# Fully Trainable Deep Differentiable Logic Gate Networks and Lookup Table Networks

arXiv: https://arxiv.org/abs/2607.09399 · HTML: https://mlsanity.com/paper/2607.09399/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 23 references that are in the map.
- First posted on arXiv 10 Jul 2026.

## Builds on (most cited first, 15 of 15)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [Spiking-YOLO: Spiking Neural Network for Energy-Efficient Object Detection](https://mlsanity.com/paper/1903.06530/) (2019)
- [Compute Trends Across Three Eras of Machine Learning](https://mlsanity.com/paper/2202.05924/) (2022)
- [Deep Neuroevolution: Genetic Algorithms Are a Competitive Alternative for Training Deep Neural Networks for Reinforcement Learning](https://mlsanity.com/paper/1712.06567/) (2017)
- [LogicNets: Co-Designed Neural Networks and Circuits for Extreme-Throughput Applications](https://mlsanity.com/paper/2004.03021/) (2020)
- [STDP Based Pruning of Connections and Weight Quantization in Spiking Neural Networks for Energy Efficient Recognition](https://mlsanity.com/paper/1710.04734/) (2017)
- [Q-SpiNN: A Framework for Quantizing Spiking Neural Networks](https://mlsanity.com/paper/2107.01807/) (2021)
- [PolyLUT: Learning Piecewise Polynomials for Ultra-Low Latency FPGA LUT-based Inference](https://mlsanity.com/paper/2309.02334/) (2023)
- [NeuraLUT: Hiding Neural Network Density in Boolean Synthesizable Functions](https://mlsanity.com/paper/2403.00849/) (2024)
- [WARP-LUTs -- Walsh-Assisted Relaxation for Probabilistic Look Up Tables](https://mlsanity.com/paper/2510.15655/) (2025)
- [TrueHappiness: Neuromorphic Emotion Recognition on TrueNorth](https://mlsanity.com/paper/1601.04183/) (2016)
- [Inter-patient ECG Arrhythmia Classification with LGNs and LUTNs](https://mlsanity.com/paper/2601.11433/) (2026)

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

- [On the Depth Scalability of Logic Gate Networks](https://mlsanity.com/paper/2607.21633/) (2026)
- [DiffLUT-Net: Differentiable Training of FPGA LUT Networks with Learnable Connectivity](https://mlsanity.com/paper/2609.09254/) (2026)

## Abstract (arXiv)

We introduce a novel method for both partial and full optimization of the connections in deep differentiable logic gate networks (LGNs) and lookup table networks (LUTNs). Our training method utilizes a probability distribution over a set of connections per gate/lookup table (LUT) input pin, selecting the connection with highest merit, all whilst the optimal gate types or LUT-entries are learned in parallel. We show that the connection-optimized LGNs outperform standard fixed-connection LGNs on the Yin-Yang, MNIST Handwritten Digits and Fashion-MNIST benchmarks, while requiring only a fraction of the number of logic gates. We achieve 98.92% on the MNIST dataset with two layers of 8000 gates. With only one layer of 8000 gates, we obtain 98.45%, showing that our method requires almost 50 times fewer gates compared to fixed-connection LGNs. Training stability up to ten layers has been ensured by employing a high learning rate, straight-through estimators and trimming constant-output gate types. Additionally, we present a LUT neuron description that enables stable training with backpropagation, tested up to 6-layer deep networks. The model requires four times fewer trainable parameters and still achieves a higher accuracy compared to the fixed-connection LGN training algorithm. Our connection-training algorithm also works well for the LUTNs, achieving an accuracy of 98.88% for two layers of 2000 6-input LUTs.