# Learning Accurate and Interpretable Decision Rule Sets from Neural Networks

arXiv: https://arxiv.org/abs/2103.02826 · HTML: https://mlsanity.com/paper/2103.02826/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 25 references that are in the map.
- First posted on arXiv 4 Mar 2021.

## Builds on (most cited first, 8 of 8)

- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Interpretable classifiers using rules and Bayesian analysis: Building a better stroke prediction model](https://mlsanity.com/paper/1511.01644/) (2015)
- [Boolean Decision Rules via Column Generation](https://mlsanity.com/paper/1805.09901/) (2018)
- [Interpretable Two-level Boolean Rule Learning for Classification](https://mlsanity.com/paper/1511.07361/) (2015)
- [L0-ARM: Network Sparsification via Stochastic Binary Optimization](https://mlsanity.com/paper/1904.04432/) (2019)

## Built on by (most cited first, 25 of 25)

- [A Comprehensive Survey on Self-Interpretable Neural Networks](https://mlsanity.com/paper/2501.15638/) (2025)
- [Differentiable Rule Induction with Learned Relational Features](https://mlsanity.com/paper/2201.06515/) (2022)
- [Learning Exceptional Subgroups by End-to-End Maximizing KL-divergence](https://mlsanity.com/paper/2402.12930/) (2024)
- [Neural-based classification rule learning for sequential data](https://mlsanity.com/paper/2302.11286/) (2023)
- [For Better or Worse: The Impact of Counterfactual Explanations' Directionality on User Behavior in xAI](https://mlsanity.com/paper/2306.07637/) (2023)
- [Compact Rule-Based Classifier Learning via Gradient Descent](https://mlsanity.com/paper/2502.01375/) (2025)
- [ESC-Rules: Explainable, Semantically Constrained Rule Sets](https://mlsanity.com/paper/2208.12523/) (2022)
- [RIFF: Inducing Rules for Fraud Detection from Decision Trees](https://mlsanity.com/paper/2408.12989/) (2024)
- [Differentiable Inductive Logic Programming for Fraud Detection](https://mlsanity.com/paper/2410.21928/) (2024)
- [Neuro-Symbolic Rule Lists](https://mlsanity.com/paper/2411.06428/) (2024)
- [Learning Interpretable Rules from Neural Networks: Neurosymbolic AI for Radar Hand Gesture Recognition](https://mlsanity.com/paper/2506.22443/) (2025)
- [Logic of Hypotheses: from Zero to Full Knowledge in Neurosymbolic Integration](https://mlsanity.com/paper/2509.21663/) (2025)
- [Personalized Interpretable Classification](https://mlsanity.com/paper/2302.02528/) (2023)
- [Explaining with Greater Support: Weighted Column Sampling Optimization for q-Consistent Summary-Explanations](https://mlsanity.com/paper/2302.04528/) (2023)
- [Hamming Encoder: Mining Discriminative k-mers for Discrete Sequence Classification](https://mlsanity.com/paper/2310.10321/) (2023)
- [Interpretable Classification via a Rule Network with Selective Logical Operators](https://mlsanity.com/paper/2408.11918/) (2024)
- [HorNets: Learning from Discrete and Continuous Signals with Routing Neural Networks](https://mlsanity.com/paper/2501.14346/) (2025)
- [Interpretable Representation Learning for Additive Rule Ensembles](https://mlsanity.com/paper/2506.20927/) (2025)
- [From Privacy to Trust in the Agentic Era: A Taxonomy of Challenges in Trustworthy Federated Learning Through the Lens of Trust Report 2.0](https://mlsanity.com/paper/2507.15796/) (2025)
- [RLIE: Rule Generation with Logistic Regression, Iterative Refinement, and Evaluation for Large Language Models](https://mlsanity.com/paper/2510.19698/) (2025)
- [A Fast Interpretable Fuzzy Tree Learner](https://mlsanity.com/paper/2512.11616/) (2025)
- [Evidential Rule Learning for Interpretable Classification with Abstention](https://mlsanity.com/paper/2608.05859/) (2026)
- [Sparse Oblique Rule Boosting for Simpler Additive Rule Ensembles](https://mlsanity.com/paper/2609.06426/) (2026)
- [Regional Explanations via Causal Sufficiency and Necessity](https://mlsanity.com/paper/2609.18049/) (2026)
- [Detecting Soft Errors in Parallel Software with LLM-tuned Instruction Duplication](https://mlsanity.com/paper/2609.19531/) (2026)

## Abstract (arXiv)

This paper proposes a new paradigm for learning a set of independent logical rules in disjunctive normal form as an interpretable model for classification. We consider the problem of learning an interpretable decision rule set as training a neural network in a specific, yet very simple two-layer architecture. Each neuron in the first layer directly maps to an interpretable if-then rule after training, and the output neuron in the second layer directly maps to a disjunction of the first-layer rules to form the decision rule set. Our representation of neurons in this first rules layer enables us to encode both the positive and the negative association of features in a decision rule. State-of-the-art neural net training approaches can be leveraged for learning highly accurate classification models. Moreover, we propose a sparsity-based regularization approach to balance between classification accuracy and the simplicity of the derived rules. Our experimental results show that our method can generate more accurate decision rule sets than other state-of-the-art rule-learning algorithms with better accuracy-simplicity trade-offs. Further, when compared with uninterpretable black-box machine learning approaches such as random forests and full-precision deep neural networks, our approach can easily find interpretable decision rule sets that have comparable predictive performance.