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The EBP method is indeed capable of learning binary NNs in a fairly effective way. The catch is though that using binary models directly (i.e. the MAP solution) at test time directly does not seem to lead to competitive results (see column "Binary EBP-D" in Table 1: the error rate is >= doubled for 4 datasets out of 7). What seems to work well is Bayesian model averaging with the binary model ("Binary EBP-P") but this is again a'continuous' computation which is at least as expensive as the computation with a normal NN. At the very least the authors need to clarify this point, currently, as the binary version is the key motivation of this research (see the first paragraph of the paper).