# Counterfactual Transition Graphs: Evaluating Cross-Class Transition Quality

arXiv: https://arxiv.org/abs/2608.23164 · HTML: https://mlsanity.com/paper/2608.23164/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 24 Aug 2026.

## Builds on (most cited first, 10 of 10)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019)
- [Instance-based Counterfactual Explanations for Time Series Classification](https://mlsanity.com/paper/2009.13211/) (2020)
- [Motif-guided Time Series Counterfactual Explanations](https://mlsanity.com/paper/2211.04411/) (2022)
- [M-CELS: Counterfactual Explanation for Multivariate Time Series Data Guided by Learned Saliency Maps](https://mlsanity.com/paper/2411.02649/) (2024)
- [Shapelet-Based Counterfactual Explanations for Multivariate Time Series](https://mlsanity.com/paper/2208.10462/) (2022)
- [MASCOTS: Model-Agnostic Symbolic COunterfactual explanations for Time Series](https://mlsanity.com/paper/2503.22389/) (2025)
- [What-If Explanations Over Time: Counterfactuals for Time Series Classification](https://mlsanity.com/paper/2603.27792/) (2026)
- [From Prototypes to Sparse ECG Explanations: SHAP-Driven Counterfactuals for Multivariate Time-Series Multi-class Classification](https://mlsanity.com/paper/2510.19514/) (2025)

## Abstract (arXiv)

Counterfactual (CF) explanations for time-series classifiers are usually evaluated one example at a time: what minimal edit flips this single window's prediction? We argue that the more informative question for diagnostic interpretability is structural: how does the classifier connect its own classes to each other? We propose a counterfactual transition graph (CGT) in which each node is a class and each edge weight is the CF reliability of the transition from one prototype to another under a proximity aware retrieval sweep. On a six-class hand-movement task, we induce a CGT that reveals a non-trivial topology, which is not predicted by the binary confusion matrix: it shows that counterfactual reachability does not align with classifier accuracy and even runs counter to it (Spearman ρ=-0.37 over the 15 pairs), i.e. the boundaries the classifier separates most confidently are among those an in-distribution edit can least often cross. Our framework is method agnostic, i.e. any CF-explainers can be used. Presently, we use it to juxtapose replacement-based CFs with gradient-based CFs; gradient-based methods reach almost any class by stepping off the data manifold, while replacement-based methods stay on it and fail on precisely the rigid boundaries.