# Counterfactual Training: Teaching Models Plausible and Actionable Explanations

arXiv: https://arxiv.org/abs/2601.16205 · HTML: https://mlsanity.com/paper/2601.16205/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 46 references that are in the map.
- First posted on arXiv 22 Jan 2026.

## Builds on (most cited first, 28 of 28)

- [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)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Polyjuice: Generating Counterfactuals for Explaining, Evaluating, and Improving Models](https://mlsanity.com/paper/2101.00288/) (2021)
- [Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review](https://mlsanity.com/paper/2010.10596/) (2020)
- [Hyperparameter Optimization: Foundations, Algorithms, Best Practices and Open Challenges](https://mlsanity.com/paper/2107.05847/) (2021)
- [Towards Realistic Individual Recourse and Actionable Explanations in Black-Box Decision Making Systems](https://mlsanity.com/paper/1907.09615/) (2019)
- [A survey of algorithmic recourse: definitions, formulations, solutions, and prospects](https://mlsanity.com/paper/2010.04050/) (2020)
- [Counterfactual Generative Networks](https://mlsanity.com/paper/2101.06046/) (2021)
- [Adversarial Robustness on In- and Out-Distribution Improves Explainability](https://mlsanity.com/paper/2003.09461/) (2020)
- [The Case for Bayesian Deep Learning](https://mlsanity.com/paper/2001.10995/) (2020)
- [Learning What Makes a Difference from Counterfactual Examples and Gradient Supervision](https://mlsanity.com/paper/2004.09034/) (2020)
- [Exploring Counterfactual Explanations Through the Lens of Adversarial Examples: A Theoretical and Empirical Analysis](https://mlsanity.com/paper/2106.09992/) (2021)
- [The Intriguing Relation Between Counterfactual Explanations and Adversarial Examples](https://mlsanity.com/paper/2009.05487/) (2020)
- [Generating Interpretable Counterfactual Explanations By Implicit Minimisation of Epistemic and Aleatoric Uncertainties](https://mlsanity.com/paper/2103.08951/) (2021)
- [Counterfactual Explanations for Arbitrary Regression Models](https://mlsanity.com/paper/2106.15212/) (2021)
- [Learning Models for Actionable Recourse](https://mlsanity.com/paper/2011.06146/) (2020)
- [CounterNet: End-to-End Training of Prediction Aware Counterfactual Explanations](https://mlsanity.com/paper/2109.07557/) (2021)
- [Fairness in Algorithmic Recourse Through the Lens of Substantive Equality of Opportunity](https://mlsanity.com/paper/2401.16088/) (2024)
- [Efficient Adversarial Training With Data Pruning](https://mlsanity.com/paper/2207.00694/) (2022)
- [Faithful Model Explanations through Energy-Constrained Conformal Counterfactuals](https://mlsanity.com/paper/2312.10648/) (2023)
- [Explaining Black-Box Models through Counterfactuals](https://mlsanity.com/paper/2308.07198/) (2023)

## Abstract (arXiv)

We propose a novel training regime termed counterfactual training that leverages counterfactual explanations to increase the explanatory capacity of models. Counterfactual explanations have emerged as a popular post-hoc explanation method for opaque machine learning models: they inform how factual inputs would need to change in order for a model to produce some desired output. To be useful in real-world decision-making systems, counterfactuals should be plausible with respect to the underlying data and actionable with respect to the feature mutability constraints. Much existing research has therefore focused on developing post-hoc methods to generate counterfactuals that meet these desiderata. In this work, we instead hold models directly accountable for the desired end goal: counterfactual training employs counterfactuals during the training phase to minimize the divergence between learned representations and plausible, actionable explanations. We demonstrate empirically and theoretically that our proposed method facilitates training models that deliver inherently desirable counterfactual explanations and additionally exhibit improved adversarial robustness.