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：本文针对布尔集合引入变分概念，并以此为基础发展了布尔逻辑反向传播原理。基于这一概念，可构建权重与激活值均为布尔数、采用布尔逻辑而非实数运算的深度模型。特别地，布尔深度模型可直接在布尔域中进行训练，无需引入隐式权重。各层间传播与合成的并非梯度，而是逻辑运算。