mlsanityData to 7 Oct 2026

Scalable Rule-Based Representation Learning for Interpretable Classification

arXiv 2109.15103 ↗First posted 30 Sep 2021cs.LG cs.AIcited by 40

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Abstract (arXiv)

Rule-based models, e.g., decision trees, are widely used in scenarios demanding high model interpretability for their transparent inner structures and good model expressivity. However, rule-based models are hard to optimize, especially on large data sets, due to their discrete parameters and structures. Ensemble methods and fuzzy/soft rules are commonly used to improve performance, but they sacrifice the model interpretability. To obtain both good scalability and interpretability, we propose a new classifier, named Rule-based Representation Learner (RRL), that automatically learns interpretable non-fuzzy rules for data representation and classification. To train the non-differentiable RRL effectively, we project it to a continuous space and propose a novel training method, called Gradient Grafting, that can directly optimize the discrete model using gradient descent. An improved design of logical activation functions is also devised to increase the scalability of RRL and enable it to discretize the continuous features end-to-end. Exhaustive experiments on nine small and four large data sets show that RRL outperforms the competitive interpretable approaches and can be easily adjusted to obtain a trade-off between classification accuracy and model complexity for different scenarios. Our code is available at: https://github.com/12wang3/rrl.

Key facts. Cited by 40 papers in the map (data through 7 Oct 2026). Builds on 22 of its 55 references that are in the map. First posted on arXiv 30 Sep 2021.

Builds on

22 of 55 references.

References · 22

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
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10 more
  1. 2015Interpretable classifiers using rules and Bayesian analysis: Building a better stroke prediction modelcited by 140
  2. 2020Generalized and Scalable Optimal Sparse Decision Treescited by 98
  3. 2018Deep Neural Decision Treescited by 72
  4. 2016Scalable Bayesian Rule Listscited by 64
  5. 2018ProxQuant: Quantized Neural Networks via Proximal Operatorscited by 56
  6. 2019Generalized Linear Rule Modelscited by 34
  7. 2018Exact and Consistent Interpretation for Piecewise Linear Neural Networks: A Closed Form Solutioncited by 31
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 7; 2023: 11; 2024: 6; 2025: 8; 2026: 7.

40 papers.

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  1. 2023Learning Transformer Programscited by 40
  2. 2021Defining and Quantifying the Emergence of Sparse Concepts in DNNscited by 36
  3. 2023ExcelFormer: A neural network surpassing GBDTs on tabular datacited by 33
  4. 2023Assessing the Quality of Multiple-Choice Questions Using GPT-4 and Rule-Based Methodscited by 23
  5. 2025A Comprehensive Survey on Self-Interpretable Neural Networkscited by 18
  6. 2023Can LLMs like GPT-4 outperform traditional AI tools in dementia diagnosis? Maybe, but not todaycited by 14
  7. 2024Learning Interpretable Differentiable Logic Networkscited by 10
  8. 2022Differentiable Rule Induction with Learned Relational Featurescited by 8
  9. 2022Neuro-symbolic Models for Interpretable Time Series Classification using Temporal Logic Descriptioncited by 7
  10. 2023Finding Interpretable Class-Specific Patterns through Efficient Neural Searchcited by 5
  11. 2024Learning Exceptional Subgroups by End-to-End Maximizing KL-divergencecited by 5
  12. 2022A Scalable, Interpretable, Verifiable & Differentiable Logic Gate Convolutional Neural Network Architecture From Truth Tablescited by 4
28 more
  1. 2022Manifoldron: Direct Space Partition via Manifold Discoverycited by 2
  2. 2025Compact Rule-Based Classifier Learning via Gradient Descentcited by 2
  3. 2025Learning Interpretable Differentiable Logic Networks for Tabular Regressioncited by 2
  4. 2025Neural Logic Networks for Interpretable Classificationcited by 2
  5. 2022RuDi: Explaining Behavior Sequence Models by Automatic Statistics Generation and Rule Distillationcited by 1
  6. 2022Learning to Advise Humans in High-Stakes Settingscited by 1
  7. 2023An Interpretable Loan Credit Evaluation Method Based on Rule Representation Learnercited by 1
  8. 2023The Computational Complexity of Concise Hypersphere Classificationcited by 1
  9. 2024Neuro-Symbolic Rule Listscited by 1
  10. 2022Bayes Point Rule Set Learningcited by 0
  11. 2023Personalized Interpretable Classificationcited by 0
  12. 2023Explaining with Greater Support: Weighted Column Sampling Optimization for q-Consistent Summary-Explanationscited by 0
  13. 2023A New Interpretable Neural Network-Based Rule Model for Healthcare Decision Makingcited by 0
  14. 2023Hamming Encoder: Mining Discriminative k-mers for Discrete Sequence Classificationcited by 0
  15. 2024Interpretable Classification via a Rule Network with Selective Logical Operatorscited by 0
  16. 2024Interpretable Responsibility Sharing as a Heuristic for Task and Motion Planningcited by 0
  17. 2024The Value of AI Advice: Personalized and Value-Maximizing AI Advisors Are Necessary to Reliably Benefit Experts and Organizationscited by 0
  18. 2025Fuzzy Rule-based Differentiable Representation Learningcited by 0
  19. 2025(Sometimes) Less is More: Mitigating the Complexity of Rule-based Representation for Interpretable Classificationcited by 0
  20. 2025A Fast Interpretable Fuzzy Tree Learnercited by 0
  21. 2025A Geometric Theory of Cognition for Machine Intelligencecited by 0
  22. 2026TT-Sparse: Learning Sparse Rule Models with Differentiable Truth Tablescited by 0
  23. 2026Deep Arguingcited by 0
  24. 2026FlagGAM: Rule-Basis Generalized Additive Models for Explainable Tabular Predictioncited by 0
  25. 2026Evidential Rule Learning for Interpretable Classification with Abstentioncited by 0
  26. 2026SAE-Xplainers: Rule-Based Feature Interpretation for Extreme Earth Eventscited by 0
  27. 2026Differentiable Interval Bottlenecks for Interpretable Anomaly Detection in Numerical Datacited by 0
  28. 2026Regional Explanations via Causal Sufficiency and Necessitycited by 0