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And around ~2012, a bunch of researchers have reported you don't even need 2nd-derivative information. You just have to initialize the neural net properly.

This sounds very interesting. How do you property initialize the weights? Do you have a link to a paper about this?

Check out this paper:

Practical recommendations for gradient-based training of deep architectures, Y. Bengio

http://arxiv.org/abs/1206.5533

There is a section on weight initialization on page 15. In general, this paper has a lot of good information in one place.

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