# Scalable Rule-Based Representation Learning for Interpretable Classification

arXiv: https://arxiv.org/abs/2109.15103 · HTML: https://mlsanity.com/paper/2109.15103/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 55 references that are in the map.
- First posted on arXiv 30 Sep 2021.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [The Mythos of Model Interpretability](https://mlsanity.com/paper/1606.03490/) (2016)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Distilling a Neural Network Into a Soft Decision Tree](https://mlsanity.com/paper/1711.09784/) (2017)
- [Binary Neural Networks: A Survey](https://mlsanity.com/paper/2004.03333/) (2020)
- [Interpretable classifiers using rules and Bayesian analysis: Building a better stroke prediction model](https://mlsanity.com/paper/1511.01644/) (2015)
- [Generalized and Scalable Optimal Sparse Decision Trees](https://mlsanity.com/paper/2006.08690/) (2020)
- [Deep Neural Decision Trees](https://mlsanity.com/paper/1806.06988/) (2018)
- [Scalable Bayesian Rule Lists](https://mlsanity.com/paper/1602.08610/) (2016)
- [ProxQuant: Quantized Neural Networks via Proximal Operators](https://mlsanity.com/paper/1810.00861/) (2018)
- [Generalized Linear Rule Models](https://mlsanity.com/paper/1906.01761/) (2019)
- [Exact and Consistent Interpretation for Piecewise Linear Neural Networks: A Closed Form Solution](https://mlsanity.com/paper/1802.06259/) (2018)
- [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)
- [Making Tree Ensembles Interpretable](https://mlsanity.com/paper/1606.05390/) (2016)

## Built on by (most cited first, 30 of 40)

- [Learning Transformer Programs](https://mlsanity.com/paper/2306.01128/) (2023)
- [Defining and Quantifying the Emergence of Sparse Concepts in DNNs](https://mlsanity.com/paper/2111.06206/) (2021)
- [ExcelFormer: A neural network surpassing GBDTs on tabular data](https://mlsanity.com/paper/2301.02819/) (2023)
- [Assessing the Quality of Multiple-Choice Questions Using GPT-4 and Rule-Based Methods](https://mlsanity.com/paper/2307.08161/) (2023)
- [A Comprehensive Survey on Self-Interpretable Neural Networks](https://mlsanity.com/paper/2501.15638/) (2025)
- [Can LLMs like GPT-4 outperform traditional AI tools in dementia diagnosis? Maybe, but not today](https://mlsanity.com/paper/2306.01499/) (2023)
- [Learning Interpretable Differentiable Logic Networks](https://mlsanity.com/paper/2407.04168/) (2024)
- [Differentiable Rule Induction with Learned Relational Features](https://mlsanity.com/paper/2201.06515/) (2022)
- [Neuro-symbolic Models for Interpretable Time Series Classification using Temporal Logic Description](https://mlsanity.com/paper/2209.09114/) (2022)
- [Finding Interpretable Class-Specific Patterns through Efficient Neural Search](https://mlsanity.com/paper/2312.04311/) (2023)
- [Learning Exceptional Subgroups by End-to-End Maximizing KL-divergence](https://mlsanity.com/paper/2402.12930/) (2024)
- [A Scalable, Interpretable, Verifiable & Differentiable Logic Gate Convolutional Neural Network Architecture From Truth Tables](https://mlsanity.com/paper/2208.08609/) (2022)
- [Manifoldron: Direct Space Partition via Manifold Discovery](https://mlsanity.com/paper/2201.05279/) (2022)
- [Compact Rule-Based Classifier Learning via Gradient Descent](https://mlsanity.com/paper/2502.01375/) (2025)
- [Learning Interpretable Differentiable Logic Networks for Tabular Regression](https://mlsanity.com/paper/2505.23615/) (2025)
- [Neural Logic Networks for Interpretable Classification](https://mlsanity.com/paper/2508.08172/) (2025)
- [RuDi: Explaining Behavior Sequence Models by Automatic Statistics Generation and Rule Distillation](https://mlsanity.com/paper/2208.07211/) (2022)
- [Learning to Advise Humans in High-Stakes Settings](https://mlsanity.com/paper/2210.12849/) (2022)
- [An Interpretable Loan Credit Evaluation Method Based on Rule Representation Learner](https://mlsanity.com/paper/2304.00731/) (2023)
- [The Computational Complexity of Concise Hypersphere Classification](https://mlsanity.com/paper/2312.07103/) (2023)
- [Neuro-Symbolic Rule Lists](https://mlsanity.com/paper/2411.06428/) (2024)
- [Bayes Point Rule Set Learning](https://mlsanity.com/paper/2204.05251/) (2022)
- [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)
- [A New Interpretable Neural Network-Based Rule Model for Healthcare Decision Making](https://mlsanity.com/paper/2309.11101/) (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)
- [Interpretable Responsibility Sharing as a Heuristic for Task and Motion Planning](https://mlsanity.com/paper/2409.05586/) (2024)
- [The Value of AI Advice: Personalized and Value-Maximizing AI Advisors Are Necessary to Reliably Benefit Experts and Organizations](https://mlsanity.com/paper/2412.19530/) (2024)
- [Fuzzy Rule-based Differentiable Representation Learning](https://mlsanity.com/paper/2503.13548/) (2025)

## 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.