# Bayesian Concept Bottleneck Models with LLM Priors

arXiv: https://arxiv.org/abs/2410.15555 · HTML: https://mlsanity.com/paper/2410.15555/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 72 references that are in the map.
- First posted on arXiv 21 Oct 2024.

## Builds on (most cited first, 30 of 43)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [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)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [Large Language Models](https://mlsanity.com/paper/2307.05782/) (2023)
- [Functional Map of the World](https://mlsanity.com/paper/1711.07846/) (2017)
- [Visual Classification via Description from Large Language Models](https://mlsanity.com/paper/2210.07183/) (2022)
- [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)
- [On Completeness-aware Concept-Based Explanations in Deep Neural Networks](https://mlsanity.com/paper/1910.07969/) (2019)
- [Large Language Models to Enhance Bayesian Optimization](https://mlsanity.com/paper/2402.03921/) (2024)
- [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)
- [Probabilistic Concept Bottleneck Models](https://mlsanity.com/paper/2306.01574/) (2023)
- [Concept Induction: Analyzing Unstructured Text with High-Level Concepts Using LLooM](https://mlsanity.com/paper/2404.12259/) (2024)
- [Goal Driven Discovery of Distributional Differences via Language Descriptions](https://mlsanity.com/paper/2302.14233/) (2023)
- [Explaining black box text modules in natural language with language models](https://mlsanity.com/paper/2305.09863/) (2023)
- [Is In-Context Learning in Large Language Models Bayesian? A Martingale Perspective](https://mlsanity.com/paper/2406.00793/) (2024)
- [Describing Differences between Text Distributions with Natural Language](https://mlsanity.com/paper/2201.12323/) (2022)
- [Describing Differences in Image Sets with Natural Language](https://mlsanity.com/paper/2312.02974/) (2023)
- [Overlooked factors in concept-based explanations: Dataset choice, concept learnability, and human capability](https://mlsanity.com/paper/2207.09615/) (2022)
- [Bayesian linear regression with sparse priors](https://mlsanity.com/paper/1403.0735/) (2014)
- [Stop Explaining Black Box Machine Learning Models for High Stakes Decisions and Use Interpretable Models Instead](https://mlsanity.com/paper/1811.10154/) (2018)
- [Augmenting Interpretable Models with LLMs during Training](https://mlsanity.com/paper/2209.11799/) (2022)
- [Bayesian Reward Models for LLM Alignment](https://mlsanity.com/paper/2402.13210/) (2024)

## Built on by (most cited first, 17 of 17)

- [Sparse Autoencoders for Hypothesis Generation](https://mlsanity.com/paper/2502.04382/) (2025)
- [If Concept Bottlenecks are the Question, are Foundation Models the Answer?](https://mlsanity.com/paper/2504.19774/) (2025)
- [Human-AI Co-design for Clinical Prediction Models](https://mlsanity.com/paper/2601.09072/) (2026)
- [Interpretable Next-token Prediction via the Generalized Induction Head](https://mlsanity.com/paper/2411.00066/) (2024)
- [Interpreting and Steering State-Space Models via Activation Subspace Bottlenecks](https://mlsanity.com/paper/2602.22719/) (2026)
- [Concepts Worth Having: Refining VLM-Guided Concept Bottleneck Models with Minimal Annotations](https://mlsanity.com/paper/2605.16405/) (2026)
- ["Who experiences large model decay and why?" A Hierarchical Framework for Diagnosing Heterogeneous Performance Drift](https://mlsanity.com/paper/2506.00756/) (2025)
- [Using Large Language Models to Suggest Informative Prior Distributions in Bayesian Statistics](https://mlsanity.com/paper/2506.21964/) (2025)
- [GenZ: Foundational models as latent variable generators within traditional statistical models](https://mlsanity.com/paper/2512.24834/) (2025)
- [Interpretability in Deep Time Series Models Demands Semantic Alignment](https://mlsanity.com/paper/2602.02239/) (2026)
- [Exploring Concept Subspace for Self-explainable Text-Attributed Graph Learning](https://mlsanity.com/paper/2604.11986/) (2026)
- [AI4BayesCode: From Natural Language Descriptions to Validated Modular Stateful Bayesian Samplers](https://mlsanity.com/paper/2605.18476/) (2026)
- [Measuring What Matters: Synthetic Benchmarks for Concept Bottleneck Models](https://mlsanity.com/paper/2606.04326/) (2026)
- [Verbalized Particle Posterior: Bayesian Inference over Natural Language Hypotheses](https://mlsanity.com/paper/2607.22961/) (2026)
- [Principal Trait Analysis: Towards Deriving "Skills" in Human-AI Collaboration](https://mlsanity.com/paper/2608.11460/) (2026)
- [Routing Without Embeddings: Fast And Interpretable Routing With Regular Expressions](https://mlsanity.com/paper/2609.34326/) (2026)
- [Learning to Detect Shifts in Unstructured Data Streams via Monitoring-by-Betting](https://mlsanity.com/paper/2610.17399/) (2026)

## Abstract (arXiv)

Concept Bottleneck Models (CBMs) have been proposed as a compromise between white-box and black-box models, aiming to achieve interpretability without sacrificing accuracy. The standard training procedure for CBMs is to predefine a candidate set of human-interpretable concepts, extract their values from the training data, and identify a sparse subset as inputs to a transparent prediction model. However, such approaches are often hampered by the tradeoff between exploring a sufficiently large set of concepts versus controlling the cost of obtaining concept extractions, resulting in a large interpretability-accuracy tradeoff. This work investigates a novel approach that sidesteps these challenges: BC-LLM iteratively searches over a potentially infinite set of concepts within a Bayesian framework, in which Large Language Models (LLMs) serve as both a concept extraction mechanism and prior. Even though LLMs can be miscalibrated and hallucinate, we prove that BC-LLM can provide rigorous statistical inference and uncertainty quantification. Across image, text, and tabular datasets, BC-LLM outperforms interpretable baselines and even black-box models in certain settings, converges more rapidly towards relevant concepts, and is more robust to out-of-distribution samples.