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{{Short description|Programming paradigm}}
{{Machine learning}}
{{Programming paradigms}}▼
'''Differentiable programming''' is a [[programming paradigm]] in which a numeric computer program can be [[Differentiation (mathematics)|differentiated]] throughout via [[automatic differentiation]].<ref name="izzo2016_dCGP">{{cite book |doi=10.1007/978-3-319-55696-3_3 |chapter=Differentiable Genetic Programming |title=Genetic Programming |series=Lecture Notes in Computer Science |date=2017 |last1=Izzo |first1=Dario |last2=Biscani |first2=Francesco |last3=Mereta |first3=Alessio |volume=10196 |pages=35–51 |arxiv=1611.04766 |isbn=978-3-319-55695-6 |s2cid=17786263 }}</ref><ref name="baydin2018automatic">{{cite journal |last1=Baydin |first1=Atilim Gunes |last2=Pearlmutter |first2=Barak A. |last3=Radul |first3=Alexey Andreyevich |last4=Siskind |first4=Jeffrey Mark |title=Automatic
▲<ref name="baydin2018automatic">{{cite journal|last1=Baydin|first1=Atilim Gunes|last2=Pearlmutter|first2=Barak|last3=Radul|first3=Alexey Andreyevich|last4=Siskind|first4=Jeffrey|title=Automatic differentiation in machine learning: a survey|journal=Journal of Machine Learning Research|year=2018|volume=18|pages=1–43|url=http://jmlr.org/papers/v18/17-468.html}}</ref><ref>{{Citation|last1=Wang|first1=Fei|title=Backpropagation with Callbacks: Foundations for Efficient and Expressive Differentiable Programming|date=2018|url=http://papers.nips.cc/paper/8221-backpropagation-with-callbacks-foundations-for-efficient-and-expressive-differentiable-programming.pdf|work=Advances in Neural Information Processing Systems 31|pages=10201–10212|editor-last=Bengio|editor-first=S.|publisher=Curran Associates, Inc.|access-date=2019-02-13|last2=Decker|first2=James|last3=Wu|first3=Xilun|last4=Essertel|first4=Gregory|last5=Rompf|first5=Tiark|editor2-last=Wallach|editor2-first=H.|editor3-last=Larochelle|editor3-first=H.|editor4-last=Grauman|editor4-first=K.}}</ref><ref name="innes">{{Cite journal|last=Innes|first=Mike|date=2018|title=On Machine Learning and Programming Languages|url=http://www.sysml.cc/doc/2018/37.pdf|journal=SysML Conference 2018}}</ref><ref name="diffprog-zygote">{{Citation|date=2019|title=∂P: A Differentiable Programming System to Bridge Machine Learning and Scientific Computing|arxiv=1907.07587|last1=Innes|first1=Mike|last2=Edelman|first2=Alan|last3=Fischer|first3=Keno|last4=Rackauckas|first4=Chris|last5=Saba|first5=Elliot|author6=Viral B Shah|last7=Tebbutt|first7=Will}}</ref> This allows for [[Gradient method|gradient-based optimization]] of parameters in the program, often via [[gradient descent]], as well as other learning approaches that are based on higher order derivative information. Differentiable programming has found use in a wide variety of areas, particularly [[scientific computing]] and [[artificial intelligence]].<ref name="diffprog-zygote" />. One of the early proposals to adopt such a framework in a systematic fashion to improve upon learning algorithms was made by the [[Advanced_Concepts_Team]] at the [[European_Space_Agency]] in early 2016.<ref name="differential intelligence">{{Cite web|url=https://www.esa.int/gsp/ACT/projects/differential_intelligence/|title=Differential Intelligence|access-date=2022-10-19}}</ref>
==Approaches==
Most differentiable programming frameworks work by constructing a graph containing the control flow and [[data structures]] in the program.<ref name="flux">{{cite arXiv |eprint=1811.01457 |last1=Innes |first1=Michael |last2=Saba |first2=Elliot |last3=Fischer |first3=Keno |last4=Gandhi |first4=Dhairya |
* ''' Static, [[compiled]] graph'''-based approaches such as [[TensorFlow]],<ref group=note>TensorFlow 1 uses the static graph approach, whereas TensorFlow 2 uses the dynamic graph approach by default.</ref> [[Theano (software)|Theano]], and [[MXNet]]. They tend to allow for good [[compiler optimization]] and easier scaling to large systems, but their static nature limits interactivity and the types of programs that can be created easily (e.g. those involving [[loop (computing)|loops]] or [[recursion]]), as well as making it harder for users to reason effectively about their programs.<ref name="flux" /> A proof
* '''[[Operator overloading]], dynamic graph'''
