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Neural nets have been around for quite some time. They have become popular only in the last few years. How come?

Neural nets have been around for a long time. Why are they popular only now?

Geoffrey Hinton quickly addresses the question in his 'talk':https://www.youtube.com/watch?v=IcOMKXAw5VA&feature=youtu.be&t=21m29s

Here are two slides from Geoffrey Hinton's talk summarizing the problems:
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Watch the entire talk!
 

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I recommend the whole talk
https://www.youtube.com/watch?v=IcOMKXAw5VA&feature=youtu.be&t=21m29s

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