# WARP Logic Neural Networks

arXiv: https://arxiv.org/abs/2602.03527 · HTML: https://mlsanity.com/paper/2602.03527/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 42 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [Training Neural Networks with Fixed Sparse Masks](https://mlsanity.com/paper/2111.09839/) (2021)
- [Binary Neural Networks: A Survey](https://mlsanity.com/paper/2004.03333/) (2020)
- [The Unreasonable Effectiveness of Random Pruning: Return of the Most Naive Baseline for Sparse Training](https://mlsanity.com/paper/2202.02643/) (2022)
- [AdderNet: Do We Really Need Multiplications in Deep Learning?](https://mlsanity.com/paper/1912.13200/) (2019)
- [Deep Differentiable Logic Gate Networks](https://mlsanity.com/paper/2210.08277/) (2022)
- [DeepShift: Towards Multiplication-Less Neural Networks](https://mlsanity.com/paper/1905.13298/) (2019)
- [Fast convolutional neural networks on FPGAs with hls4ml](https://mlsanity.com/paper/2101.05108/) (2021)
- [Convolutional Differentiable Logic Gate Networks](https://mlsanity.com/paper/2411.04732/) (2024)
- [PolyLUT: Learning Piecewise Polynomials for Ultra-Low Latency FPGA LUT-based Inference](https://mlsanity.com/paper/2309.02334/) (2023)
- [Differentiable Weightless Neural Networks](https://mlsanity.com/paper/2410.11112/) (2024)
- [NeuraLUT: Hiding Neural Network Density in Boolean Synthesizable Functions](https://mlsanity.com/paper/2403.00849/) (2024)
- [TreeLUT: An Efficient Alternative to Deep Neural Networks for Inference Acceleration Using Gradient Boosted Decision Trees](https://mlsanity.com/paper/2501.01511/) (2025)
- [NeuraLUT-Assemble: Hardware-aware Assembling of Sub-Neural Networks for Efficient LUT Inference](https://mlsanity.com/paper/2504.00592/) (2025)
- [Weightless Neural Networks for Efficient Edge Inference](https://mlsanity.com/paper/2203.01479/) (2022)
- [KANEL'E: Kolmogorov-Arnold Networks for Efficient LUT-based Evaluation](https://mlsanity.com/paper/2512.12850/) (2025)
- [Learning Interpretable Differentiable Logic Networks](https://mlsanity.com/paper/2407.04168/) (2024)
- [Light Differentiable Logic Gate Networks](https://mlsanity.com/paper/2510.03250/) (2025)
- [A Method for Optimizing Connections in Differentiable Logic Gate Networks](https://mlsanity.com/paper/2507.06173/) (2025)
- [Scalable Interconnect Learning in Boolean Networks](https://mlsanity.com/paper/2507.02585/) (2025)
- [BOLD: Boolean Logic Deep Learning](https://mlsanity.com/paper/2405.16339/) (2024)
- [nanoML for Human Activity Recognition](https://mlsanity.com/paper/2502.12173/) (2025)

## Built on by (most cited first, 2 of 2)

- [From Arithmetic to Logic: The Resilience of Logic and Lookup-Based Neural Networks Under Parameter Bit-Flips](https://mlsanity.com/paper/2603.22770/) (2026)
- [Task-Aware Discretization of Differentiable Logic Gate Networks](https://mlsanity.com/paper/2609.33747/) (2026)

## Abstract (arXiv)

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.