# Hoeffding Concept Bottleneck Models with Applications to Overhead Images

arXiv: https://arxiv.org/abs/2606.00082 · HTML: https://mlsanity.com/paper/2606.00082/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 51 references that are in the map.
- First posted on arXiv 22 May 2026.

## Builds on (most cited first, 30 of 35)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Remote Sensing Image Scene Classification: Benchmark and State of the Art](https://mlsanity.com/paper/1703.00121/) (2017)
- [Language in a Bottle: Language Model Guided Concept Bottlenecks for Interpretable Image Classification](https://mlsanity.com/paper/2211.11158/) (2022)
- [Post-hoc Concept Bottleneck Models](https://mlsanity.com/paper/2205.15480/) (2022)
- [Label-Free Concept Bottleneck Models](https://mlsanity.com/paper/2304.06129/) (2023)
- [InterpretML: A Unified Framework for Machine Learning Interpretability](https://mlsanity.com/paper/1909.09223/) (2019)
- [RTMDet: An Empirical Study of Designing Real-Time Object Detectors](https://mlsanity.com/paper/2212.07784/) (2022)
- [CRAFT: Concept Recursive Activation FacTorization for Explainability](https://mlsanity.com/paper/2211.10154/) (2022)
- [Abduction-Based Explanations for Machine Learning Models](https://mlsanity.com/paper/1811.10656/) (2018)
- [xView: Objects in Context in Overhead Imagery](https://mlsanity.com/paper/1802.07856/) (2018)
- [A Symbolic Approach to Explaining Bayesian Network Classifiers](https://mlsanity.com/paper/1805.03364/) (2018)
- [On The Reasons Behind Decisions](https://mlsanity.com/paper/2002.09284/) (2020)
- [Concept-based Explainable Artificial Intelligence: A Survey](https://mlsanity.com/paper/2312.12936/) (2023)
- [Discover-then-Name: Task-Agnostic Concept Bottlenecks via Automated Concept Discovery](https://mlsanity.com/paper/2407.14499/) (2024)
- [Learning Concise and Descriptive Attributes for Visual Recognition](https://mlsanity.com/paper/2308.03685/) (2023)
- [Discover and Cure: Concept-aware Mitigation of Spurious Correlation](https://mlsanity.com/paper/2305.00650/) (2023)
- [Look at the Variance! Efficient Black-box Explanations with Sobol-based Sensitivity Analysis](https://mlsanity.com/paper/2111.04138/) (2021)
- [VLG-CBM: Training Concept Bottleneck Models with Vision-Language Guidance](https://mlsanity.com/paper/2408.01432/) (2024)
- [Stochastic Concept Bottleneck Models](https://mlsanity.com/paper/2406.19272/) (2024)
- [Incremental Residual Concept Bottleneck Models](https://mlsanity.com/paper/2404.08978/) (2024)
- [Purifying Interaction Effects with the Functional ANOVA: An Efficient Algorithm for Recovering Identifiable Additive Models](https://mlsanity.com/paper/1911.04974/) (2019)
- [Coarse-to-Fine Concept Bottleneck Models](https://mlsanity.com/paper/2310.02116/) (2023)
- [Leakage and Interpretability in Concept-Based Models](https://mlsanity.com/paper/2504.14094/) (2025)

## Built on by (most cited first, 1 of 1)

- [CHOQOLATE: Organizing Concept Bottleneck Latent Spaces with Choquet Integrals](https://mlsanity.com/paper/2609.37786/) (2026)

## Abstract (arXiv)

Explainability of deep learning algorithms is critical for computer-vision applications with high-stakes decisions. Concept bottleneck models (CBM) have recently shown promising performance to provide explainable and accurate predictions for classification problems, based on a bottleneck of high-level concepts. Existing CBM methods rely on a linear aggregation of the concept scores to compute predictions. However, a large number of concepts is often used in this linear approach, which undermines explainability and favors information leakage. In general, the underlying relation between concepts and output logits is not linear. Therefore, we introduce Hoeffding Concept Bottleneck Models (HCBM), which build on the Hoeffding functional decomposition of gradient-boosted trees to provide non-linear and sparse aggregations of concept scores, and generate compact predictions using prime implicants. HCBM have strong theoretical properties of robustness to interconcept leakage, and outperform sparse linear CBM in practice, as shown in extensive experiments. Beyond classification, HCBM can be adapted to object detection, and we focus on a challenging case with overhead images to show the high performance of HCBM in these settings.