Practice question · Multiple choice
Automatic differentiation computes exact derivatives of a program without symbolic algebra and without finite differences. What makes that possible?
Hints
- Ask what every line of a numeric program is made of, and whether each piece's derivative is known.
- Finite differences approximate. What is different about this?
Show the answer
D. The chain rule applied mechanically to elementary operations
Why
Every operation has a known derivative and the chain rule composes them, so the derivative is computed exactly to machine precision alongside the value, no step size, no symbolic blowup. It is what PyTorch and JAX do, and why backpropagation is a special case rather than a separate invention.
Practise Differentiation Rules
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