Structural Compactness as a Complementary Criterion for Explanation Quality

2026-03-31

AI Summary

Existing attribution quality metrics struggle to quantify the interpretability of explanations because they rely on the spatial structure of attributions, which cannot be adequately captured by simple statistical measures. This work proposes a novel metric—Minimum Spanning Tree Compactness (MST-C)—that introduces high-order geometric characteristics into attribution evaluation for the first time. By constructing a minimum spanning tree over the set of attribution points, MST-C holistically assesses both the dispersion and clustering cohesion of their spatial distribution, yielding a self-contained, structure-aware compactness measure. Empirically, MST-C effectively differentiates among explanation methods, reveals structural differences between models, and provides stable, reliable diagnostic capability for attributions, thereby addressing critical limitations of existing complexity-based metrics.

Abstract

In the evaluation of attribution quality, the quantitative assessment of explanation legibility is particularly difficult, as it is influenced by varying shapes and internal organization of attributions not captured by simple statistics. To address this issue, we introduce Minimum Spanning Tree Compactness (MST-C), a graph-based structural metric that captures higher-order geometric properties of attributions, such as spread and cohesion. These components are combined into a single score that evaluates compactness, favoring attributions with salient points spread across a small area and spatially organized into few but cohesive clusters. We show that MST-C reliably distinguishes between explanation methods, exposes fundamental structural differences between models, and provides a robust, self-contained diagnostic for explanation compactness that complements existing notions of attribution complexity.

Problem

• attribution quality
• explanation legibility
• structural compactness
• explanation evaluation

Innovation

• Minimum Spanning Tree Compactness
• attribution quality
• explanation legibility
• structural metric
• graph-based evaluation