# Convolutional Differentiable Logic Gate Networks

arXiv: https://arxiv.org/abs/2411.04732 · HTML: https://mlsanity.com/paper/2411.04732/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 46 references that are in the map.
- First posted on arXiv 7 Nov 2024.

## Builds on (most cited first, 28 of 28)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [PACT: Parameterized Clipping Activation for Quantized Neural Networks](https://mlsanity.com/paper/1805.06085/) (2018)
- [Differentiable Soft Quantization: Bridging Full-Precision and Low-Bit Neural Networks](https://mlsanity.com/paper/1908.05033/) (2019)
- [Binary Neural Networks: A Survey](https://mlsanity.com/paper/2004.03333/) (2020)
- [Forward and Backward Information Retention for Accurate Binary Neural Networks](https://mlsanity.com/paper/1909.10788/) (2019)
- [FINN: A Framework for Fast, Scalable Binarized Neural Network Inference](https://mlsanity.com/paper/1612.07119/) (2016)
- [More ConvNets in the 2020s: Scaling up Kernels Beyond 51x51 using Sparsity](https://mlsanity.com/paper/2207.03620/) (2022)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)
- [The Unreasonable Effectiveness of Random Pruning: Return of the Most Naive Baseline for Sparse Training](https://mlsanity.com/paper/2202.02643/) (2022)
- [Convolutional Networks for Fast, Energy-Efficient Neuromorphic Computing](https://mlsanity.com/paper/1603.08270/) (2016)
- [Deep Differentiable Logic Gate Networks](https://mlsanity.com/paper/2210.08277/) (2022)
- [Compute and Energy Consumption Trends in Deep Learning Inference](https://mlsanity.com/paper/2109.05472/) (2021)
- [AdaBin: Improving Binary Neural Networks with Adaptive Binary Sets](https://mlsanity.com/paper/2208.08084/) (2022)
- [FracBNN: Accurate and FPGA-Efficient Binary Neural Networks with Fractional Activations](https://mlsanity.com/paper/2012.12206/) (2020)
- [LUTNet: Rethinking Inference in FPGA Soft Logic](https://mlsanity.com/paper/1904.00938/) (2019)
- [Differentiable Weightless Neural Networks](https://mlsanity.com/paper/2410.11112/) (2024)
- [LUTNet: Learning FPGA Configurations for Highly Efficient Neural Network Inference](https://mlsanity.com/paper/1910.12625/) (2019)
- [Balanced Binary Neural Networks with Gated Residual](https://mlsanity.com/paper/1909.12117/) (2019)
- [Don't Be So Dense: Sparse-to-Sparse GAN Training Without Sacrificing Performance](https://mlsanity.com/paper/2203.02770/) (2022)
- [A Scalable, Interpretable, Verifiable & Differentiable Logic Gate Convolutional Neural Network Architecture From Truth Tables](https://mlsanity.com/paper/2208.08609/) (2022)
- [RBNN: Memory-Efficient Reconfigurable Deep Binary Neural Network with IP Protection for Internet of Things](https://mlsanity.com/paper/2105.03822/) (2021)
- [RedBit: An End-to-End Flexible Framework for Evaluating the Accuracy of Quantized CNNs](https://mlsanity.com/paper/2301.06193/) (2023)

