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

翻译：本文引入布尔集上的变分概念，并基于此发展了布尔逻辑反向传播原理。利用该概念，可构建权重与激活值为布尔数且通过布尔逻辑（而非实数运算）运行的深度模型。特别地，布尔深度模型可直接在布尔域内进行训练而无需潜在权重。通过各层合成并反向传播的是逻辑而非梯度。