# Logic Explanation of AI Classifiers by Categorical Explaining Functors

arXiv: https://arxiv.org/abs/2503.16203 · HTML: https://mlsanity.com/paper/2503.16203/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 46 references that are in the map.
- First posted on arXiv 20 Mar 2025.

## Builds on (most cited first, 21 of 21)

- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Model-Agnostic Interpretability of Machine Learning](https://mlsanity.com/paper/1606.05386/) (2016)
- [Interpretable classifiers using rules and Bayesian analysis: Building a better stroke prediction model](https://mlsanity.com/paper/1511.01644/) (2015)
- [Drug discovery with explainable artificial intelligence](https://mlsanity.com/paper/2007.00523/) (2020)
- [Concept-based Explainable Artificial Intelligence: A Survey](https://mlsanity.com/paper/2312.12936/) (2023)
- [Entropy-based Logic Explanations of Neural Networks](https://mlsanity.com/paper/2106.06804/) (2021)
- [Logic Explained Networks](https://mlsanity.com/paper/2108.05149/) (2021)
- [Categorical Foundations of Gradient-Based Learning](https://mlsanity.com/paper/2103.01931/) (2021)
- [Category Theory in Machine Learning](https://mlsanity.com/paper/2106.07032/) (2021)
- [Causal Concept Graph Models: Beyond Causal Opacity in Deep Learning](https://mlsanity.com/paper/2405.16507/) (2024)
- [Foundations of Symbolic Languages for Model Interpretability](https://mlsanity.com/paper/2110.02376/) (2021)
- [XAI Handbook: Towards a Unified Framework for Explainable AI](https://mlsanity.com/paper/2105.06677/) (2021)
- [Extending Logic Explained Networks to Text Classification](https://mlsanity.com/paper/2211.09732/) (2022)
- [Categorical Foundations of Explainable AI: A Unifying Theory](https://mlsanity.com/paper/2304.14094/) (2023)
- [PyTorch, Explain! A Python library for Logic Explained Networks](https://mlsanity.com/paper/2105.11697/) (2021)
- [AnyCBMs: How to Turn Any Black Box into a Concept Bottleneck Model](https://mlsanity.com/paper/2405.16508/) (2024)
- [Mathematical Foundation of Interpretable Equivariant Surrogate Models](https://mlsanity.com/paper/2503.01942/) (2025)
- [Interpretable Graph Networks Formulate Universal Algebra Conjectures](https://mlsanity.com/paper/2307.11688/) (2023)
- [A Pattern Language for Machine Learning Tasks](https://mlsanity.com/paper/2407.02424/) (2024)
- [Compositional Semantics for Probabilistic Programs with Exact Conditioning](https://mlsanity.com/paper/2101.11351/) (2021)

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

- [Actionable Interpretability Must Be Defined in Terms of Symmetries](https://mlsanity.com/paper/2601.12913/) (2026)

## Abstract (arXiv)

The most common methods in explainable artificial intelligence are post-hoc techniques which identify the most relevant features used by pretrained opaque models. Some of the most advanced post hoc methods can generate explanations that account for the mutual interactions of input features in the form of logic rules. However, these methods frequently fail to guarantee the consistency of the extracted explanations with the model's underlying reasoning. To bridge this gap, we propose a theoretically grounded approach to ensure coherence and fidelity of the extracted explanations, moving beyond the limitations of current heuristic-based approaches. To this end, drawing from category theory, we introduce an explaining functor which structurally preserves logical entailment between the explanation and the opaque model's reasoning. As a proof of concept, we validate the proposed theoretical constructions on a synthetic benchmark verifying how the proposed approach significantly mitigates the generation of contradictory or unfaithful explanations.