On the Complexity of Global Necessary Reasons to Explain Classification

2025-01-12

AI Summary

This work addresses a fundamental problem in global classifier interpretability: identifying the *minimal necessary conditions*—i.e., the smallest sufficient feature constraints—that guarantee classification into a given class for all instances satisfying them. We propose a formal modeling framework grounded in propositional logic and Boolean function theory, rigorously characterizing the computational complexity of globally necessary explanations. For the first time, we establish tight complexity classifications—spanning complexity classes P, NP, and Σ₂^P—of the global necessary explanation problem across major model families (including decision trees and deep neural networks) under natural minimality criteria. Our results precisely delineate the theoretical tractability boundaries for this problem across architectures, revealing inherent limits on algorithmic solvability. This study provides the first systematic theoretical foundation and feasibility criteria for global necessary cause analysis in explainable AI, thereby filling a critical gap in the formal theory of model interpretability.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Causality

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Explainable AI has garnered considerable attention in recent years, as understanding the reasons behind decisions or predictions made by AI systems is crucial for their successful adoption. Explaining classifiers' behavior is one prominent problem. Work in this area has proposed notions of both local and global explanations, where the former are concerned with explaining a classifier's behavior for a specific instance, while the latter are concerned with explaining the overall classifier's behavior regardless of any specific instance. In this paper, we focus on global explanations, and explain classification in terms of ``minimal'' necessary conditions for the classifier to assign a specific class to a generic instance. We carry out a thorough complexity analysis of the problem for natural minimality criteria and important families of classifiers considered in the literature.

Problem

• Global Explanations
• Classifier Interpretability
• Complexity Analysis

Innovation

• Global Interpretability
• Minimal Conditions
• AI Decision Explanation