Can someone explain to me the benefits of using TensorFlow over Theano?
Theano is better for the expert, TF is better for the beginner.
Long term planning is the key, TF is a modeling tool, but TF-Learn is better for testing architectures and algorithms.
Once your ready to go to a production system you would need to ditch all, and fall back to a solid environ that support C++ and distributed systems.
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ML/DL by language/library
http://www.teglor.com/b/deep-learning-libraries-language-cm5...
Comparing Deep Language Software
https://en.m.wikipedia.org/wiki/Comparison_of_deep_learning_...
Note who support OPEN-MP, and who supports AMD GPU library's.
Long term most important consideration is how to you go to production.
Another problem with all this GOOGLE/AMAZON/MICROSOFT free ML/DL software is they all want to corral the users to a distributive system of running your algo's on THEIR servers for XXX $$/MIN, which means a taxi meter to run your own code; I think most people would prefer NOT to pay RENT to the NSA to research.
All these free frameworks are designed so that eventually people can 'automatically' have BIG-COMPANYS (NSA/CIA) keep their data & code and run it for them, which of course means in time little people may lose the ability to innovate and/or develop.