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* ''' 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
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.
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