Deep Differentiable Logic Gate Networks Based on Fuzzy Łukasiewicz T-norm

Differentiable Logic Gate Networks (DLNs) offer a compelling framework for symbolic interpretability and reducing inference cost.Building on prior works using Menger and Zadeh T-norms, we investigate the ukasiewicz T-norm as an alternative relaxation for classical logic gates.While it provides strong gradients in some regions, its flat areas result in vanishing gradients that hinder training.To address this issue, we use an initialization strategy that is analogous to residual connection in Neural Networks to encourage error signal propagation during training.Our empirical results show that ukasiewicz based DLNs, though slightly less accurate, benefit from faster inference and lower memory requirements compared to Neural Networks, giving the opportunity of practical application in, e.g., resource constrained devices.Due to the structural clarity, DLNs facilitate direct inspection and tracing of information flow, which makes them suitable for application in explainable artificial intelligence (XAI).