The use of just-in-time compilation has emerged recently{{when|date=April 2025}} as a possible solution to overcome some of the bottlenecks of interpreted languages. The C++ [https://bluescarni.github.io/heyoka/index.html heyoka] and Python package [https://bluescarni.github.io/heyoka.py/index.html heyoka.py] make large use of this technique to offer advanced differentiable programming capabilities (also at high orders). A package for the [[Julia (programming language)|Julia]] programming language{{snd}} [https://github.com/FluxML/Zygote.jl Zygote]{{snd}} works directly on Julia's [[intermediate representation]].<ref name="flux" /><ref>{{cite arXiv |eprint=1810.07951 |last1=Innes |first1=Michael |title=Don't Unroll Adjoint: Differentiating SSA-Form Programs |date=2018 |class=cs.PL }}</ref><ref name="diffprog-zygote" />
▲* ''' Static, [[compiled]] graph'''-based approaches such as [[TensorFlow]],<ref group=note>TensorFlow 1 uses the static graph approach, whereas TensorFlow 2 uses the dynamic graph approach by default.</ref> [[Theano (software)|Theano]], and [[MXNet]]. They tend to allow for good [[compiler optimization]] and easier scaling to large systems, but their static nature limits interactivity and the types of programs that can be created easily (e.g. those involving [[loop (computing)|loops]] or [[recursion]]), as well as making it harder for users to reason effectively about their programs.<ref name="flux" /> A proof of concept compiler toolchain called Myia uses a subset of Python as a front end and supports higher-order functions, recursion, and higher-order derivatives.<ref>{{cite journal |last1=Merriënboer |first1=Bart van |last2=Breuleux |first2=Olivier |last3=Bergeron |first3=Arnaud |last4=Lamblin |first4=Pascal |title=Automatic differentiation in ML: where we are and where we should be going |journal=Proceedings of the 32nd International Conference on Neural Information Processing Systems |date=3 December 2018|volume=31 |pages=8771–8781|url = https://papers.nips.cc/paper/2018/hash/770f8e448d07586afbf77bb59f698587-Abstract.html}}</ref><ref name="myia1">{{Cite web|url=https://www.sysml.cc/doc/2018/39.pdf|title=Automatic Differentiation in Myia|access-date=2019-06-24}}</ref><ref name="pytorchtut">{{Cite web|url=https://pytorch.org/tutorials/beginner/examples_autograd/tf_two_layer_net.html|title=TensorFlow: Static Graphs|access-date=2019-03-04}}</ref>
▲* '''[[Operator overloading]], dynamic graph''' based approaches such as [[PyTorch]] and [[AutoGrad (NumPy)|AutoGrad]]. Their dynamic and interactive nature lets most programs be written and reasoned about more easily. However, they lead to [[interpreter (computing)|interpreter]] overhead (particularly when composing many small operations), poorer scalability, and reduced benefit from compiler optimization.<ref name="myia1" /><ref name="pytorchtut" /> A package for the [[Julia (programming language)|Julia]] programming language{{snd}} [https://github.com/FluxML/Zygote.jl Zygote]{{snd}} works directly on Julia's [[intermediate representation]], allowing it to still be [[compiler optimization|optimized]] by Julia's just-in-time compiler.<ref name="flux" /><ref>{{cite arXiv|last=Innes|first=Michael|date=2018-10-18|title=Don't Unroll Adjoint: Differentiating SSA-Form Programs|eprint=1810.07951|class=cs.PL}}</ref><ref name="diffprog-zygote" />
A limitation of earlier approaches is that they are only able to differentiate code written in a suitable manner for the framework, limiting their interoperability with other programs. Newer approaches resolve this issue by constructing the graph from the language's syntax or IR, allowing arbitrary code to be differentiated.<ref name="flux" /><ref name="myia1" />
==Applications==
Differentiable programming has been applied in areas such as combining [[deep learning]] with [[physics engines]] in [[robotics]],
==Multidisciplinary application==
Differentiable programming is making significant strides in various fields beyond its traditional applications. In healthcare and life sciences, for example, it is being used for deep learning in biophysics-based modelling of molecular mechanisms, in areas such as protein structure prediction and drug discovery. These applications demonstrate the potential of differentiable programming in contributing to significant advancements in understanding complex biological systems and improving healthcare solutions.<ref>{{cite journal |last1=AlQuraishi |first1=Mohammed |last2=Sorger |first2=Peter K. |title=Differentiable biology: using deep learning for biophysics-based and data-driven modeling of molecular mechanisms |journal=Nature Methods |date=October 2021 |volume=18 |issue=10 |pages=1169–1180 |doi=10.1038/s41592-021-01283-4 |pmid=34608321 |pmc=8793939 }}</ref>
==See also==
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{{Differentiable computing}}
▲{{Programming paradigms navbox}}
[[Category:Differential calculus]]
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