## Built on by (most cited first, 30 of 37)

- [A Comprehensive Survey on Self-Interpretable Neural Networks](https://mlsanity.com/paper/2501.15638/) (2025)
- [Differentiable Logic Cellular Automata: From Game of Life to Pattern Generation](https://mlsanity.com/paper/2506.04912/) (2025)
- [Light Differentiable Logic Gate Networks](https://mlsanity.com/paper/2510.03250/) (2025)
- [WARP-LUTs -- Walsh-Assisted Relaxation for Probabilistic Look Up Tables](https://mlsanity.com/paper/2510.15655/) (2025)
- [LILogic Net: Compact Logic Gate Networks with Learnable Connectivity for Efficient Hardware Deployment](https://mlsanity.com/paper/2511.12340/) (2025)
- [A Method for Optimizing Connections in Differentiable Logic Gate Networks](https://mlsanity.com/paper/2507.06173/) (2025)
- [Logic Gate Neural Networks are Good for Verification](https://mlsanity.com/paper/2505.19932/) (2025)
- [Scalable Interconnect Learning in Boolean Networks](https://mlsanity.com/paper/2507.02585/) (2025)
- [LL-ViT: Edge Deployable Vision Transformers with Look Up Table Neurons](https://mlsanity.com/paper/2511.00812/) (2025)
- [Explicit Fuzzy Logic in the Feed-Forward Layer: Self-Forgetting Quantifiers Discover Legible Grammatical-Licensing Detectors](https://mlsanity.com/paper/2606.31845/) (2026)
- [Learning Interpretable Differentiable Logic Networks for Tabular Regression](https://mlsanity.com/paper/2505.23615/) (2025)
- [WARP Logic Neural Networks](https://mlsanity.com/paper/2602.03527/) (2026)
- [Polynomial Surrogate Training for Differentiable Ternary Logic Gate Networks](https://mlsanity.com/paper/2603.00302/) (2026)
- [Logic of Hypotheses: from Zero to Full Knowledge in Neurosymbolic Integration](https://mlsanity.com/paper/2509.21663/) (2025)
- [From MNIST to ImageNet: Understanding the Scalability Boundaries of Differentiable Logic Gate Networks](https://mlsanity.com/paper/2509.25933/) (2025)
- [Differentiable Weightless Controllers: Learning Logic Circuits for Continuous Control](https://mlsanity.com/paper/2512.01467/) (2025)
- [Inter-patient ECG Arrhythmia Classification with LGNs and LUTNs](https://mlsanity.com/paper/2601.11433/) (2026)
- [Differentiable Logic Synthesis: Spectral Coefficient Selection via Sinkhorn-Constrained Composition](https://mlsanity.com/paper/2601.13953/) (2026)
- [Learning Compact Boolean Networks](https://mlsanity.com/paper/2602.05830/) (2026)
- [BitLogic: Training Framework for Gradient-Based FPGA-Native Neural Networks](https://mlsanity.com/paper/2602.07400/) (2026)
- [LogicIR: Logic Gate Networks for Image Restoration](https://mlsanity.com/paper/2606.26609/) (2026)
- [FPGN: Redefining Ultra-Fast Programmable Gate-based Neural Acceleration with Differentiable LUTs](https://mlsanity.com/paper/2607.08427/) (2026)
- [GLANCE: Graph Logic Attention Network with Cluster Enhancement for Heterophilous Graph Representation Learning](https://mlsanity.com/paper/2507.18521/) (2025)
- [Learning Interpretable Differentiable Logic Networks for Time-Series Classification](https://mlsanity.com/paper/2508.17512/) (2025)
- [A Framework Based on Graph Cellular Automata for Similarity Evaluation in Urban Spatial Networks](https://mlsanity.com/paper/2511.00768/) (2025)
- [Hardware Software Optimizations for Fast Model Recovery on Reconfigurable Architectures](https://mlsanity.com/paper/2512.06113/) (2025)
- [Chimera: Neuro-Symbolic Attention Primitives for Trustworthy Dataplane Intelligence](https://mlsanity.com/paper/2602.12851/) (2026)
- [TT-Sparse: Learning Sparse Rule Models with Differentiable Truth Tables](https://mlsanity.com/paper/2603.07606/) (2026)
- [From Arithmetic to Logic: The Resilience of Logic and Lookup-Based Neural Networks Under Parameter Bit-Flips](https://mlsanity.com/paper/2603.22770/) (2026)
- [THEIA: Learning Complete Kleene Three-Valued Logic in a Pure-Neural Modular Architecture](https://mlsanity.com/paper/2604.11284/) (2026)

## Abstract (arXiv)

With the increasing inference cost of machine learning models, there is a growing interest in models with fast and efficient inference. Recently, an approach for learning logic gate networks directly via a differentiable relaxation was proposed. Logic gate networks are faster than conventional neural network approaches because their inference only requires logic gate operators such as NAND, OR, and XOR, which are the underlying building blocks of current hardware and can be efficiently executed. We build on this idea, extending it by deep logic gate tree convolutions, logical OR pooling, and residual initializations. This allows scaling logic gate networks up by over one order of magnitude and utilizing the paradigm of convolution. On CIFAR-10, we achieve an accuracy of 86.29% using only 61 million logic gates, which improves over the SOTA while being 29x smaller.