Practical Boolean Backpropagation
Simon Golbert
TL;DR
The paper addresses training neural networks using purely Boolean computations to eliminate numeric gradients and floating-point operations. It introduces a composite gate $y = \bigvee_{i=1}^{n} (x_i \wedge w_i) \oplus b$, a Row Activation operator $Z = \mathcal{A}(X,W)$, and a fully connected layer $Y = \mathcal{A}(X,W) \oplus B$ to enable Boolean inference. Training is framed via Activation Sensitivity and Error Projection, with both general and specialized backpropagation procedures that produce difference masks $D^w$ and $D^x$ to adjust weights and propagate errors across layers. A specialized variant reduces computational load at the cost of learning capacity, and initial experiments on MNIST with a 4-layer architecture show feasibility, achieving around 75% accuracy after 30 minutes on a laptop CPU. Overall, the work demonstrates a viable path toward purely Boolean training, highlighting practical trade-offs and directions for scalable Boolean hardware learning.
Abstract
Boolean neural networks offer hardware-efficient alternatives to real-valued models. While quantization is common, purely Boolean training remains underexplored. We present a practical method for purely Boolean backpropagation for networks based on a single specific gate we chose, operating directly in Boolean algebra involving no numerics. Initial experiments confirm its feasibility.