# ECINN: Efficient Counterfactuals from Invertible Neural Networks

arXiv: https://arxiv.org/abs/2103.13701 · HTML: https://mlsanity.com/paper/2103.13701/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 49 references that are in the map.
- First posted on arXiv 25 Mar 2021.

## Builds on (most cited first, 30 of 35)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- ["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)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (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)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Self-training with Noisy Student improves ImageNet classification](https://mlsanity.com/paper/1911.04252/) (2019)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [One pixel attack for fooling deep neural networks](https://mlsanity.com/paper/1710.08864/) (2017)
- [Evaluating the visualization of what a Deep Neural Network has learned](https://mlsanity.com/paper/1509.06321/) (2015)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Counterfactual Visual Explanations](https://mlsanity.com/paper/1904.07451/) (2019)
- [Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives](https://mlsanity.com/paper/1802.07623/) (2018)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Visualizing Deep Neural Network Decisions: Prediction Difference Analysis](https://mlsanity.com/paper/1702.04595/) (2017)
- [Explaining Image Classifiers by Counterfactual Generation](https://mlsanity.com/paper/1807.08024/) (2018)
- [Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers](https://mlsanity.com/paper/1912.03277/) (2019)
- [Benchmarking and Survey of Explanation Methods for Black Box Models](https://mlsanity.com/paper/2102.13076/) (2021)
- [Semi-Supervised Learning with Normalizing Flows](https://mlsanity.com/paper/1912.13025/) (2019)
- [Contrastive Explanations for Model Interpretability](https://mlsanity.com/paper/2103.01378/) (2021)
- [SCOUT: Self-aware Discriminant Counterfactual Explanations](https://mlsanity.com/paper/2004.07769/) (2020)
- [DECE: Decision Explorer with Counterfactual Explanations for Machine Learning Models](https://mlsanity.com/paper/2008.08353/) (2020)

## Built on by (most cited first, 26 of 26)

- [Diffusion Causal Models for Counterfactual Estimation](https://mlsanity.com/paper/2202.10166/) (2022)
- [Diffusion Models for Counterfactual Explanations](https://mlsanity.com/paper/2203.15636/) (2022)
- [Counterfactual Interventions Reveal the Causal Effect of Relative Clause Representations on Agreement Prediction](https://mlsanity.com/paper/2105.06965/) (2021)
- [Adversarial Counterfactual Visual Explanations](https://mlsanity.com/paper/2303.09962/) (2023)
- [Making Heads or Tails: Towards Semantically Consistent Visual Counterfactuals](https://mlsanity.com/paper/2203.12892/) (2022)
- [Towards Trustworthy and Aligned Machine Learning: A Data-centric Survey with Causality Perspectives](https://mlsanity.com/paper/2307.16851/) (2023)
- [Diffeomorphic Counterfactuals with Generative Models](https://mlsanity.com/paper/2206.05075/) (2022)
- [Counterfactual Learning on Graphs: A Survey](https://mlsanity.com/paper/2304.01391/) (2023)
- [Latent Diffusion Counterfactual Explanations](https://mlsanity.com/paper/2310.06668/) (2023)
- [Global Counterfactual Directions](https://mlsanity.com/paper/2404.12488/) (2024)
- [Gumbel Counterfactual Generation From Language Models](https://mlsanity.com/paper/2411.07180/) (2024)
- [Do Users Benefit From Interpretable Vision? A User Study, Baseline, And Dataset](https://mlsanity.com/paper/2204.11642/) (2022)
- [Causality-Inspired Taxonomy for Explainable Artificial Intelligence](https://mlsanity.com/paper/2208.09500/) (2022)
- [CeFlow: A Robust and Efficient Counterfactual Explanation Framework for Tabular Data using Normalizing Flows](https://mlsanity.com/paper/2303.14668/) (2023)
- [TABCF: Counterfactual Explanations for Tabular Data Using a Transformer-Based VAE](https://mlsanity.com/paper/2410.10463/) (2024)
- [On Quantitative Evaluations of Counterfactuals](https://mlsanity.com/paper/2111.00177/) (2021)
- [Fighting Money Laundering with Statistics and Machine Learning](https://mlsanity.com/paper/2201.04207/) (2022)
- [The Gaussian Discriminant Variational Autoencoder (GdVAE): A Self-Explainable Model with Counterfactual Explanations](https://mlsanity.com/paper/2409.12952/) (2024)
- [Explainable AI needs formalization](https://mlsanity.com/paper/2409.14590/) (2024)
- [LeapFactual: Reliable Visual Counterfactual Explanation Using Conditional Flow Matching](https://mlsanity.com/paper/2510.14623/) (2025)
- [When less is more: Simplifying inputs aids neural network understanding](https://mlsanity.com/paper/2201.05610/) (2022)
- [Causal Generative Explainers using Counterfactual Inference: A Case Study on the Morpho-MNIST Dataset](https://mlsanity.com/paper/2401.11394/) (2024)
- [A Rigorous Study Of The Deep Taylor Decomposition](https://mlsanity.com/paper/2211.08425/) (2022)
- [On Modifying a Neural Network's Perception](https://mlsanity.com/paper/2303.02655/) (2023)
- [Counterfactual Visual Explanation via Causally-Guided Adversarial Steering](https://mlsanity.com/paper/2507.09881/) (2025)
- [Galaxy Morphology Classification with Counterfactual Explanation](https://mlsanity.com/paper/2510.14655/) (2025)

## Abstract (arXiv)

Counterfactual examples identify how inputs can be altered to change the predicted class of a classifier, thus opening up the black-box nature of, e.g., deep neural networks. We propose a method, ECINN, that utilizes the generative capacities of invertible neural networks for image classification to generate counterfactual examples efficiently. In contrast to competing methods that sometimes need a thousand evaluations or more of the classifier, ECINN has a closed-form expression and generates a counterfactual in the time of only two evaluations. Arguably, the main challenge of generating counterfactual examples is to alter only input features that affect the predicted outcome, i.e., class-dependent features. Our experiments demonstrate how ECINN alters class-dependent image regions to change the perceptual and predicted class of the counterfactuals. Additionally, we extend ECINN to also produce heatmaps (ECINNh) for easy inspection of, e.g., pairwise class-dependent changes in the generated counterfactual examples. Experimentally, we find that ECINNh outperforms established methods that generate heatmap-based explanations.