  Binary networks are extremely efficient as they use only two symbols to
define the network: $\{+1,-1\}$. One can make the prior distribution of these
symbols a design choice. The recent IR-Net of Qin et al. argues that imposing a
Bernoulli distribution with equal priors (equal bit ratios) over the binary
weights leads to maximum entropy and thus minimizes information loss. However,
prior work cannot precisely control the binary weight distribution during
training, and therefore cannot guarantee maximum entropy. Here, we show that
quantizing using optimal transport can guarantee any bit ratio, including equal
ratios. We investigate experimentally that equal bit ratios are indeed
preferable and show that our method leads to optimization benefits. We show
that our quantization method is effective when compared to state-of-the-art
binarization methods, even when using binary weight pruning.
