# EQ-CBM: A Probabilistic Concept Bottleneck with Energy-based Models and Quantized Vectors

arXiv: https://arxiv.org/abs/2409.14630 · HTML: https://mlsanity.com/paper/2409.14630/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 44 references that are in the map.
- First posted on arXiv 22 Sep 2024.

## Builds on (most cited first, 28 of 28)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Grad-CAM++: Improved Visual Explanations for Deep Convolutional Networks](https://mlsanity.com/paper/1710.11063/) (2017)
- [Zero-Shot Learning -- A Comprehensive Evaluation of the Good, the Bad and the Ugly](https://mlsanity.com/paper/1707.00600/) (2017)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [Post-hoc Concept Bottleneck Models](https://mlsanity.com/paper/2205.15480/) (2022)
- [Neural Prototype Trees for Interpretable Fine-grained Image Recognition](https://mlsanity.com/paper/2012.02046/) (2020)
- [Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model](https://mlsanity.com/paper/1904.09770/) (2019)
- [Energy-based Generative Adversarial Network](https://mlsanity.com/paper/1609.03126/) (2016)
- [On the Anatomy of MCMC-Based Maximum Likelihood Learning of Energy-Based Models](https://mlsanity.com/paper/1903.12370/) (2019)
- [Learning Latent Space Energy-Based Prior Model](https://mlsanity.com/paper/2006.08205/) (2020)
- [Probabilistic Concept Bottleneck Models](https://mlsanity.com/paper/2306.01574/) (2023)
- [Interactive Concept Bottleneck Models](https://mlsanity.com/paper/2212.07430/) (2022)
- [Unsupervised Learning of Compositional Energy Concepts](https://mlsanity.com/paper/2111.03042/) (2021)
- [A Framework for Learning Ante-hoc Explainable Models via Concepts](https://mlsanity.com/paper/2108.11761/) (2021)
- [Auxiliary Losses for Learning Generalizable Concept-based Models](https://mlsanity.com/paper/2311.11108/) (2023)
- [Learning Energy-Based Models as Generative ConvNets via Multi-grid Modeling and Sampling](https://mlsanity.com/paper/1709.08868/) (2017)
- [Joint Training of Variational Auto-Encoder and Latent Energy-Based Model](https://mlsanity.com/paper/2006.06059/) (2020)
- [JEM++: Improved Techniques for Training JEM](https://mlsanity.com/paper/2109.09032/) (2021)
- [EGC: Image Generation and Classification via a Diffusion Energy-Based Model](https://mlsanity.com/paper/2304.02012/) (2023)
- [Energy-Based Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2202.04933/) (2022)

## Built on by (most cited first, 6 of 6)

- [Representation Engineering for Large-Language Models: Survey and Research Challenges](https://mlsanity.com/paper/2502.17601/) (2025)
- [Leakage and Interpretability in Concept-Based Models](https://mlsanity.com/paper/2504.14094/) (2025)
- [Addressing Concept Mislabeling in Concept Bottleneck Models Through Preference Optimization](https://mlsanity.com/paper/2504.18026/) (2025)
- [Parameter-Efficient Construction of the Rashomon Slice for Concept Bottleneck Models](https://mlsanity.com/paper/2511.19636/) (2025)
- [CoBELa: Steering Transparent Generation via Concept Bottlenecks on Energy Landscapes](https://mlsanity.com/paper/2507.08334/) (2025)
- [Measuring What Matters: Synthetic Benchmarks for Concept Bottleneck Models](https://mlsanity.com/paper/2606.04326/) (2026)

## Abstract (arXiv)

The demand for reliable AI systems has intensified the need for interpretable deep neural networks. Concept bottleneck models (CBMs) have gained attention as an effective approach by leveraging human-understandable concepts to enhance interpretability. However, existing CBMs face challenges due to deterministic concept encoding and reliance on inconsistent concepts, leading to inaccuracies. We propose EQ-CBM, a novel framework that enhances CBMs through probabilistic concept encoding using energy-based models (EBMs) with quantized concept activation vectors (qCAVs). EQ-CBM effectively captures uncertainties, thereby improving prediction reliability and accuracy. By employing qCAVs, our method selects homogeneous vectors during concept encoding, enabling more decisive task performance and facilitating higher levels of human intervention. Empirical results using benchmark datasets demonstrate that our approach outperforms the state-of-the-art in both concept and task accuracy.