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fix typo and formatting
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kshitij12345 authored Jan 27, 2024
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!!! terminology "pushforward and pullback"

_Pushforward_ and _pullback_ are fancy words that the autodiff community recently adopted from Differential Geometry.
The are broadly in agreement with the use of [pullback](https://en.wikipedia.org/wiki/Pullback_(differential_geometry)) and [pushforward](https://en.wikipedia.org/wiki/Pushforward_(differential)) in differential geometry.
They are broadly in agreement with the use of [pullback](https://en.wikipedia.org/wiki/Pullback_(differential_geometry)) and [pushforward](https://en.wikipedia.org/wiki/Pushforward_(differential)) in differential geometry.
But any geometer will tell you these are the super-boring flat cases. Some will also frown at you.
They are also sometimes described in terms of the jacobian:
The _pushforward_ is _jacobian vector product_ (`jvp`), and _pullback_ is _jacobian transpose vector product_ (`j'vp`).
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- The **pullback** takes wobbliness information with respect to the function's output, and tells the equivalent wobbliness with respect to the functions input.

#### More formally
The **pushforward** of ``f`` takes the _sensitivity_ of the input of ``f`` to a quantity, and gives the _sensitivity_ of the output of ``f`` to that quantity
The **pushforward** of ``f`` takes the _sensitivity_ of the input of ``f`` to a quantity, and gives the _sensitivity_ of the output of ``f`` to that quantity.

The **pullback** of ``f`` takes the _sensitivity_ of a quantity to the output of ``f``, and gives the _sensitivity_ of that quantity to the input of ``f``.

### Math
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