# Analyzing Explainer Robustness via Probabilistic Lipschitzness of Prediction Functions

arXiv: https://arxiv.org/abs/2206.12481 · HTML: https://mlsanity.com/paper/2206.12481/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 69 references that are in the map.
- First posted on arXiv 24 Jun 2022.

## Builds on (most cited first, 30 of 39)

- [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)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [RISE: Randomized Input Sampling for Explanation of Black-box Models](https://mlsanity.com/paper/1806.07421/) (2018)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [On the Robustness of Interpretability Methods](https://mlsanity.com/paper/1806.08049/) (2018)
- [On the (In)fidelity and Sensitivity for Explanations](https://mlsanity.com/paper/1901.09392/) (2019)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Consistent Individualized Feature Attribution for Tree Ensembles](https://mlsanity.com/paper/1802.03888/) (2018)
- [Learning to Explain: An Information-Theoretic Perspective on Model Interpretation](https://mlsanity.com/paper/1802.07814/) (2018)
- [Explaining by Removing: A Unified Framework for Model Explanation](https://mlsanity.com/paper/2011.14878/) (2020)
- [Explanations can be manipulated and geometry is to blame](https://mlsanity.com/paper/1906.07983/) (2019)
- [Sensitivity and Generalization in Neural Networks: an Empirical Study](https://mlsanity.com/paper/1802.08760/) (2018)
- [Visualizing Deep Neural Network Decisions: Prediction Difference Analysis](https://mlsanity.com/paper/1702.04595/) (2017)
- [Towards Robust and Reliable Algorithmic Recourse](https://mlsanity.com/paper/2102.13620/) (2021)
- [CXPlain: Causal Explanations for Model Interpretation under Uncertainty](https://mlsanity.com/paper/1910.12336/) (2019)
- [Rethinking Stability for Attribution-based Explanations](https://mlsanity.com/paper/2203.06877/) (2022)
- [Robust and Stable Black Box Explanations](https://mlsanity.com/paper/2011.06169/) (2020)
- [Towards the Unification and Robustness of Perturbation and Gradient Based Explanations](https://mlsanity.com/paper/2102.10618/) (2021)
- [A case for new neural network smoothness constraints](https://mlsanity.com/paper/2012.07969/) (2020)
- [Fairness via Explanation Quality: Evaluating Disparities in the Quality of Post hoc Explanations](https://mlsanity.com/paper/2205.07277/) (2022)
- [Smoothed Geometry for Robust Attribution](https://mlsanity.com/paper/2006.06643/) (2020)

## Built on by (most cited first, 6 of 6)

- [Probabilistic Stability Guarantees for Feature Attributions](https://mlsanity.com/paper/2504.13787/) (2025)
- [Probabilistic Lipschitzness and the Stable Rank for Comparing Explanation Models](https://mlsanity.com/paper/2402.18863/) (2024)
- [Faithfulness and the Notion of Adversarial Sensitivity in NLP Explanations](https://mlsanity.com/paper/2409.17774/) (2024)
- [Axiomatic Explainer Globalness via Optimal Transport](https://mlsanity.com/paper/2411.01126/) (2024)
- [Attribution Explanations for Deep Neural Networks: A Theoretical Perspective](https://mlsanity.com/paper/2508.07636/) (2025)
- [OrdShap: Feature Position Importance for Sequential Black-Box Models](https://mlsanity.com/paper/2507.11855/) (2025)

## Abstract (arXiv)

Machine learning methods have significantly improved in their predictive capabilities, but at the same time they are becoming more complex and less transparent. As a result, explainers are often relied on to provide interpretability to these black-box prediction models. As crucial diagnostics tools, it is important that these explainers themselves are robust. In this paper we focus on one particular aspect of robustness, namely that an explainer should give similar explanations for similar data inputs. We formalize this notion by introducing and defining explainer astuteness, analogous to astuteness of prediction functions. Our formalism allows us to connect explainer robustness to the predictor's probabilistic Lipschitzness, which captures the probability of local smoothness of a function. We provide lower bound guarantees on the astuteness of a variety of explainers (e.g., SHAP, RISE, CXPlain) given the Lipschitzness of the prediction function. These theoretical results imply that locally smooth prediction functions lend themselves to locally robust explanations. We evaluate these results empirically on simulated as well as real datasets.