Automatic differentiation in machine learning: a survey

Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD) is a technique for calculating derivatives of numeric functions expressed as computer programs efficiently and accurately, used in fields such as computational fluid dynamics, nuclear engineering, and atmospheric sciences. Despite its advantages and use in other fields, machine learning practitioners have been little influenced by AD and make scant use of available tools. We survey the intersection of AD and machine learning, cover applications where AD has the potential to make a big impact, and report on some recent developments in the adoption of this technique. We aim to dispel some misconceptions that we contend have impeded the use of AD within the machine learning community

Automatic differentiation in machine learning: a survey

Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD) is a technique for calculating derivatives of numeric functions expressed as computer programs efficiently and accurately, used in fields such as computational fluid dynamics, nuclear engineering, and atmospheric sciences. Despite its advantages and use in other fields, machine learning practitioners have been little influenced by AD and make scant use of available tools. We survey the intersection of AD and machine learning, cover applications where AD has the potential to make a big impact, and report on some recent developments in the adoption of this technique. We aim to dispel some misconceptions that we contend have impeded the use of AD within the machine learning community

Confusion of Tagged Perturbations in Forward Automatic Differentiation of Higher-Order Functions

Forward Automatic Differentiation (AD) is a technique for augmenting programs to both perform their original calculation and also compute its directional derivative. The essence of Forward AD is to attach a derivative value to each number, and propagate these through the computation. When derivatives are nested, the distinct derivative calculations, and their associated attached values, must be distinguished. In dynamic languages this is typically accomplished by creating a unique tag for each application of the derivative operator, tagging the attached values, and overloading the arithmetic operators. We exhibit a subtle bug, present in fielded implementations, in which perturbations are confused despite the tagging machinery