Structural Compactness as a Complementary Criterion for Explanation Quality

TL;DR

This paper introduces MST-C, a graph-based metric that quantifies the structural compactness of attributions, improving the evaluation of explanation quality by capturing geometric properties.

Contribution

The paper presents MST-C, a novel structural metric for attribution explanations that complements existing complexity measures and reveals model-specific structural differences.

Findings

MST-C effectively distinguishes between different explanation methods.

MST-C exposes fundamental structural differences between models.

MST-C provides a robust diagnostic for explanation compactness.

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.