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This is the trained neural network for the XOR operator:

enter image description here

Can I find something like a trained network for recognizing hand writing digits somewhere on the internet? Is there an "official format" for trained neural networks?

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    $\begingroup$ Yes there is popular ("official format") for trained neural network model, for example tensorflow use .pb file to store the model weights and biases $\endgroup$ Oct 11 '17 at 15:36
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What about the super popular and classical MINIST? Tensorflow has a nice tutorial:

https://www.tensorflow.org/get_started/mnist/beginners

Just follow the instructions!

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There are many pre-trained models but for more complicated task, I recommend to check out Caffe Model Zoo.

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