# Measuring Leakage in Concept-Based Methods: An Information Theoretic Approach

arXiv: https://arxiv.org/abs/2504.09459 · HTML: https://mlsanity.com/paper/2504.09459/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 13 references that are in the map.
- First posted on arXiv 13 Apr 2025.

## Builds on (most cited first, 8 of 8)

- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [On Completeness-aware Concept-Based Explanations in Deep Neural Networks](https://mlsanity.com/paper/1910.07969/) (2019)
- [Promises and Pitfalls of Black-Box Concept Learning Models](https://mlsanity.com/paper/2106.13314/) (2021)
- [Do Concept Bottleneck Models Learn as Intended?](https://mlsanity.com/paper/2105.04289/) (2021)
- [Stochastic Concept Bottleneck Models](https://mlsanity.com/paper/2406.19272/) (2024)
- [Influence-Directed Explanations for Deep Convolutional Networks](https://mlsanity.com/paper/1802.03788/) (2018)
- [Interpretable and intervenable ultrasonography-based machine learning models for pediatric appendicitis](https://mlsanity.com/paper/2302.14460/) (2023)

## Built on by (most cited first, 9 of 9)

- [Leakage and Interpretability in Concept-Based Models](https://mlsanity.com/paper/2504.14094/) (2025)
- [There Was Never a Bottleneck in Concept Bottleneck Models](https://mlsanity.com/paper/2506.04877/) (2025)
- [Towards Reasonable Concept Bottleneck Models](https://mlsanity.com/paper/2506.05014/) (2025)
- [Interpretable Reward Modeling with Active Concept Bottlenecks](https://mlsanity.com/paper/2507.04695/) (2025)
- [Rethinking Concept Bottleneck Models: From Pitfalls to Solutions](https://mlsanity.com/paper/2603.05629/) (2026)
- [Post-hoc Stochastic Concept Bottleneck Models](https://mlsanity.com/paper/2510.08219/) (2025)
- [Measuring What Matters: Synthetic Benchmarks for Concept Bottleneck Models](https://mlsanity.com/paper/2606.04326/) (2026)
- [In Defense of Information Leakage in Concept-based Models](https://mlsanity.com/paper/2606.10669/) (2026)
- [On the Faithfulness of Post-Hoc Concept Bottleneck Models](https://mlsanity.com/paper/2606.30498/) (2026)

## Abstract (arXiv)

Concept Bottleneck Models (CBMs) aim to enhance interpretability by structuring predictions around human-understandable concepts. However, unintended information leakage, where predictive signals bypass the concept bottleneck, compromises their transparency. This paper introduces an information-theoretic measure to quantify leakage in CBMs, capturing the extent to which concept embeddings encode additional, unintended information beyond the specified concepts. We validate the measure through controlled synthetic experiments, demonstrating its effectiveness in detecting leakage trends across various configurations. Our findings highlight that feature and concept dimensionality significantly influence leakage, and that classifier choice impacts measurement stability, with XGBoost emerging as the most reliable estimator. Additionally, preliminary investigations indicate that the measure exhibits the anticipated behavior when applied to soft joint CBMs, suggesting its reliability in leakage quantification beyond fully synthetic settings. While this study rigorously evaluates the measure in controlled synthetic experiments, future work can extend its application to real-world datasets.