# Stochastic Concept Bottleneck Models

arXiv: https://arxiv.org/abs/2406.19272 · HTML: https://mlsanity.com/paper/2406.19272/

## Key facts

- Cited by 51 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 46 references that are in the map.
- First posted on arXiv 27 Jun 2024.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [The Mythos of Model Interpretability](https://mlsanity.com/paper/1606.03490/) (2016)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [Post-hoc Concept Bottleneck Models](https://mlsanity.com/paper/2205.15480/) (2022)
- [Label-Free Concept Bottleneck Models](https://mlsanity.com/paper/2304.06129/) (2023)
- [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 Segmentation Networks: Modelling Spatially Correlated Aleatoric Uncertainty](https://mlsanity.com/paper/2006.06015/) (2020)
- [Probabilistic Concept Bottleneck Models](https://mlsanity.com/paper/2306.01574/) (2023)
- [Interactive Concept Bottleneck Models](https://mlsanity.com/paper/2212.07430/) (2022)
- [A Closer Look at the Intervention Procedure of Concept Bottleneck Models](https://mlsanity.com/paper/2302.14260/) (2023)
- [Learning to Receive Help: Intervention-Aware Concept Embedding Models](https://mlsanity.com/paper/2309.16928/) (2023)
- [Human Uncertainty in Concept-Based AI Systems](https://mlsanity.com/paper/2303.12872/) (2023)
- [Influence-Directed Explanations for Deep Convolutional Networks](https://mlsanity.com/paper/1802.03788/) (2018)
- [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)
- [Beyond Concept Bottleneck Models: How to Make Black Boxes Intervenable?](https://mlsanity.com/paper/2401.13544/) (2024)
- [Sparse Linear Concept Discovery Models](https://mlsanity.com/paper/2308.10782/) (2023)
- [Interpretable and intervenable ultrasonography-based machine learning models for pediatric appendicitis](https://mlsanity.com/paper/2302.14460/) (2023)
- [Improving Intervention Efficacy via Concept Realignment in Concept Bottleneck Models](https://mlsanity.com/paper/2405.01531/) (2024)

## Built on by (most cited first, 30 of 51)

- [A Comprehensive Survey on Self-Interpretable Neural Networks](https://mlsanity.com/paper/2501.15638/) (2025)
- [Causally Reliable Concept Bottleneck Models](https://mlsanity.com/paper/2503.04363/) (2025)
- [If Concept Bottlenecks are the Question, are Foundation Models the Answer?](https://mlsanity.com/paper/2504.19774/) (2025)
- [Leakage and Interpretability in Concept-Based Models](https://mlsanity.com/paper/2504.14094/) (2025)
- [Measuring Leakage in Concept-Based Methods: An Information Theoretic Approach](https://mlsanity.com/paper/2504.09459/) (2025)
- [Avoiding Leakage Poisoning: Concept Interventions Under Distribution Shifts](https://mlsanity.com/paper/2504.17921/) (2025)
- [Graph Concept Bottleneck Models](https://mlsanity.com/paper/2508.14255/) (2025)
- [There Was Never a Bottleneck in Concept Bottleneck Models](https://mlsanity.com/paper/2506.04877/) (2025)
- [Addressing Concept Mislabeling in Concept Bottleneck Models Through Preference Optimization](https://mlsanity.com/paper/2504.18026/) (2025)
- [Neural Probabilistic Circuits: Enabling Compositional and Interpretable Predictions through Logical Reasoning](https://mlsanity.com/paper/2501.07021/) (2025)
- [Enhancing Concept Localization in CLIP-based Concept Bottleneck Models](https://mlsanity.com/paper/2510.07115/) (2025)
- [An Analysis of Concept Bottleneck Models: Measuring, Understanding, and Mitigating the Impact of Noisy Annotations](https://mlsanity.com/paper/2505.16705/) (2025)
- [LogicCBMs: Logic-Enhanced Concept-Based Learning](https://mlsanity.com/paper/2512.07383/) (2025)
- [Towards Reasonable Concept Bottleneck Models](https://mlsanity.com/paper/2506.05014/) (2025)
- [Interpretable Hierarchical Concept Reasoning through Attention-Guided Graph Learning](https://mlsanity.com/paper/2506.21102/) (2025)
- [Interpretable Reward Modeling with Active Concept Bottlenecks](https://mlsanity.com/paper/2507.04695/) (2025)
- [Quantifying the Accuracy-Interpretability Trade-Off in Concept-Based Sidechannel Models](https://mlsanity.com/paper/2510.05670/) (2025)
- [A Geometric Unification of Concept Learning with Concept Cones](https://mlsanity.com/paper/2512.07355/) (2025)
- [Hierarchical Concept-based Interpretable Models](https://mlsanity.com/paper/2602.23947/) (2026)
- [From Pixels to Perception: Interpretable Predictions via Instance-wise Grouped Feature Selection](https://mlsanity.com/paper/2505.06003/) (2025)
- [Process-Guided Concept Bottleneck Model](https://mlsanity.com/paper/2601.10562/) (2026)
- [Mixture of Concept Bottleneck Experts](https://mlsanity.com/paper/2602.02886/) (2026)
- [Prototype-Grounded Concept Models for Verifiable Concept Alignment](https://mlsanity.com/paper/2604.16076/) (2026)
- [Concepts Worth Having: Refining VLM-Guided Concept Bottleneck Models with Minimal Annotations](https://mlsanity.com/paper/2605.16405/) (2026)
- [Matryoshka Concept Bottleneck Models](https://mlsanity.com/paper/2605.20612/) (2026)
- [Exploiting Interpretable Capabilities with Concept-Enhanced Diffusion and Prototype Networks](https://mlsanity.com/paper/2410.18705/) (2024)
- [Automated Genomic Interpretation via Concept Bottleneck Models for Medical Robotics](https://mlsanity.com/paper/2510.01618/) (2025)
- [Parameter-Efficient Construction of the Rashomon Slice for Concept Bottleneck Models](https://mlsanity.com/paper/2511.19636/) (2025)
- [SALVE: Sparse Autoencoder-Latent Vector Editing for Mechanistic Control of Neural Networks](https://mlsanity.com/paper/2512.15938/) (2025)
- [Differentiable Logic Synthesis: Spectral Coefficient Selection via Sinkhorn-Constrained Composition](https://mlsanity.com/paper/2601.13953/) (2026)

## Abstract (arXiv)

Concept Bottleneck Models (CBMs) have emerged as a promising interpretable method whose final prediction is based on intermediate, human-understandable concepts rather than the raw input. Through time-consuming manual interventions, a user can correct wrongly predicted concept values to enhance the model's downstream performance. We propose Stochastic Concept Bottleneck Models (SCBMs), a novel approach that models concept dependencies. In SCBMs, a single-concept intervention affects all correlated concepts, thereby improving intervention effectiveness. Unlike previous approaches that model the concept relations via an autoregressive structure, we introduce an explicit, distributional parameterization that allows SCBMs to retain the CBMs' efficient training and inference procedure. Additionally, we leverage the parameterization to derive an effective intervention strategy based on the confidence region. We show empirically on synthetic tabular and natural image datasets that our approach improves intervention effectiveness significantly. Notably, we showcase the versatility and usability of SCBMs by examining a setting with CLIP-inferred concepts, alleviating the need for manual concept annotations.