# The Shape of Explanations: A Topological Account of Rule-Based Explanations in Machine Learning

arXiv: https://arxiv.org/abs/2301.09042 · HTML: https://mlsanity.com/paper/2301.09042/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 26 references that are in the map.
- First posted on arXiv 22 Jan 2023.

## Builds on (most cited first, 12 of 12)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [A Survey on the Explainability of Supervised Machine Learning](https://mlsanity.com/paper/2011.07876/) (2020)
- [Local Rule-Based Explanations of Black Box Decision Systems](https://mlsanity.com/paper/1805.10820/) (2018)
- [Abduction-Based Explanations for Machine Learning Models](https://mlsanity.com/paper/1811.10656/) (2018)
- [Interpreting Blackbox Models via Model Extraction](https://mlsanity.com/paper/1705.08504/) (2017)
- [On Validating, Repairing and Refining Heuristic ML Explanations](https://mlsanity.com/paper/1907.02509/) (2019)
- [LoRMIkA: Local rule-based model interpretability with k-optimal associations](https://mlsanity.com/paper/1908.03840/) (2019)
- [LIMREF: Local Interpretable Model Agnostic Rule-based Explanations for Forecasting, with an Application to Electricity Smart Meter Data](https://mlsanity.com/paper/2202.07766/) (2022)
- [Identifying the Most Explainable Classifier](https://mlsanity.com/paper/1910.08595/) (2019)

## Built on by (most cited first, 1 of 1)

- [xpSHACL: Explainable SHACL Validation using Retrieval-Augmented Generation and Large Language Models](https://mlsanity.com/paper/2507.08432/) (2025)

## Abstract (arXiv)

Rule-based explanations provide simple reasons explaining the behavior of machine learning classifiers at given points in the feature space. Several recent methods (Anchors, LORE, etc.) purport to generate rule-based explanations for arbitrary or black-box classifiers. But what makes these methods work in general? We introduce a topological framework for rule-based explanation methods and provide a characterization of explainability in terms of the definability of a classifier relative to an explanation scheme. We employ this framework to consider various explanation schemes and argue that the preferred scheme depends on how much the user knows about the domain and the probability measure over the feature space.