# Causal Explanations for Image Classifiers

arXiv: https://arxiv.org/abs/2411.08875 · HTML: https://mlsanity.com/paper/2411.08875/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 60 references that are in the map.
- First posted on arXiv 13 Nov 2024.

## Builds on (most cited first, 27 of 27)

- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [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)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [Grad-CAM++: Improved Visual Explanations for Deep Convolutional Networks](https://mlsanity.com/paper/1710.11063/) (2017)
- [RISE: Randomized Input Sampling for Explanation of Black-box Models](https://mlsanity.com/paper/1806.07421/) (2018)
- [Captum: A unified and generic model interpretability library for PyTorch](https://mlsanity.com/paper/2009.07896/) (2020)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Understanding Deep Networks via Extremal Perturbations and Smooth Masks](https://mlsanity.com/paper/1910.08485/) (2019)
- [Learning to Explain: An Information-Theoretic Perspective on Model Interpretation](https://mlsanity.com/paper/1802.07814/) (2018)
- [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019)
- [A Comprehensive Taxonomy for Explainable Artificial Intelligence: A Systematic Survey of Surveys on Methods and Concepts](https://mlsanity.com/paper/2105.07190/) (2021)
- [Towards Unifying Feature Attribution and Counterfactual Explanations: Different Means to the Same End](https://mlsanity.com/paper/2011.04917/) (2020)
- [A Modification of the Halpern-Pearl Definition of Causality](https://mlsanity.com/paper/1505.00162/) (2015)
- [One Explanation is Not Enough: Structured Attention Graphs for Image Classification](https://mlsanity.com/paper/2011.06733/) (2020)
- [Causal Explanations and XAI](https://mlsanity.com/paper/2201.13169/) (2022)
- [Causal Sufficiency and Actual Causation](https://mlsanity.com/paper/2102.02311/) (2021)
- [Beyond Pixels: Enhancing LIME with Hierarchical Features and Segmentation Foundation Models](https://mlsanity.com/paper/2403.07733/) (2024)
- [MRxaI: Black-Box Explainability for Image Classifiers in a Medical Setting](https://mlsanity.com/paper/2311.14471/) (2023)
- [Defining Explanation in Probabilistic Systems](https://mlsanity.com/paper/1302.1526/) (2013)
- [Real-Time Incremental Explanations for Object Detectors in Autonomous Driving](https://mlsanity.com/paper/2408.11963/) (2024)

## Built on by (most cited first, 9 of 9)

- [Explaining, Fast and Slow: Abstraction and Refinement of Provable Explanations](https://mlsanity.com/paper/2506.08505/) (2025)
- [Explain Yourself, Briefly! Self-Explaining Neural Networks with Concise Sufficient Reasons](https://mlsanity.com/paper/2502.03391/) (2025)
- [SpecReX: Explainable AI for Raman Spectroscopy](https://mlsanity.com/paper/2503.14567/) (2025)
- [Out-of-the-box: Black-box Causal Attacks on Object Detectors](https://mlsanity.com/paper/2512.03730/) (2025)
- [I Guess That's Why They Call it the Blues: Causal Analysis for Audio Classifiers](https://mlsanity.com/paper/2601.16675/) (2026)
- [Activation-Deactivation: A General Framework for Robust Post-hoc Explainable AI](https://mlsanity.com/paper/2510.01038/) (2025)
- [Quantifying Explainable AI-introduced signal noise on ECG data with Spectral Entropy](https://mlsanity.com/paper/2606.24974/) (2026)
- [Limitations of Synthetic Data Generation in Specialized Data-Scarce Domains](https://mlsanity.com/paper/2608.13729/) (2026)
- [Generating Medical Image Counterfactuals using Causal Explanations](https://mlsanity.com/paper/2609.02697/) (2026)

## Abstract (arXiv)

Existing algorithms for explaining the output of image classifiers use different definitions of explanations and a variety of techniques to find them. However, none of the existing tools use a principled approach based on formal definitions of cause and explanation. In this paper we present a novel black-box approach to computing explanations grounded in the theory of actual causality. We prove relevant theoretical results and present an algorithm for computing approximate explanations based on these definitions. We prove termination of our algorithm and discuss its complexity and the amount of approximation compared to the precise definition. We implemented the framework in a tool ReX and we present experimental results and a comparison with state-of-the-art tools. We demonstrate that ReX is the most efficient black-box tool and produces the smallest explanations, in addition to outperforming other black-box tools on standard quality measures.