FOLD-SE: An Efficient Rule-based Machine Learning Algorithm with Scalable Explainability
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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.
Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). Builds on 4 of its 31 references that are in the map. First posted on arXiv 16 Aug 2022.
Builds on
4 of 31 references.
References · 4
- 2020Inductive logic programming at 30: a new introductioncited by 83
- 2017A New Algorithm to Automate Inductive Learning of Default Theoriescited by 14
- 2021FOLD-R++: A Scalable Toolset for Automated Inductive Learning of Default Theories from Mixed Datacited by 10
- 2022FOLD-RM: A Scalable, Efficient, and Explainable Inductive Learning Algorithm for Multi-Category Classification of Mixed Datacited by 7
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Citing papers per year: 2023: 2; 2024: 6; 2025: 5; 2026: 2.
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- 2023Using Logic Programming and Kernel-Grouping for Improving Interpretability of Convolutional Neural Networkscited by 4
- 2025Symbolic Rule Extraction from Attention-Guided Sparse Representations in Vision Transformerscited by 3
- 2023NeSyFOLD: Neurosymbolic Framework for Interpretable Image Classificationcited by 2
- 2024CON-FOLD -- Explainable Machine Learning with Confidencecited by 2
- 2025MC3G: Model Agnostic Causally Constrained Counterfactual Generationcited by 2
- 2024CoGS: Causality Constrained Counterfactual Explanations using goal-directed ASPcited by 1
- 2026Neuro-Symbolic Artificial Intelligence: A Task-Directed Survey in the Black-Box Models Eracited by 1
- 2026Mechanistic Interpretability for Neural Networks: Circuits, Sparse Features and Symbolic Reasoningcited by 1
- 2024Counterfactual Generation with Answer Set Programmingcited by 0
- 2024A Neurosymbolic Framework for Bias Correction in Convolutional Neural Networkscited by 0
- 2024CFGs: Causality Constrained Counterfactual Explanations using goal-directed ASPcited by 0
- 2024CoGS: Model Agnostic Causality Constrained Counterfactual Explanations using goal-directed ASPcited by 0
3 more
- 2025Generating Causally Compliant Counterfactual Explanations using ASPcited by 0
- 2025A Community-driven vision for a new Knowledge Resource for AIcited by 0
- 2025P2C: Path to Counterfactualscited by 0
- 2026Mechanistic Interpretability for Neural Networks: Circuits, Sparse Features and Symbolic Reasoning8 Jul 2026
- 2026Neuro-Symbolic Artificial Intelligence: A Task-Directed Survey in the Black-Box Models Era3 Mar 2026
- 2025P2C: Path to Counterfactuals28 Aug 2025
- 2025MC3G: Model Agnostic Causally Constrained Counterfactual Generation24 Aug 2025
- 2025A Community-driven vision for a new Knowledge Resource for AI19 Jun 2025
- 2025Symbolic Rule Extraction from Attention-Guided Sparse Representations in Vision Transformers10 May 2025
- 2025Generating Causally Compliant Counterfactual Explanations using ASP13 Feb 2025
- 2024CoGS: Model Agnostic Causality Constrained Counterfactual Explanations using goal-directed ASP30 Oct 2024
- 2024CON-FOLD -- Explainable Machine Learning with Confidence14 Aug 2024
- 2024CoGS: Causality Constrained Counterfactual Explanations using goal-directed ASP11 Jul 2024
- 2024CFGs: Causality Constrained Counterfactual Explanations using goal-directed ASP24 May 2024
- 2024A Neurosymbolic Framework for Bias Correction in Convolutional Neural Networks24 May 2024
- 2023Using Logic Programming and Kernel-Grouping for Improving Interpretability of Convolutional Neural Networkscited by 4
- 2025Symbolic Rule Extraction from Attention-Guided Sparse Representations in Vision Transformerscited by 3
- 2023NeSyFOLD: Neurosymbolic Framework for Interpretable Image Classificationcited by 2
- 2024CON-FOLD -- Explainable Machine Learning with Confidencecited by 2
- 2025MC3G: Model Agnostic Causally Constrained Counterfactual Generationcited by 2
- 2024CoGS: Causality Constrained Counterfactual Explanations using goal-directed ASPcited by 1
- 2026Neuro-Symbolic Artificial Intelligence: A Task-Directed Survey in the Black-Box Models Eracited by 1
- 2024Counterfactual Generation with Answer Set Programmingcited by 0
- 2024A Neurosymbolic Framework for Bias Correction in Convolutional Neural Networkscited by 0
- 2024CFGs: Causality Constrained Counterfactual Explanations using goal-directed ASPcited by 0
- 2024CoGS: Model Agnostic Causality Constrained Counterfactual Explanations using goal-directed ASPcited by 0
- 2025Generating Causally Compliant Counterfactual Explanations using ASPcited by 0
12 most cited of 14 All 14 (JSON)
- 2026Neuro-Symbolic Artificial Intelligence: A Task-Directed Survey in the Black-Box Models Era3 Mar 2026
- 2025P2C: Path to Counterfactuals28 Aug 2025
- 2025MC3G: Model Agnostic Causally Constrained Counterfactual Generation24 Aug 2025
- 2025A Community-driven vision for a new Knowledge Resource for AI19 Jun 2025
- 2025Symbolic Rule Extraction from Attention-Guided Sparse Representations in Vision Transformers10 May 2025
- 2025Generating Causally Compliant Counterfactual Explanations using ASP13 Feb 2025
- 2024CoGS: Model Agnostic Causality Constrained Counterfactual Explanations using goal-directed ASP30 Oct 2024
- 2024CON-FOLD -- Explainable Machine Learning with Confidence14 Aug 2024
- 2024CoGS: Causality Constrained Counterfactual Explanations using goal-directed ASP11 Jul 2024
- 2024CFGs: Causality Constrained Counterfactual Explanations using goal-directed ASP24 May 2024
- 2024A Neurosymbolic Framework for Bias Correction in Convolutional Neural Networks24 May 2024
- 2024Counterfactual Generation with Answer Set Programming6 Feb 2024
12 newest of 14 All 14 (JSON)