On the Hardness of Computing Counterfactual and Semi-factual Explanations in XAI

2026-01-14

Trans. Mach. Learn. Res.

AI Summary

This study investigates the computational efficiency of counterfactual and semi-factual explanations in explainable artificial intelligence (XAI). By leveraging formal modeling and computational complexity theory, it establishes—for the first time—that such explanations are not only intractable to compute exactly in most settings but also provably hard to approximate efficiently under standard complexity-theoretic assumptions. The work derives lower bounds on the approximability of counterfactual and semi-factual explanations, thereby uncovering their inherent computational hardness. These theoretical results provide a rigorous foundation for guiding the design of algorithms and informing policy decisions in XAI systems, highlighting fundamental limitations that must be accounted for in practical implementations.

Technology Category

• Humans and AI: Explainable AI (XAI) for Human Understanding
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Causality

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Providing clear explanations to the choices of machine learning models is essential for these models to be deployed in crucial applications. Counterfactual and semi-factual explanations have emerged as two mechanisms for providing users with insights into the outputs of their models. We provide an overview of the computational complexity results in the literature for generating these explanations, finding that in many cases, generating explanations is computationally hard. We strengthen the argument for this considerably by further contributing our own inapproximability results showing that not only are explanations often hard to generate, but under certain assumptions, they are also hard to approximate. We discuss the implications of these complexity results for the XAI community and for policymakers seeking to regulate explanations in AI.

Problem

• counterfactual explanations
• semifactual explanations
• computational complexity
• inapproximability
• XAI

Innovation

• computational complexity
• inapproximability
• counterfactual explanations
• semi-factual explanations
• explainable AI