Boolean Variation and Boolean Logic BackPropagation

The notion of variation is introduced for the <PRE_TAG>Boolean set</POST_TAG> and based on which <PRE_TAG>Boolean logic backpropagation</POST_TAG> principle is developed. Using this concept, deep models can be built with weights and activations being <PRE_TAG>Boolean numbers</POST_TAG> and operated with Boolean logic instead of real arithmetic. In particular, Boolean deep models can be trained directly in the <PRE_TAG>Boolean domain</POST_TAG> without latent weights. No gradient but logic is synthesized and backpropagated through layers.