Approximating Deep Neural Networks (DNNs) with Binarized Neural Networks (BNNs) I am working currently as a research intern on Binarized Neural Networks where the weights and the activations of the network are binary. The architecture of this type of networks makes them memory efficient and computationally efficient, which makes them ideal for resource constrained environments, like embedded devices and mobile phones.

The interesting part about BNNs is that we can encode a binarized network as a CNF formula (Boolean Formula). Using this formula, we can verify some properties of the network like Robustness against adversarial examples (carefully crafted samples looking similar to usual inputs but designed to mislead a pre-trained model). We can also extract explanations that support neural network decisions, hence make the neural network explainable.

Currently, I am trying to make a DNN explainable by verifying its decisions using BNNs. The first direction of research is to reduce a DNN to a BNN. Of course the two networks should be equivalent. I am researching ways to make this reduction but I haven't found any works in the subject. 
Is it possible to carry out this transformation ? Is there any techniques that can "binarize" a DNN ?

Thanks :)
I expect you'll run into two challenges in this line of research: (1) there are no known ways to construct a BNN that exactly matches an ordinary neural network; (2) verifying a BNN with a SAT solver won't scale to the size models needed for most interesting tasks.

Since you asked specifically about (1), no, I don't know of any way to do that.  Probably you won't find exact equivalence.  You might be able to train a BNN that has a very high agreement with the ordinary neural network on the training set; I don't know whether it will have the same adversarial examples or not.