The notion of Boolean logic backpropagation was introduced to build neural networks with weights and activations being Boolean numbers. Most of computations can be done with Boolean logic instead of real arithmetic, both during training and inference phases. But the underlying discrete optimization problem is NP-hard, and the Boolean logic has no guarantee. In this work we propose the first convergence analysis, under standard non-convex assumptions.

翻译：布尔逻辑反向传播的概念被引入，用于构建权重和激活均为布尔数的神经网络。在训练和推理阶段，大部分计算可通过布尔逻辑而非实数运算完成。但其所涉及的离散优化问题本质上是NP难的，且布尔逻辑不具备收敛保证。本研究首次在标准非凸假设下提出收敛性分析。