Well, for a single run of the network, that random binarized network is really noisy and any single output is pretty likely to be wrong.  But if you do this many times, those samples create a distribution which… amazingly… looks like a distribution you would want from a classifier! 5/

The paper – which is pretty short – goes into all of the details. But punchlines: 1) it works. With minimal impact on training, majority vote of samples gets pretty close to deterministic accuracy in classification. 6/