# FOLD-SE: An Efficient Rule-based Machine Learning Algorithm with Scalable Explainability

arXiv: https://arxiv.org/abs/2208.07912 · HTML: https://mlsanity.com/paper/2208.07912/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 31 references that are in the map.
- First posted on arXiv 16 Aug 2022.

## Builds on (most cited first, 4 of 4)

- [Inductive logic programming at 30: a new introduction](https://mlsanity.com/paper/2008.07912/) (2020)
- [A New Algorithm to Automate Inductive Learning of Default Theories](https://mlsanity.com/paper/1707.02693/) (2017)
- [FOLD-R++: A Scalable Toolset for Automated Inductive Learning of Default Theories from Mixed Data](https://mlsanity.com/paper/2110.07843/) (2021)
- [FOLD-RM: A Scalable, Efficient, and Explainable Inductive Learning Algorithm for Multi-Category Classification of Mixed Data](https://mlsanity.com/paper/2202.06913/) (2022)

## Built on by (most cited first, 15 of 15)

- [Using Logic Programming and Kernel-Grouping for Improving Interpretability of Convolutional Neural Networks](https://mlsanity.com/paper/2310.13073/) (2023)
- [Symbolic Rule Extraction from Attention-Guided Sparse Representations in Vision Transformers](https://mlsanity.com/paper/2505.06745/) (2025)
- [NeSyFOLD: Neurosymbolic Framework for Interpretable Image Classification](https://mlsanity.com/paper/2301.12667/) (2023)
- [CON-FOLD -- Explainable Machine Learning with Confidence](https://mlsanity.com/paper/2408.07854/) (2024)
- [MC3G: Model Agnostic Causally Constrained Counterfactual Generation](https://mlsanity.com/paper/2508.17221/) (2025)
- [Neuro-Symbolic Artificial Intelligence: A Task-Directed Survey in the Black-Box Models Era](https://mlsanity.com/paper/2603.03177/) (2026)
- [CoGS: Causality Constrained Counterfactual Explanations using goal-directed ASP](https://mlsanity.com/paper/2407.08179/) (2024)
- [Mechanistic Interpretability for Neural Networks: Circuits, Sparse Features and Symbolic Reasoning](https://mlsanity.com/paper/2607.07316/) (2026)
- [Counterfactual Generation with Answer Set Programming](https://mlsanity.com/paper/2402.04382/) (2024)
- [A Neurosymbolic Framework for Bias Correction in Convolutional Neural Networks](https://mlsanity.com/paper/2405.15886/) (2024)
- [CFGs: Causality Constrained Counterfactual Explanations using goal-directed ASP](https://mlsanity.com/paper/2405.15956/) (2024)
- [CoGS: Model Agnostic Causality Constrained Counterfactual Explanations using goal-directed ASP](https://mlsanity.com/paper/2410.22615/) (2024)
- [Generating Causally Compliant Counterfactual Explanations using ASP](https://mlsanity.com/paper/2502.09226/) (2025)
- [A Community-driven vision for a new Knowledge Resource for AI](https://mlsanity.com/paper/2506.16596/) (2025)
- [P2C: Path to Counterfactuals](https://mlsanity.com/paper/2508.20371/) (2025)

## Abstract (arXiv)

We present FOLD-SE, an efficient, explainable machine learning algorithm for classification tasks given tabular data containing numerical and categorical values. FOLD-SE generates a set of default rules-essentially a stratified normal logic program-as an (explainable) trained model. Explainability provided by FOLD-SE is scalable, meaning that regardless of the size of the dataset, the number of learned rules and learned literals stay quite small while good accuracy in classification is maintained. A model with smaller number of rules and literals is easier to understand for human beings. FOLD-SE is competitive with state-of-the-art machine learning algorithms such as XGBoost and Multi-Layer Perceptrons (MLP) wrt accuracy of prediction. However, unlike XGBoost and MLP, the FOLD-SE algorithm is explainable. The FOLD-SE algorithm builds upon our earlier work on developing the explainable FOLD-R++ machine learning algorithm for binary classification and inherits all of its positive features. Thus, pre-processing of the dataset, using techniques such as one-hot encoding, is not needed. Like FOLD-R++, FOLD-SE uses prefix sum to speed up computations resulting in FOLD-SE being an order of magnitude faster than XGBoost and MLP in execution speed. The FOLD-SE algorithm outperforms FOLD-R++ as well as other rule-learning algorithms such as RIPPER in efficiency, performance and scalability, especially for large datasets. A major reason for scalable explainability of FOLD-SE is the use of a literal selection heuristics based on Gini Impurity, as opposed to Information Gain used in FOLD-R++. A multi-category classification version of FOLD-SE is also presented.