Fast and efficient machine learning is of growing interest to the scientific community and has spurred significant research into novel model architectures and hardware-aware design. Recent hard? and software co-design approaches have demonstrated impressive results with entirely multiplication-free models. Differentiable Logic Gate Networks (DLGNs), for instance, provide a gradient-based framework for learning optimal combinations of low-level logic gates, setting state-of-the-art trade-offs between accuracy, resource usage, and latency. However, these models suffer from high computational cost during training and do not generalize well to logic blocks with more inputs. In this work, we introduce Walsh-Assisted Relaxation for Probabilistic Look-Up Tables (WARP-LUTs) - a novel gradient-based method that efficiently learns combinations of logic gates with substantially fewer trainable parameters. We demonstrate that WARP-LUTs achieve significantly faster convergence on CIFAR-10 compared to DLGNs, while maintaining comparable accuracy. Furthermore, our approach suggests potential for extension to higher-input logic blocks, motivating future research on extremely efficient deployment on modern FPGAs and its real-time science applications.

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