Boolean Variation and Boolean Logic BackPropagation
Van Minh Nguyen
TL;DR
The paper addresses the substantial compute and memory demands of gradient-based deep learning by introducing Boolean variation and Boolean logic backpropagation to train models entirely within the Boolean domain. It formalizes a variation-based calculus over Boolean logic, defines per-weight optimization and backpropagation rules, and demonstrates a Boolean neuron with a Logic Threshold Gate that uses a pre-activation $s$ and threshold $\tau$ to emit $y = T$ if $s \geq \tau$, else $F$. The key contributions include a full theoretical framework for Boolean variation, a concrete backpropagation-like mechanism using Boolean signals, and an empirical CIFAR-10 evaluation showing competitive performance, especially with batch normalization. This work suggests a pathway toward energy- and memory-efficient deep learning by eliminating real-valued gradients and relying on logic-based updates.
Abstract
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.