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The recent progress in neural networks is summarized by a sequence of novel architectures characterized mainly by its growing design complexity. From LeNet5 (1994) to AlexNet (2012), to Overfeat (2013) and GoogleLeNet/Inception (2014) and so on...

Is there any attempt to let the machine decide/design which architecture to be used depending on the data?

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You may also want to look at the literature on neuro-evolution. Examples:

Reinforcement learning:

Miscellaneous:

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It seems research is moving towards such direction:

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Google's AutoML is one such example. It was successfully applied on the ImageNet dataset, resulting NASNet, which as of this writing, has surpassed all other models in terms of accuracy. The main paper is here:

Learning Transferable Architectures for Scalable Image Recognition -- Zoph, et. al.

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