partialmathbbB nets: learning discrete functions by gradient descent

partialmathbbB nets are differentiable neural networks that learn discrete boolean-valued functions by gradient descent. partialmathbbB nets have two semantically equivalent aspects: a differentiable soft-net, with real weights, and a non-differentiable hard-net, with boolean weights. We train the soft-net by backpropagation and then `harden' the learned weights to yield boolean weights that bind with the hard-net. The result is a learned discrete function. `Hardening' involves no loss of accuracy, unlike existing approaches to neural network binarization. Preliminary experiments demonstrate that partialmathbbB nets achieve comparable performance on standard machine learning problems yet are compact (due to 1-bit weights) and interpretable (due to the logical nature of the learnt functions).