You should definitely have a look at theano that will probably run
much faster than pure numpy for this kind of models (esp. if you have
access to a GPU with the CUDA runtime).

http://deeplearning.net/software/theano/

The deep learning tutorial [1] have a section on backpropagation [2]
and also on RBMs and DBN. You should also have a look at the Efficient
Backprop paper by Lecun et al. [5]

[1] http://www.deeplearning.net/tutorial/
[2] http://www.deeplearning.net/tutorial/mlp.html#mlp
[3] http://www.deeplearning.net/tutorial/rbm.html#rbm
[4] http://www.deeplearning.net/tutorial/DBN.html#dbn
[5] http://yann.lecun.com/exdb/publis/#lecun-98b

Best,

-- 
Olivier

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