# Tree-Based Leakage Inspection and Control in Concept Bottleneck Models

arXiv: https://arxiv.org/abs/2410.06352 · HTML: https://mlsanity.com/paper/2410.06352/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 40 references that are in the map.
- First posted on arXiv 8 Oct 2024.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Post-hoc Concept Bottleneck Models](https://mlsanity.com/paper/2205.15480/) (2022)
- [Label-Free Concept Bottleneck Models](https://mlsanity.com/paper/2304.06129/) (2023)
- [On Completeness-aware Concept-Based Explanations in Deep Neural Networks](https://mlsanity.com/paper/1910.07969/) (2019)
- [Concept Whitening for Interpretable Image Recognition](https://mlsanity.com/paper/2002.01650/) (2020)
- [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)
- [Optimal Sparse Decision Trees](https://mlsanity.com/paper/1904.12847/) (2019)
- [Interpreting Deep Visual Representations via Network Dissection](https://mlsanity.com/paper/1711.05611/) (2017)
- [Probabilistic Concept Bottleneck Models](https://mlsanity.com/paper/2306.01574/) (2023)
- [GlanceNets: Interpretabile, Leak-proof Concept-based Models](https://mlsanity.com/paper/2205.15612/) (2022)
- [Beyond Sparsity: Tree Regularization of Deep Models for Interpretability](https://mlsanity.com/paper/1711.06178/) (2017)
- [Entropy-based Logic Explanations of Neural Networks](https://mlsanity.com/paper/2106.06804/) (2021)
- [Incremental Residual Concept Bottleneck Models](https://mlsanity.com/paper/2404.08978/) (2024)
- [Influence-Directed Explanations for Deep Convolutional Networks](https://mlsanity.com/paper/1802.03788/) (2018)
- [Regional Tree Regularization for Interpretability in Black Box Models](https://mlsanity.com/paper/1908.04494/) (2019)
- [Sparse Concept Bottleneck Models: Gumbel Tricks in Contrastive Learning](https://mlsanity.com/paper/2404.03323/) (2024)
- [Dividing and Conquering a BlackBox to a Mixture of Interpretable Models: Route, Interpret, Repeat](https://mlsanity.com/paper/2307.05350/) (2023)
- [Benchmarking and Enhancing Disentanglement in Concept-Residual Models](https://mlsanity.com/paper/2312.00192/) (2023)

## Built on by (most cited first, 8 of 8)

- [Bayesian Concept Bottleneck Models with LLM Priors](https://mlsanity.com/paper/2410.15555/) (2024)
- [Leakage and Interpretability in Concept-Based Models](https://mlsanity.com/paper/2504.14094/) (2025)
- [Human-AI Co-design for Clinical Prediction Models](https://mlsanity.com/paper/2601.09072/) (2026)
- [A Comprehensive Survey on the Risks and Limitations of Concept-based Models](https://mlsanity.com/paper/2506.04237/) (2025)
- [Towards Reasonable Concept Bottleneck Models](https://mlsanity.com/paper/2506.05014/) (2025)
- [DeCoDe: Defer-and-Complement Decision-Making via Decoupled Concept Bottleneck Models](https://mlsanity.com/paper/2505.19220/) (2025)
- [In Defense of Information Leakage in Concept-based Models](https://mlsanity.com/paper/2606.10669/) (2026)
- [Concept Flow Models: Anchoring Concept-Based Reasoning with Hierarchical Bottlenecks](https://mlsanity.com/paper/2606.19489/) (2026)

## Abstract (arXiv)

As AI models grow larger, the demand for accountability and interpretability has become increasingly critical for understanding their decision-making processes. Concept Bottleneck Models (CBMs) have gained attention for enhancing interpretability by mapping inputs to intermediate concepts before making final predictions. However, CBMs often suffer from information leakage, where additional input data, not captured by the concepts, is used to improve task performance, complicating the interpretation of downstream predictions. In this paper, we introduce a novel approach for training both joint and sequential CBMs that allows us to identify and control leakage using decision trees. Our method quantifies leakage by comparing the decision paths of hard CBMs with their soft, leaky counterparts. Specifically, we show that soft leaky CBMs extend the decision paths of hard CBMs, particularly in cases where concept information is incomplete. Using this insight, we develop a technique to better inspect and manage leakage, isolating the subsets of data most affected by this. Through synthetic and real-world experiments, we demonstrate that controlling leakage in this way not only improves task accuracy but also yields more informative and transparent explanations.