# Navigating Explanatory Multiverse Through Counterfactual Path Geometry

arXiv: https://arxiv.org/abs/2306.02786 · HTML: https://mlsanity.com/paper/2306.02786/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 62 references that are in the map.
- First posted on arXiv 5 Jun 2023.

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

- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [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)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [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)
- [MedMNIST Classification Decathlon: A Lightweight AutoML Benchmark for Medical Image Analysis](https://mlsanity.com/paper/2010.14925/) (2020)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review](https://mlsanity.com/paper/2010.10596/) (2020)
- [Learning Model-Agnostic Counterfactual Explanations for Tabular Data](https://mlsanity.com/paper/1910.09398/) (2019)
- [The Hidden Assumptions Behind Counterfactual Explanations and Principal Reasons](https://mlsanity.com/paper/1912.04930/) (2019)
- [Efficient Search for Diverse Coherent Explanations](https://mlsanity.com/paper/1901.04909/) (2019)
- [Explainability Fact Sheets: A Framework for Systematic Assessment of Explainable Approaches](https://mlsanity.com/paper/1912.05100/) (2019)
- [If Only We Had Better Counterfactual Explanations: Five Key Deficits to Rectify in the Evaluation of Counterfactual XAI Techniques](https://mlsanity.com/paper/2103.01035/) (2021)
- [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)
- [Interpretable Predictions of Tree-based Ensembles via Actionable Feature Tweaking](https://mlsanity.com/paper/1706.06691/) (2017)
- [Explainable AI is Dead, Long Live Explainable AI! Hypothesis-driven decision support](https://mlsanity.com/paper/2302.12389/) (2023)
- [One Explanation Does Not Fit All: The Promise of Interactive Explanations for Machine Learning Transparency](https://mlsanity.com/paper/2001.09734/) (2020)
- [Probabilistically Robust Recourse: Navigating the Trade-offs between Costs and Robustness in Algorithmic Recourse](https://mlsanity.com/paper/2203.06768/) (2022)
- [Principles of Explanation in Human-AI Systems](https://mlsanity.com/paper/2102.04972/) (2021)
- [Amortized Generation of Sequential Algorithmic Recourses for Black-box Models](https://mlsanity.com/paper/2106.03962/) (2021)
- [Synthesizing Action Sequences for Modifying Model Decisions](https://mlsanity.com/paper/1910.00057/) (2019)
- [Impact Of Explainable AI On Cognitive Load: Insights From An Empirical Study](https://mlsanity.com/paper/2304.08861/) (2023)
- [Achieving Diversity in Counterfactual Explanations: a Review and Discussion](https://mlsanity.com/paper/2305.05840/) (2023)
- [Mind the Gap! Bridging Explainable Artificial Intelligence and Human Understanding with Luhmann's Functional Theory of Communication](https://mlsanity.com/paper/2302.03460/) (2023)
- [LIMEtree: Consistent and Faithful Surrogate Explanations of Multiple Classes](https://mlsanity.com/paper/2005.01427/) (2020)
- [Helpful, Misleading or Confusing: How Humans Perceive Fundamental Building Blocks of Artificial Intelligence Explanations](https://mlsanity.com/paper/2303.00934/) (2023)

## Built on by (most cited first, 5 of 5)

- [Artificial Intelligence Should Genuinely Support Clinical Reasoning and Decision Making To Bridge the Translational Gap](https://mlsanity.com/paper/2506.05030/) (2025)
- [Counterfactual Explanations via Locally-guided Sequential Algorithmic Recourse](https://mlsanity.com/paper/2309.04211/) (2023)
- [TraCE: Trajectory Counterfactual Explanation Scores](https://mlsanity.com/paper/2309.15965/) (2023)
- [Uncertainty Quantification as a Principled Foundation for Explainable Artificial Intelligence: A Case Study of Counterfactual Explanations](https://mlsanity.com/paper/2502.17007/) (2025)
- [Counterfactual Explanations for Clustering Models](https://mlsanity.com/paper/2409.12632/) (2024)

## Abstract (arXiv)

Counterfactual explanations are the de facto standard when tasked with interpreting decisions of (opaque) predictive models. Their generation is often subject to technical and domain-specific constraints that aim to maximise their real-life utility. In addition to considering desiderata pertaining to the counterfactual instance itself, guaranteeing existence of a viable path connecting it with the factual data point has recently gained relevance. While current explainability approaches ensure that the steps of such a journey as well as its destination adhere to selected constraints, they neglect the multiplicity of these counterfactual paths. To address this shortcoming we introduce the novel concept of explanatory multiverse that encompasses all the possible counterfactual journeys. We define it using vector spaces, showing how to navigate, reason about and compare the geometry of counterfactual trajectories found within it. To this end, we overview their spatial properties -- such as affinity, branching, divergence and possible future convergence -- and propose an all-in-one metric, called opportunity potential, to quantify them. Notably, the explanatory process offered by our method grants explainees more agency by allowing them to select counterfactuals not only based on their absolute differences but also according to the properties of their connecting paths. To demonstrate real-life flexibility, benefit and efficacy of explanatory multiverse we propose its graph-based implementation, which we use for qualitative and quantitative evaluation on six tabular and image data sets.