# Probabilistic Concept Bottleneck Models

arXiv: https://arxiv.org/abs/2306.01574 · HTML: https://mlsanity.com/paper/2306.01574/

## Key facts

- Cited by 101 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 44 references that are in the map.
- First posted on arXiv 2 Jun 2023.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [This Looks Like That: Deep Learning for Interpretable Image Recognition](https://mlsanity.com/paper/1806.10574/) (2018)
- [Zero-Shot Learning -- A Comprehensive Evaluation of the Good, the Bad and the Ugly](https://mlsanity.com/paper/1707.00600/) (2017)
- [Towards Robust Interpretability with Self-Explaining Neural Networks](https://mlsanity.com/paper/1806.07538/) (2018)
- [Counterfactual Visual Explanations](https://mlsanity.com/paper/1904.07451/) (2019)
- [Post-hoc Concept Bottleneck Models](https://mlsanity.com/paper/2205.15480/) (2022)
- [Concept Whitening for Interpretable Image Recognition](https://mlsanity.com/paper/2002.01650/) (2020)
- [Probabilistic Face Embeddings](https://mlsanity.com/paper/1904.09658/) (2019)
- [Probabilistic Embeddings for Cross-Modal Retrieval](https://mlsanity.com/paper/2101.05068/) (2021)
- [Promises and Pitfalls of Black-Box Concept Learning Models](https://mlsanity.com/paper/2106.13314/) (2021)
- [Interactive Concept Bottleneck Models](https://mlsanity.com/paper/2212.07430/) (2022)
- [GlanceNets: Interpretabile, Leak-proof Concept-based Models](https://mlsanity.com/paper/2205.15612/) (2022)
- [NSML: Meet the MLaaS platform with a real-world case study](https://mlsanity.com/paper/1810.09957/) (2018)
- [A Closer Look at the Intervention Procedure of Concept Bottleneck Models](https://mlsanity.com/paper/2302.14260/) (2023)
- [Concept Embedding Models: Beyond the Accuracy-Explainability Trade-Off](https://mlsanity.com/paper/2209.09056/) (2022)
- [Convolutional Dynamic Alignment Networks for Interpretable Classifications](https://mlsanity.com/paper/2104.00032/) (2021)
- [Meaningfully Debugging Model Mistakes using Conceptual Counterfactual Explanations](https://mlsanity.com/paper/2106.12723/) (2021)
- [A Framework for Learning Ante-hoc Explainable Models via Concepts](https://mlsanity.com/paper/2108.11761/) (2021)
- [iCaps: An Interpretable Classifier via Disentangled Capsule Networks](https://mlsanity.com/paper/2008.08756/) (2020)

## Built on by (most cited first, 30 of 101)

- [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)
- [Stochastic Concept Bottleneck Models](https://mlsanity.com/paper/2406.19272/) (2024)
- [Learning to Receive Help: Intervention-Aware Concept Embedding Models](https://mlsanity.com/paper/2309.16928/) (2023)
- [BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcuts](https://mlsanity.com/paper/2402.12240/) (2024)
- [Auxiliary Losses for Learning Generalizable Concept-based Models](https://mlsanity.com/paper/2311.11108/) (2023)
- [Energy-Based Concept Bottleneck Models: Unifying Prediction, Concept Intervention, and Probabilistic Interpretations](https://mlsanity.com/paper/2401.14142/) (2024)
- [Coarse-to-Fine Concept Bottleneck Models](https://mlsanity.com/paper/2310.02116/) (2023)
- [Learning to Intervene on Concept Bottlenecks](https://mlsanity.com/paper/2308.13453/) (2023)
- [Causal Concept Graph Models: Beyond Causal Opacity in Deep Learning](https://mlsanity.com/paper/2405.16507/) (2024)
- [Beyond Concept Bottleneck Models: How to Make Black Boxes Intervenable?](https://mlsanity.com/paper/2401.13544/) (2024)
- [Editable Concept Bottleneck Models](https://mlsanity.com/paper/2405.15476/) (2024)
- [Semi-supervised Concept Bottleneck Models](https://mlsanity.com/paper/2406.18992/) (2024)
- [A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcuts](https://mlsanity.com/paper/2406.10368/) (2024)
- [A Comprehensive Survey on Self-Interpretable Neural Networks](https://mlsanity.com/paper/2501.15638/) (2025)
- [Learning Discrete Concepts in Latent Hierarchical Models](https://mlsanity.com/paper/2406.00519/) (2024)
- [Interpretable Concept-Based Memory Reasoning](https://mlsanity.com/paper/2407.15527/) (2024)
- [Bayesian Concept Bottleneck Models with LLM Priors](https://mlsanity.com/paper/2410.15555/) (2024)
- [Causally Reliable Concept Bottleneck Models](https://mlsanity.com/paper/2503.04363/) (2025)
- [Relational Concept Bottleneck Models](https://mlsanity.com/paper/2308.11991/) (2023)
- [If Concept Bottlenecks are the Question, are Foundation Models the Answer?](https://mlsanity.com/paper/2504.19774/) (2025)
- [Neural Concept Binder](https://mlsanity.com/paper/2406.09949/) (2024)
- [Understanding Inter-Concept Relationships in Concept-Based Models](https://mlsanity.com/paper/2405.18217/) (2024)
- [Shortcuts and Identifiability in Concept-based Models from a Neuro-Symbolic Lens](https://mlsanity.com/paper/2502.11245/) (2025)
- [Leakage and Interpretability in Concept-Based Models](https://mlsanity.com/paper/2504.14094/) (2025)
- [Explain Yourself, Briefly! Self-Explaining Neural Networks with Concise Sufficient Reasons](https://mlsanity.com/paper/2502.03391/) (2025)
- [Concept-Attention Whitening for Interpretable Skin Lesion Diagnosis](https://mlsanity.com/paper/2404.05997/) (2024)
- [Do Concept Bottleneck Models Respect Localities?](https://mlsanity.com/paper/2401.01259/) (2024)
- [Pretrained Visual Uncertainties](https://mlsanity.com/paper/2402.16569/) (2024)
- [Avoiding Leakage Poisoning: Concept Interventions Under Distribution Shifts](https://mlsanity.com/paper/2504.17921/) (2025)

## Abstract (arXiv)

Interpretable models are designed to make decisions in a human-interpretable manner. Representatively, Concept Bottleneck Models (CBM) follow a two-step process of concept prediction and class prediction based on the predicted concepts. CBM provides explanations with high-level concepts derived from concept predictions; thus, reliable concept predictions are important for trustworthiness. In this study, we address the ambiguity issue that can harm reliability. While the existence of a concept can often be ambiguous in the data, CBM predicts concepts deterministically without considering this ambiguity. To provide a reliable interpretation against this ambiguity, we propose Probabilistic Concept Bottleneck Models (ProbCBM). By leveraging probabilistic concept embeddings, ProbCBM models uncertainty in concept prediction and provides explanations based on the concept and its corresponding uncertainty. This uncertainty enhances the reliability of the explanations. Furthermore, as class uncertainty is derived from concept uncertainty in ProbCBM, we can explain class uncertainty by means of concept uncertainty. Code is publicly available at https://github.com/ejkim47/prob-cbm.