# Compact Rule-Based Classifier Learning via Gradient Descent

arXiv: https://arxiv.org/abs/2502.01375 · HTML: https://mlsanity.com/paper/2502.01375/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 62 references that are in the map.
- First posted on arXiv 3 Feb 2025.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Understanding Straight-Through Estimator in Training Activation Quantized Neural Nets](https://mlsanity.com/paper/1903.05662/) (2019)
- [Sanity Checks for Saliency Metrics](https://mlsanity.com/paper/1912.01451/) (2019)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)
- [Concrete Autoencoders for Differentiable Feature Selection and Reconstruction](https://mlsanity.com/paper/1901.09346/) (2019)
- [Interpreting CNNs via Decision Trees](https://mlsanity.com/paper/1802.00121/) (2018)
- [Deep Differentiable Logic Gate Networks](https://mlsanity.com/paper/2210.08277/) (2022)
- [Interpretable Neural-Symbolic Concept Reasoning](https://mlsanity.com/paper/2304.14068/) (2023)
- [Scalable Rule-Based Representation Learning for Interpretable Classification](https://mlsanity.com/paper/2109.15103/) (2021)
- [Fast Sparse Decision Tree Optimization via Reference Ensembles](https://mlsanity.com/paper/2112.00798/) (2021)
- [Generalized Linear Rule Models](https://mlsanity.com/paper/1906.01761/) (2019)
- [Learning Accurate and Interpretable Decision Rule Sets from Neural Networks](https://mlsanity.com/paper/2103.02826/) (2021)
- [Interpretable Random Forests via Rule Extraction](https://mlsanity.com/paper/2004.14841/) (2020)
- [Learning Interpretable Rules for Scalable Data Representation and Classification](https://mlsanity.com/paper/2310.14336/) (2023)
- [Learning Interpretable Decision Rule Sets: A Submodular Optimization Approach](https://mlsanity.com/paper/2206.03718/) (2022)
- [T-Norms Driven Loss Functions for Machine Learning](https://mlsanity.com/paper/1907.11468/) (2019)
- [Custom Gradient Estimators are Straight-Through Estimators in Disguise](https://mlsanity.com/paper/2405.05171/) (2024)
- [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)

## Built on by (most cited first, 2 of 2)

- [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)

## Abstract (arXiv)

Rule-based models are essential for high-stakes decision-making due to their transparency and interpretability, but their discrete nature creates challenges for optimization and scalability. In this work, we present the Fuzzy Rule-based Reasoner (FRR), a novel gradient-based rule learning system that supports strict user constraints over rule-based complexity while achieving competitive performance. To maximize interpretability, the FRR uses semantically meaningful fuzzy logic partitions, unattainable with existing neuro-fuzzy approaches, and sufficient (single-rule) decision-making, which avoids the combinatorial complexity of additive rule ensembles. Through extensive evaluation across 40 datasets, FRR demonstrates: (1) superior performance to traditional rule-based methods (e.g., 5% average accuracy over RIPPER); (2) comparable accuracy to tree-based models (e.g., CART) using rule bases 90% more compact; and (3) achieves 96% of the accuracy of state-of-the-art additive rule-based models while using only sufficient rules and requiring only 3% of their rule base size.