Distance-Restricted Explanations: Theoretical Underpinnings & Efficient Implementation
Yacine Izza, Xuanxiang Huang, Antonio Morgado, Jordi Planes, Alexey Ignatiev, Joao Marques-Silva
TL;DR
This work formalizes distance-restricted explanations (DRX) for ML models by extending abductive (AXp) and contrastive (CXp) explanations with a distance constraint under a chosen $l_p$ norm. It establishes monotonicity and duality properties, linking distance-restricted AXps/CXps to minimal hitting sets and enabling MUS/MCS-inspired reasoning. The paper introduces algorithms for computing and enumerating DRX explanations, notably deletion-based and dichotomic search approaches, and presents SwiftXplain, a parallel framework that markedly accelerates finding a single DRX explanation on large feature sets. Experimental results on MNIST and GTSRB demonstrate substantial speedups (up to ~4x) and scalability advantages over baseline methods, highlighting practical potential for rigorous, scalable XAI in neural networks. Overall, the work advances rigorous, scalable explainability by marrying logic-based foundations with adversarial robustness techniques and parallel computation, enabling reliable explanations for high-dimensional ML models.
Abstract
The uses of machine learning (ML) have snowballed in recent years. In many cases, ML models are highly complex, and their operation is beyond the understanding of human decision-makers. Nevertheless, some uses of ML models involve high-stakes and safety-critical applications. Explainable artificial intelligence (XAI) aims to help human decision-makers in understanding the operation of such complex ML models, thus eliciting trust in their operation. Unfortunately, the majority of past XAI work is based on informal approaches, that offer no guarantees of rigor. Unsurprisingly, there exists comprehensive experimental and theoretical evidence confirming that informal methods of XAI can provide human-decision makers with erroneous information. Logic-based XAI represents a rigorous approach to explainability; it is model-based and offers the strongest guarantees of rigor of computed explanations. However, a well-known drawback of logic-based XAI is the complexity of logic reasoning, especially for highly complex ML models. Recent work proposed distance-restricted explanations, i.e. explanations that are rigorous provided the distance to a given input is small enough. Distance-restricted explainability is tightly related with adversarial robustness, and it has been shown to scale for moderately complex ML models, but the number of inputs still represents a key limiting factor. This paper investigates novel algorithms for scaling up the performance of logic-based explainers when computing and enumerating ML model explanations with a large number of inputs.