Structural Compactness as a Complementary Criterion for Explanation Quality

arXiv cs.AI / 4/1/2026

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Key Points

The paper proposes Minimum Spanning Tree Compactness (MST-C), a graph-based metric to quantify explanation/attribution structural legibility beyond simple statistics.
MST-C aggregates higher-order geometric properties—such as spread and cohesion—into a single compactness score that rewards salient points being dispersed within a small area.
The authors argue the metric favors attributions that form a small number of cohesive clusters, capturing internal spatial organization not reflected by standard complexity measures.
Experiments indicate MST-C can reliably distinguish between different explanation methods and reveal structural differences between models.
The paper positions MST-C as a robust, self-contained diagnostic that complements existing attribution complexity notions.

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.