# Theoretical Behavior of XAI Methods in the Presence of Suppressor Variables

arXiv: https://arxiv.org/abs/2306.01464 · HTML: https://mlsanity.com/paper/2306.01464/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 53 references that are in the map.
- First posted on arXiv 2 Jun 2023.

## Builds on (most cited first, 30 of 31)

- [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)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [Towards Faithfully Interpretable NLP Systems: How should we define and evaluate faithfulness?](https://mlsanity.com/paper/2004.03685/) (2020)
- [Evaluating the visualization of what a Deep Neural Network has learned](https://mlsanity.com/paper/1509.06321/) (2015)
- [All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously](https://mlsanity.com/paper/1801.01489/) (2018)
- [Unmasking Clever Hans Predictors and Assessing What Machines Really Learn](https://mlsanity.com/paper/1902.10178/) (2019)
- [Methods for Interpreting and Understanding Deep Neural Networks](https://mlsanity.com/paper/1706.07979/) (2017)
- [On the Robustness of Interpretability Methods](https://mlsanity.com/paper/1806.08049/) (2018)
- [Visualizing the Effects of Predictor Variables in Black Box Supervised Learning Models](https://mlsanity.com/paper/1612.08468/) (2016)
- [Explaining individual predictions when features are dependent: More accurate approximations to Shapley values](https://mlsanity.com/paper/1903.10464/) (2019)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (2019)
- [OpenXAI: Towards a Transparent Evaluation of Model Explanations](https://mlsanity.com/paper/2206.11104/) (2022)
- [Drug discovery with explainable artificial intelligence](https://mlsanity.com/paper/2007.00523/) (2020)
- [When Explanations Lie: Why Many Modified BP Attributions Fail](https://mlsanity.com/paper/1912.09818/) (2019)
- [Benchmarking Attribution Methods with Relative Feature Importance](https://mlsanity.com/paper/1907.09701/) (2019)
- [Explaining the Explainer: A First Theoretical Analysis of LIME](https://mlsanity.com/paper/2001.03447/) (2020)
- [Learning how to explain neural networks: PatternNet and PatternAttribution](https://mlsanity.com/paper/1705.05598/) (2017)
- [Towards Best Practice in Explaining Neural Network Decisions with LRP](https://mlsanity.com/paper/1910.09840/) (2019)
- [Scrutinizing XAI using linear ground-truth data with suppressor variables](https://mlsanity.com/paper/2111.07473/) (2021)

## Built on by (most cited first, 12 of 12)

- [Decoupling Pixel Flipping and Occlusion Strategy for Consistent XAI Benchmarks](https://mlsanity.com/paper/2401.06654/) (2024)
- [Benchmarking the Influence of Pre-training on Explanation Performance in MR Image Classification](https://mlsanity.com/paper/2306.12150/) (2023)
- [XAI-TRIS: Non-linear image benchmarks to quantify false positive post-hoc attribution of feature importance](https://mlsanity.com/paper/2306.12816/) (2023)
- [GECOBench: A Gender-Controlled Text Dataset and Benchmark for Quantifying Biases in Explanations](https://mlsanity.com/paper/2406.11547/) (2024)
- [Explainable AI needs formalization](https://mlsanity.com/paper/2409.14590/) (2024)
- [EXACT: Towards a platform for empirically benchmarking Machine Learning model explanation methods](https://mlsanity.com/paper/2405.12261/) (2024)
- [On Spectral Properties of Gradient-based Explanation Methods](https://mlsanity.com/paper/2508.10595/) (2025)
- [Feature salience - not task-informativeness - drives machine learning model explanations](https://mlsanity.com/paper/2602.09238/) (2026)
- [Minimizing False-Positive Attributions in Explanations of Non-Linear Models](https://mlsanity.com/paper/2505.11210/) (2025)
- [The effect of whitening on explanation performance](https://mlsanity.com/paper/2602.09278/) (2026)
- [cc-Shapley: Measuring Multivariate Feature Importance Needs Causal Context](https://mlsanity.com/paper/2602.20396/) (2026)
- [Local Label-Informed Feature Transfer for Generating Ground-Truth Medical Images: A Comparison of GAN- and Diffusion-Based Approaches](https://mlsanity.com/paper/2607.18882/) (2026)

## Abstract (arXiv)

In recent years, the community of 'explainable artificial intelligence' (XAI) has created a vast body of methods to bridge a perceived gap between model 'complexity' and 'interpretability'. However, a concrete problem to be solved by XAI methods has not yet been formally stated. As a result, XAI methods are lacking theoretical and empirical evidence for the 'correctness' of their explanations, limiting their potential use for quality-control and transparency purposes. At the same time, Haufe et al. (2014) showed, using simple toy examples, that even standard interpretations of linear models can be highly misleading. Specifically, high importance may be attributed to so-called suppressor variables lacking any statistical relation to the prediction target. This behavior has been confirmed empirically for a large array of XAI methods in Wilming et al. (2022). Here, we go one step further by deriving analytical expressions for the behavior of a variety of popular XAI methods on a simple two-dimensional binary classification problem involving Gaussian class-conditional distributions. We show that the majority of the studied approaches will attribute non-zero importance to a non-class-related suppressor feature in the presence of correlated noise. This poses important limitations on the interpretations and conclusions that the outputs of these XAI methods can afford.