Structural Compactness as a Complementary Criterion for Explanation Quality
Summary: arXiv:2603.29491v1 Announce Type: new
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.
Introduction
The demand for explainable artificial intelligence (XAI) has surged in recent years as organizations seek transparency in machine learning models. However, the complexity of explanations often poses challenges in evaluating their effectiveness. Traditional metrics may fall short in capturing the nuanced qualities of different explanation methods.
The Challenge of Attribution Quality
Attribution quality refers to how well an explanation method can clarify the decision-making process of a model. Several factors complicate this evaluation:
- Variability in Shapes: Different methods produce attributions with varying geometric characteristics.
- Internal Organization: The organization of attribution points can significantly affect legibility.
- Simplicity of Statistics: Basic statistical measures often fail to capture the intricacies involved in understanding attributions.
Introducing Minimum Spanning Tree Compactness (MST-C)
To address these challenges, we propose the Minimum Spanning Tree Compactness (MST-C) metric. This innovative approach leverages graph theory to assess the structural properties of attributions:
- Higher-Order Geometric Properties: MST-C captures essential characteristics such as the spread of points and the cohesion of clusters.
- Single Compactness Score: The metric combines various components into a unified score that reflects the compactness of attributions.
- Focus on Salient Points: MST-C prioritizes attributions that feature prominent points condensed within minimal space and forming cohesive clusters.
Benefits of MST-C
The adoption of MST-C brings several advantages to the evaluation of explanation methods:
- Reliable Distinction: MST-C effectively differentiates between various explanation methods, providing clarity in model evaluation.
- Exposure of Structural Differences: It reveals fundamental differences in how models generate attributions, enhancing the understanding of their operational mechanisms.
- Robust Diagnostic Tool: As a self-contained diagnostic, MST-C complements existing measures of attribution complexity, offering a more holistic perspective on explanation quality.
Conclusion
In conclusion, the introduction of Minimum Spanning Tree Compactness represents a significant advancement in the evaluation of explanation quality within AI systems. By addressing the shortcomings of traditional metrics, MST-C provides a valuable framework for understanding and improving the legibility and effectiveness of attributions in machine learning models.