WARP Logic Neural Networks

Abstract: Fast and efficient AI inference is increasingly important, and recent models that directly learn low-level logic operations have achieved state-of-the-art performance. However, existing logic neural networks incur high training costs, introduce redundancy or rely on approximate gradients, which limits scalability. To overcome these limitations, we introduce WAlsh Relaxation for Probabilistic (WARP) logic neural networks -- a novel gradient-based framework that efficiently learns combinations of hardware-native logic blocks. We show that WARP yields the most parameter-efficient representation for exactly learning Boolean functions and that several prior approaches arise as restricted special cases. Training is improved by introducing learnable thresholding and residual initialization, while we bridge the gap between relaxed training and discrete logic inference through stochastic smoothing. Experiments demonstrate faster convergence than state-of-the-art baselines, while scaling effectively to deeper architectures and logic functions with higher input arity.