# Structural Compactness as a Complementary Criterion for Explanation Quality

arXiv: https://arxiv.org/abs/2603.29491 · HTML: https://mlsanity.com/paper/2603.29491/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 32 references that are in the map.
- First posted on arXiv 31 Mar 2026.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Improving the Adversarial Robustness and Interpretability of Deep Neural Networks by Regularizing their Input Gradients](https://mlsanity.com/paper/1711.09404/) (2017)
- [Evaluating and Aggregating Feature-based Model Explanations](https://mlsanity.com/paper/2005.00631/) (2020)
- [Quantus: An Explainable AI Toolkit for Responsible Evaluation of Neural Network Explanations and Beyond](https://mlsanity.com/paper/2202.06861/) (2022)
- [Ground Truth Evaluation of Neural Network Explanations with CLEVR-XAI](https://mlsanity.com/paper/2003.07258/) (2020)
- [On quantitative aspects of model interpretability](https://mlsanity.com/paper/2007.07584/) (2020)
- [Beyond Explaining: Opportunities and Challenges of XAI-Based Model Improvement](https://mlsanity.com/paper/2203.08008/) (2022)
- [IROF: a low resource evaluation metric for explanation methods](https://mlsanity.com/paper/2003.08747/) (2020)
- [The Meta-Evaluation Problem in Explainable AI: Identifying Reliable Estimators with MetaQuantus](https://mlsanity.com/paper/2302.07265/) (2023)
- [Mechanistic understanding and validation of large AI models with SemanticLens](https://mlsanity.com/paper/2501.05398/) (2025)
- [A Fresh Look at Sanity Checks for Saliency Maps](https://mlsanity.com/paper/2405.02383/) (2024)
- [Benchmarking XAI Explanations with Human-Aligned Evaluations](https://mlsanity.com/paper/2411.02470/) (2024)
- [Efficient and Flexible Neural Network Training through Layer-wise Feedback Propagation](https://mlsanity.com/paper/2308.12053/) (2023)
- [See What I Mean? CUE: A Cognitive Model of Understanding Explanations](https://mlsanity.com/paper/2506.14775/) (2025)

## Abstract (arXiv)

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.