Chapter 9. Differentiation of Control Flow

A conditional is a program construct that chooses one computation among several possible computations. In ordinary code, this is written as if, else, switch, case, pattern...

8 items

Section	Title
1	Chapter 9. Differentiation of Control Flow
2	forward
3	Recursion
4	Dynamic Graphs
5	Piecewise Differentiability
6	Non-Smooth Programs
7	Differentiating Stateful Systems
8	Exception Handling and Undefined Regions

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Chapter 9. Differentiation of Control Flow

A conditional is a program construct that chooses one computation among several possible computations. In ordinary code, this is written as if, else, switch, case, pattern...

Writes › Book › Auto Diff › Chapter 9. Differentiation of Control Flow ›

forward

A loop repeats a computation until a condition fails or a fixed iteration count is reached. In automatic differentiation, loops are important because many numerical algorithms...

Writes › Book › Auto Diff › Chapter 9. Differentiation of Control Flow ›

Recursion

Recursion is control flow where a function calls itself. In automatic differentiation, recursion behaves like a loop with a call stack. Each recursive call contributes one...

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Dynamic Graphs

A dynamic graph is a computation graph built while the program runs. Its structure depends on ordinary runtime values: branches, loop counts, recursive calls, tensor shapes,...

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Piecewise Differentiability

A piecewise differentiable function is built from several differentiable pieces joined by boundaries. Each piece has an ordinary derivative inside its region. At the...

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Non-Smooth Programs

A non-smooth program contains operations where the derivative is undefined, discontinuous, set-valued, or unstable under small perturbations. These programs arise naturally in...

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Differentiating Stateful Systems

A stateful system is a program whose output depends not only on its explicit inputs, but also on stored state. The state may live in variables, objects, arrays, files, random...

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Exception Handling and Undefined Regions

Programs do not only branch between valid computations. They also fail, stop early, raise exceptions, return sentinel values, or enter undefined numerical regions. These...