# Interpretable Classification via a Rule Network with Selective Logical Operators

arXiv: https://arxiv.org/abs/2408.11918 · HTML: https://mlsanity.com/paper/2408.11918/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 64 references that are in the map.
- First posted on arXiv 21 Aug 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)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [Revisiting Deep Learning Models for Tabular Data](https://mlsanity.com/paper/2106.11959/) (2021)
- [TabNet: Attentive Interpretable Tabular Learning](https://mlsanity.com/paper/1908.07442/) (2019)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [TabTransformer: Tabular Data Modeling Using Contextual Embeddings](https://mlsanity.com/paper/2012.06678/) (2020)
- [SAINT: Improved Neural Networks for Tabular Data via Row Attention and Contrastive Pre-Training](https://mlsanity.com/paper/2106.01342/) (2021)
- [Distilling a Neural Network Into a Soft Decision Tree](https://mlsanity.com/paper/1711.09784/) (2017)
- [Bi-Real Net: Enhancing the Performance of 1-bit CNNs With Improved Representational Capability and Advanced Training Algorithm](https://mlsanity.com/paper/1808.00278/) (2018)
- [Understanding Straight-Through Estimator in Training Activation Quantized Neural Nets](https://mlsanity.com/paper/1903.05662/) (2019)
- [Interpretable classifiers using rules and Bayesian analysis: Building a better stroke prediction model](https://mlsanity.com/paper/1511.01644/) (2015)
- [XNOR-Net++: Improved Binary Neural Networks](https://mlsanity.com/paper/1909.13863/) (2019)
- [Deep Differentiable Logic Gate Networks](https://mlsanity.com/paper/2210.08277/) (2022)
- [Scalable Bayesian Rule Lists](https://mlsanity.com/paper/1602.08610/) (2016)
- [Scalable Rule-Based Representation Learning for Interpretable Classification](https://mlsanity.com/paper/2109.15103/) (2021)
- [Exact and Consistent Interpretation for Piecewise Linear Neural Networks: A Closed Form Solution](https://mlsanity.com/paper/1802.06259/) (2018)
- [Learning Accurate and Interpretable Decision Rule Sets from Neural Networks](https://mlsanity.com/paper/2103.02826/) (2021)
- [Learning Algorithms via Neural Logic Networks](https://mlsanity.com/paper/1904.01554/) (2019)
- [Transparent Classification with Multilayer Logical Perceptrons and Random Binarization](https://mlsanity.com/paper/1912.04695/) (2019)
- [Learning Interpretable Rules for Scalable Data Representation and Classification](https://mlsanity.com/paper/2310.14336/) (2023)
- [Self-Binarizing Networks](https://mlsanity.com/paper/1902.00730/) (2019)
- [Straight-Through Estimator as Projected Wasserstein Gradient Flow](https://mlsanity.com/paper/1910.02176/) (2019)
- [Logical Activation Functions: Logit-space equivalents of Probabilistic Boolean Operators](https://mlsanity.com/paper/2110.11940/) (2021)
- [Probabilistic Truly Unordered Rule Sets](https://mlsanity.com/paper/2401.09918/) (2024)

## Abstract (arXiv)

We introduce the Rule Network with Selective Logical Operators (RNS), a novel neural architecture that employs selective logical operators to adaptively choose between AND and OR operations at each neuron during training. Unlike existing approaches that rely on fixed architectural designs with predetermined logical operations, our selective logical operators treat weight parameters as hard selectors, enabling the network to automatically discover optimal logical structures while learning rules. The core innovation lies in our selective logical operators implemented through specialized Logic Selection Layers (LSLs) with adaptable AND/OR neurons, a Negation Layer for input negations, and a Heterogeneous Connection Constraint (HCC) to streamline neuron connections. We demonstrate that this selective logical operator framework can be effectively optimized using adaptive gradient updates with the Straight-Through Estimator to overcome gradient vanishing challenges. Through extensive experiments on 13 datasets, RNS demonstrates superior classification performance, rule quality, and efficiency compared to 25 state-of-the-art alternatives, showcasing the power of RNS in rule learning. Code and data are available at https://anonymous.4open.science/r/RNS_-3DDD.