# Consistent Counterfactuals for Deep Models

arXiv: https://arxiv.org/abs/2110.03109 · HTML: https://mlsanity.com/paper/2110.03109/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 69 references that are in the map.
- First posted on arXiv 6 Oct 2021.

## Builds on (most cited first, 30 of 42)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [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)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Improving Transferability of Adversarial Examples with Input Diversity](https://mlsanity.com/paper/1803.06978/) (2018)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives](https://mlsanity.com/paper/1802.07623/) (2018)
- [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Explanations can be manipulated and geometry is to blame](https://mlsanity.com/paper/1906.07983/) (2019)
- [Adversarial Robustness Toolbox v1.0.0](https://mlsanity.com/paper/1807.01069/) (2018)
- [Local Rule-Based Explanations of Black Box Decision Systems](https://mlsanity.com/paper/1805.10820/) (2018)
- [Predictive Multiplicity in Classification](https://mlsanity.com/paper/1909.06677/) (2019)
- [Deep ReLU Networks Have Surprisingly Few Activation Patterns](https://mlsanity.com/paper/1906.00904/) (2019)
- [Multi-Objective Counterfactual Explanations](https://mlsanity.com/paper/2004.11165/) (2020)
- [EAD: Elastic-Net Attacks to Deep Neural Networks via Adversarial Examples](https://mlsanity.com/paper/1709.04114/) (2017)
- [Learning Model-Agnostic Counterfactual Explanations for Tabular Data](https://mlsanity.com/paper/1910.09398/) (2019)
- [Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers](https://mlsanity.com/paper/1912.03277/) (2019)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [Towards Realistic Individual Recourse and Actionable Explanations in Black-Box Decision Making Systems](https://mlsanity.com/paper/1907.09615/) (2019)
- [The Hidden Assumptions Behind Counterfactual Explanations and Principal Reasons](https://mlsanity.com/paper/1912.04930/) (2019)
- [Fooling Neural Network Interpretations via Adversarial Model Manipulation](https://mlsanity.com/paper/1902.02041/) (2019)
- [Good Counterfactuals and Where to Find Them: A Case-Based Technique for Generating Counterfactuals for Explainable AI (XAI)](https://mlsanity.com/paper/2005.13997/) (2020)

## Built on by (most cited first, 30 of 37)

- [On the Adversarial Robustness of Causal Algorithmic Recourse](https://mlsanity.com/paper/2112.11313/) (2021)
- [Robust Counterfactual Explanations for Tree-Based Ensembles](https://mlsanity.com/paper/2207.02739/) (2022)
- [Robust Counterfactual Explanations for Neural Networks With Probabilistic Guarantees](https://mlsanity.com/paper/2305.11997/) (2023)
- [Probabilistically Robust Recourse: Navigating the Trade-offs between Costs and Robustness in Algorithmic Recourse](https://mlsanity.com/paper/2203.06768/) (2022)
- [A Survey on the Robustness of Feature Importance and Counterfactual Explanations](https://mlsanity.com/paper/2111.00358/) (2021)
- [Robust Counterfactual Explanations in Machine Learning: A Survey](https://mlsanity.com/paper/2402.01928/) (2024)
- [Attribution-based Explanations that Provide Recourse Cannot be Robust](https://mlsanity.com/paper/2205.15834/) (2022)
- [On the Trade-Off between Actionable Explanations and the Right to be Forgotten](https://mlsanity.com/paper/2208.14137/) (2022)
- [Provably Robust and Plausible Counterfactual Explanations for Neural Networks via Robust Optimisation](https://mlsanity.com/paper/2309.12545/) (2023)
- [Finding Regions of Counterfactual Explanations via Robust Optimization](https://mlsanity.com/paper/2301.11113/) (2023)
- [Recourse under Model Multiplicity via Argumentative Ensembling (Technical Report)](https://mlsanity.com/paper/2312.15097/) (2023)
- [Model Reconstruction Using Counterfactual Explanations: A Perspective From Polytope Theory](https://mlsanity.com/paper/2405.05369/) (2024)
- [Generating robust counterfactual explanations](https://mlsanity.com/paper/2304.12943/) (2023)
- [Distributionally Robust Recourse Action](https://mlsanity.com/paper/2302.11211/) (2023)
- [RoCourseNet: Distributionally Robust Training of a Prediction Aware Recourse Model](https://mlsanity.com/paper/2206.00700/) (2022)
- [Be Intentional About Fairness!: Fairness, Size, and Multiplicity in the Rashomon Set](https://mlsanity.com/paper/2501.15634/) (2025)
- [Performative Validity of Recourse Explanations](https://mlsanity.com/paper/2506.15366/) (2025)
- [Interval Abstractions for Robust Counterfactual Explanations](https://mlsanity.com/paper/2404.13736/) (2024)
- [Boundary-Aware Uncertainty for Feature Attribution Explainers](https://mlsanity.com/paper/2210.02419/) (2022)
- [Flexible and Robust Counterfactual Explanations with Minimal Satisfiable Perturbations](https://mlsanity.com/paper/2309.04676/) (2023)
- [Quantifying Prediction Consistency Under Fine-Tuning Multiplicity in Tabular LLMs](https://mlsanity.com/paper/2407.04173/) (2024)
- [Rigorous Probabilistic Guarantees for Robust Counterfactual Explanations](https://mlsanity.com/paper/2407.07482/) (2024)
- [Procedural Adherence and Interpretability Through Neuro-Symbolic Generative Agents](https://mlsanity.com/paper/2402.16905/) (2024)
- [The Gaussian Discriminant Variational Autoencoder (GdVAE): A Self-Explainable Model with Counterfactual Explanations](https://mlsanity.com/paper/2409.12952/) (2024)
- [Counterfactual Explanations for Model Ensembles Using Entropic Risk Measures](https://mlsanity.com/paper/2503.07934/) (2025)
- [From Search To Sampling: Generative Models For Robust Algorithmic Recourse](https://mlsanity.com/paper/2505.07351/) (2025)
- [Trust Regions for Explanations via Black-Box Probabilistic Certification](https://mlsanity.com/paper/2402.11168/) (2024)
- [Learning-Augmented Robust Algorithmic Recourse](https://mlsanity.com/paper/2410.01580/) (2024)
- [Optimal Robust Recourse with Lp-Bounded Model Change](https://mlsanity.com/paper/2509.21293/) (2025)
- [Verified Training for Counterfactual Explanation Robustness under Data Shift](https://mlsanity.com/paper/2403.03773/) (2024)

## Abstract (arXiv)

Counterfactual examples are one of the most commonly-cited methods for explaining the predictions of machine learning models in key areas such as finance and medical diagnosis. Counterfactuals are often discussed under the assumption that the model on which they will be used is static, but in deployment models may be periodically retrained or fine-tuned. This paper studies the consistency of model prediction on counterfactual examples in deep networks under small changes to initial training conditions, such as weight initialization and leave-one-out variations in data, as often occurs during model deployment. We demonstrate experimentally that counterfactual examples for deep models are often inconsistent across such small changes, and that increasing the cost of the counterfactual, a stability-enhancing mitigation suggested by prior work in the context of simpler models, is not a reliable heuristic in deep networks. Rather, our analysis shows that a model's local Lipschitz continuity around the counterfactual is key to its consistency across related models. To this end, we propose Stable Neighbor Search as a way to generate more consistent counterfactual explanations, and illustrate the effectiveness of this approach on several benchmark datasets.