# Learning Interpretable Differentiable Logic Networks

arXiv: https://arxiv.org/abs/2407.04168 · HTML: https://mlsanity.com/paper/2407.04168/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 34 references that are in the map.
- First posted on arXiv 4 Jul 2024.

## Builds on (most cited first, 26 of 26)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Wide & Deep Learning for Recommender Systems](https://mlsanity.com/paper/1606.07792/) (2016)
- [Ray: A Distributed Framework for Emerging AI Applications](https://mlsanity.com/paper/1712.05889/) (2017)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [On Embeddings for Numerical Features in Tabular Deep Learning](https://mlsanity.com/paper/2203.05556/) (2022)
- [FINN: A Framework for Fast, Scalable Binarized Neural Network Inference](https://mlsanity.com/paper/1612.07119/) (2016)
- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [Generalized and Scalable Optimal Sparse Decision Trees](https://mlsanity.com/paper/2006.08690/) (2020)
- [Supersparse Linear Integer Models for Optimized Medical Scoring Systems](https://mlsanity.com/paper/1502.04269/) (2015)
- [Deep Differentiable Logic Gate Networks](https://mlsanity.com/paper/2210.08277/) (2022)
- [Scalable Rule-Based Representation Learning for Interpretable Classification](https://mlsanity.com/paper/2109.15103/) (2021)
- [Learning Algorithms via Neural Logic Networks](https://mlsanity.com/paper/1904.01554/) (2019)
- [Learning Symbolic Expressions via Gumbel-Max Equation Learner Networks](https://mlsanity.com/paper/2012.06921/) (2020)
- [Neural Logic Networks](https://mlsanity.com/paper/1910.08629/) (2019)

## Built on by (most cited first, 10 of 10)

- [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)
- [Scalable Interconnect Learning in Boolean Networks](https://mlsanity.com/paper/2507.02585/) (2025)
- [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)
- [Differentiable Weightless Controllers: Learning Logic Circuits for Continuous Control](https://mlsanity.com/paper/2512.01467/) (2025)
- [LogicIR: Logic Gate Networks for Image Restoration](https://mlsanity.com/paper/2606.26609/) (2026)
- [Learning Interpretable Differentiable Logic Networks for Time-Series Classification](https://mlsanity.com/paper/2508.17512/) (2025)
- [A Composite Activation Function for Learning Stable Binary Representations](https://mlsanity.com/paper/2605.11558/) (2026)
- [Beyond Affine Transformations: A Soft Dominance Layer for Coordinate-Wise Neural Computation](https://mlsanity.com/paper/2610.00563/) (2026)

## Abstract (arXiv)

The ubiquity of neural networks (NNs) in real-world applications, from healthcare to natural language processing, underscores their immense utility in capturing complex relationships within high-dimensional data. However, NNs come with notable disadvantages, such as their "black-box" nature, which hampers interpretability, as well as their tendency to overfit the training data. We introduce a novel method for learning interpretable differentiable logic networks (DLNs) that are architectures that employ multiple layers of binary logic operators. We train these networks by softening and differentiating their discrete components, e.g., through binarization of inputs, binary logic operations, and connections between neurons. This approach enables the use of gradient-based learning methods. Experimental results on twenty classification tasks indicate that differentiable logic networks can achieve accuracies comparable to or exceeding that of traditional NNs. Equally importantly, these networks offer the advantage of interpretability. Moreover, their relatively simple structure results in the number of logic gate-level operations during inference being up to a thousand times smaller than NNs, making them suitable for deployment on edge devices.