# Sufficient, Necessary and Complete Causal Explanations in Image Classification

arXiv: https://arxiv.org/abs/2507.23497 · HTML: https://mlsanity.com/paper/2507.23497/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 39 references that are in the map.
- First posted on arXiv 31 Jul 2025.

## Builds on (most cited first, 16 of 16)

- [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)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [The (Un)reliability of saliency methods](https://mlsanity.com/paper/1711.00867/) (2017)
- [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019)
- [Full-Gradient Representation for Neural Network Visualization](https://mlsanity.com/paper/1905.00780/) (2019)
- [Abduction-Based Explanations for Machine Learning Models](https://mlsanity.com/paper/1811.10656/) (2018)
- [A Symbolic Approach to Explaining Bayesian Network Classifiers](https://mlsanity.com/paper/1805.03364/) (2018)
- [Towards Unifying Feature Attribution and Counterfactual Explanations: Different Means to the Same End](https://mlsanity.com/paper/2011.04917/) (2020)
- [Explanations for Monotonic Classifiers](https://mlsanity.com/paper/2106.00154/) (2021)
- [Causal Sufficiency and Actual Causation](https://mlsanity.com/paper/2102.02311/) (2021)
- [On Relating 'Why?' and 'Why Not?' Explanations](https://mlsanity.com/paper/2012.11067/) (2020)
- [MRxaI: Black-Box Explainability for Image Classifiers in a Medical Setting](https://mlsanity.com/paper/2311.14471/) (2023)
- [Sufficient and Necessary Explanations (and What Lies in Between)](https://mlsanity.com/paper/2409.20427/) (2024)

## Built on by (most cited first, 4 of 4)

- [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)
- [Quantifying Explainable AI-introduced signal noise on ECG data with Spectral Entropy](https://mlsanity.com/paper/2606.24974/) (2026)
- [Generating Medical Image Counterfactuals using Causal Explanations](https://mlsanity.com/paper/2609.02697/) (2026)

## Abstract (arXiv)

Existing algorithms for explaining the outputs of image classifiers are based on a variety of approaches and produce explanations that frequently lack formal rigour. On the other hand, logic-based explanations are formally and rigorously defined but their computability relies on strict assumptions about the model that do not hold on image classifiers. In this paper, we show that causal explanations, in addition to being formally and rigorously defined, enjoy the same formal properties as logic-based ones, while still lending themselves to black-box algorithms and being a natural fit for image classifiers. We prove formal properties of causal explanations and their equivalence to logic-based explanations. We demonstrate how to subdivide an image into its sufficient and necessary components. We introduce δ-complete explanations, which have a minimum confidence threshold and 1-complete causal explanations, explanations that are classified with the same confidence as the original image. We implement our definitions, and our experimental results demonstrate that different models have different patterns of sufficiency, necessity, and completeness. Our algorithms are efficiently computable, taking on average 6s per image on a ResNet model to compute all types of explanations, and are totally black-box, needing no knowledge of the model, no access to model internals, no access to gradient, nor requiring any properties, such as monotonicity, of the model.