Beautiful differentiation (Conal Elliott) - Revision history

Apm: added == Notes ==

2023-07-11T10:01:32Z

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	There is need for nontrivial differentiation in machine learning.		There is need for nontrivial differentiation in machine learning.

			== Notes ==

			Automatic differentiation in general is …
			* neither symbolic math like in a computer algebra system
			* nor numeric using a small step-size to calculate the derivative

	== Related ==		== Related ==

Apm: /* Concrete output at the end */

2023-07-11T09:59:30Z

Concrete output at the end

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	----		----
	With "beautiful differentiation" all that falls out naturally. <br>		With "beautiful differentiation" all that falls out naturally. <br>
	Just ask for a certain max order of derivative.		'''Just ask for a certain derivative or max order of derivative and it gets spat out.'''

	== Use cases ==		== Use cases ==

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 * generalized to arbitrary order
 * employing lazy evaluation – <small>allowing to avoid obfuscation of code</small>
 == Related ==

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2023-01-01T12:03:09Z

added back-links * Diffing * Useful math

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	* [[Constructive solid geometry]]		* [[Constructive solid geometry]]
			* [[Diffing]]
			* [[Useful math]]

	== External links ==		== External links ==

Apm: /* External links */ added link to MemoTrie library

2021-10-19T13:27:32Z

External links: added link to MemoTrie library

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	* http://conal.net/papers/beautiful-differentiation/		* http://conal.net/papers/beautiful-differentiation/

	'''Actually usable implementation:'''		'''Actually usable implementation (Haskell library):'''
	* ~~Haskell library~~ [https://hackage.haskell.org/package/vector-space '''vector-space''': Vector & affine spaces, linear maps, and derivatives]		* [https://hackage.haskell.org/package/vector-space '''vector-space:''' Vector & affine spaces, linear maps, and derivatives]
	vector-space provides classes and generic operations for vector spaces and affine spaces. <br>		vector-space provides classes and generic operations for vector spaces and affine spaces. <br>
	It also defines a type of infinite towers of generalized derivatives. <br>		It also defines a type of infinite towers of generalized derivatives. <br>
	A generalized derivative is a linear transformation rather than one of the common concrete representations (scalars, vectors, matrices, ...).		A generalized derivative is a linear transformation rather than one of the common concrete representations (scalars, vectors, matrices, ...).

			* Underlying data storage method: <br>[https://hackage.haskell.org/package/MemoTrie '''MemoTrie:''' Trie-based memo functions]

	'''Wikipedia:'''		'''Wikipedia:'''

Apm: basic page

2021-07-13T15:39:58Z

basic page

New page

{{Stub}}

'''Automatic differentiation but:'''
* generalized to arbitrary dimensionality
* generalized to arbitrary order
* employing lazy evaluation – <small>allowing to avoid obfuscation of code</small>

== Related ==

* [[Constructive solid geometry]]

== External links ==

'''Central page linking to all relevant material:'''
* http://conal.net/papers/beautiful-differentiation/

'''Actually usable implementation:'''
* Haskell library [https://hackage.haskell.org/package/vector-space '''vector-space''': Vector & affine spaces, linear maps, and derivatives]
vector-space provides classes and generic operations for vector spaces and affine spaces. <br>
It also defines a type of infinite towers of generalized derivatives. <br>
A generalized derivative is a linear transformation rather than one of the common concrete representations (scalars, vectors, matrices, ...).

'''Wikipedia:'''
* [https://en.wikipedia.org/wiki/Automatic_differentiation Automatic differentiation]

[[Category:Conal Elliott]]