# Counterfactual Explanations via Riemannian Latent Space Traversal

arXiv: https://arxiv.org/abs/2411.02259 · HTML: https://mlsanity.com/paper/2411.02259/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 47 references that are in the map.
- First posted on arXiv 4 Nov 2024.

## Builds on (most cited first, 30 of 36)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Deep Neural Networks and Tabular Data: A Survey](https://mlsanity.com/paper/2110.01889/) (2021)
- [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)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review](https://mlsanity.com/paper/2010.10596/) (2020)
- [Local Rule-Based Explanations of Black Box Decision Systems](https://mlsanity.com/paper/1805.10820/) (2018)
- [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)
- [Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry](https://mlsanity.com/paper/2307.12868/) (2023)
- [Riemannian Diffusion Models](https://mlsanity.com/paper/2208.07949/) (2022)
- [Efficient Search for Diverse Coherent Explanations](https://mlsanity.com/paper/1901.04909/) (2019)
- [Getting a CLUE: A Method for Explaining Uncertainty Estimates](https://mlsanity.com/paper/2006.06848/) (2020)
- [CARLA: A Python Library to Benchmark Algorithmic Recourse and Counterfactual Explanation Algorithms](https://mlsanity.com/paper/2108.00783/) (2021)
- [Diffusion Models for Counterfactual Explanations](https://mlsanity.com/paper/2203.15636/) (2022)
- [Explanation by Progressive Exaggeration](https://mlsanity.com/paper/1911.00483/) (2019)
- [Reliable training and estimation of variance networks](https://mlsanity.com/paper/1906.03260/) (2019)
- [Geometrically Enriched Latent Spaces](https://mlsanity.com/paper/2008.00565/) (2020)
- [Fast Diffusion-Based Counterfactuals for Shortcut Removal and Generation](https://mlsanity.com/paper/2312.14223/) (2023)
- [Variational Autoencoders with Riemannian Brownian Motion Priors](https://mlsanity.com/paper/2002.05227/) (2020)
- [Diffeomorphic Counterfactuals with Generative Models](https://mlsanity.com/paper/2206.05075/) (2022)

## Built on by (most cited first, 9 of 9)

- [Causally Steered Diffusion for Automated Video Counterfactual Generation](https://mlsanity.com/paper/2506.14404/) (2025)
- [Graph Counterfactual Explainable AI via Latent Space Traversal](https://mlsanity.com/paper/2501.08850/) (2025)
- [Counterfactual Explanations on Robust Perceptual Geodesics](https://mlsanity.com/paper/2601.18678/) (2026)
- [A Theory of Speciation in Generative Diffusion Models on Compact Riemannian Manifolds](https://mlsanity.com/paper/2608.23798/) (2026)
- [Geometric Embedding Alignment via Curvature Matching in Transfer Learning](https://mlsanity.com/paper/2506.13015/) (2025)
- [On the notion of missingness for path attribution explainability methods in medical settings: Guiding the selection of medically meaningful baselines](https://mlsanity.com/paper/2508.14482/) (2025)
- [PepCompass: Navigating peptide embedding spaces using Riemannian Geometry](https://mlsanity.com/paper/2510.01988/) (2025)
- [RecourseBench: A Modular Framework for Reproducible Algorithmic Recourse Evaluation](https://mlsanity.com/paper/2606.16113/) (2026)
- [Play Like Champions: Counterfactual Feedback Generation in Latent Space](https://mlsanity.com/paper/2607.00190/) (2026)

## Abstract (arXiv)

The adoption of increasingly complex deep models has fueled an urgent need for insight into how these models make predictions. Counterfactual explanations form a powerful tool for providing actionable explanations to practitioners. Previously, counterfactual explanation methods have been designed by traversing the latent space of generative models. Yet, these latent spaces are usually greatly simplified, with most of the data distribution complexity contained in the decoder rather than the latent embedding. Thus, traversing the latent space naively without taking the nonlinear decoder into account can lead to unnatural counterfactual trajectories. We introduce counterfactual explanations obtained using a Riemannian metric pulled back via the decoder and the classifier under scrutiny. This metric encodes information about the complex geometric structure of the data and the learned representation, enabling us to obtain robust counterfactual trajectories with high fidelity, as demonstrated by our experiments in real-world tabular datasets.