# A Method for Optimizing Connections in Differentiable Logic Gate Networks

arXiv: https://arxiv.org/abs/2507.06173 · HTML: https://mlsanity.com/paper/2507.06173/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 17 references that are in the map.
- First posted on arXiv 8 Jul 2025.

## Builds on (most cited first, 12 of 12)

- [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)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [Training Spiking Neural Networks Using Lessons From Deep Learning](https://mlsanity.com/paper/2109.12894/) (2021)
- [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 Differentiable Logic Gate Networks](https://mlsanity.com/paper/2210.08277/) (2022)
- [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)
- [Convolutional Differentiable Logic Gate Networks](https://mlsanity.com/paper/2411.04732/) (2024)
- [LUTNet: Rethinking Inference in FPGA Soft Logic](https://mlsanity.com/paper/1904.00938/) (2019)
- [TrueHappiness: Neuromorphic Emotion Recognition on TrueNorth](https://mlsanity.com/paper/1601.04183/) (2016)

## Built on by (most cited first, 5 of 5)

- [WARP-LUTs -- Walsh-Assisted Relaxation for Probabilistic Look Up Tables](https://mlsanity.com/paper/2510.15655/) (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)
- [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)

## Abstract (arXiv)

We introduce a novel method for partial optimization of the connections in Deep Differentiable Logic Gate Networks (LGNs). Our training method utilizes a probability distribution over a subset of connections per gate input, selecting the connection with highest merit, after which the gate-types are selected. We show that the connection-optimized LGNs outperform standard fixed-connection LGNs on the Yin-Yang, MNIST and Fashion-MNIST benchmarks, while requiring only a fraction of the number of logic gates. When training all connections, we demonstrate that 8000 simple logic gates are sufficient to achieve over 98% on the MNIST data set. Additionally, we show that our network has 24 times fewer gates, while performing better on the MNIST data set compared to standard fully connected LGNs. As such, our work shows a pathway towards fully trainable Boolean logic.