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Most differentiable programming frameworks work by constructing a graph containing the control flow and [[data structures]] in the program.<ref name="flux">{{cite arxiv|last=Innes|first=Michael|last2=Saba|first2=Elliot|last3=Fischer|first3=Keno|last4=Gandhi|first4=Dhairya|last5=Rudilosso|first5=Marco Concetto|last6=Joy|first6=Neethu Mariya|last7=Karmali|first7=Tejan|last8=Pal|first8=Avik|last9=Shah|first9=Viral|date=2018-10-31|title=Fashionable Modelling with Flux|eprint=1811.01457|class=cs.PL}}</ref> Earlier attempts generally fall into two groups:
* ''' 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" /><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 cannot gain benefit from compiler optimization.<ref name="myia1" /><ref name="pytorchtut" />
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Both of these early approaches are only able to differentiate code written in a suitable manner for the framework, limiting their interoperability with other programs.
A more recent package in the [[Julia (programming language)|Julia]] programming language — [https://github.com/FluxML/Zygote.jl Zygote] — resolves the issues that earlier attempts faced by treating the language's syntax as the graph; the design of the Julia language makes it easy for the [[intermediate representation]] of arbitrary Julia code to be differentiated directly, [[compiler optimization|optimized]], and compiled.<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> An in-development differentiable programming language called [[Myia (programming language)|Myia]] also uses a similar approach
==See also==
* [[Machine learning]]
==Notes==
{{reflist|group=note}}
==References==
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