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Bayesian Concept Bottleneck Models with LLM Priors
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Proposes BC-LLM, a Bayesian Metropolis-within-Gibbs procedure where an LLM proposes concepts from partial posteriors on split data and annotates them, yielding concept-based CBMs with uncertainty quantification.
Problem
Concept bottleneck models require a predefined candidate concept pool, which may miss relevant concepts in domains with effectively infinite candidate concepts; standard CBMs also trade accuracy for interpretability and are costly to annotate.
Approach
Treat the LLM as both a concept proposal distribution (partial posterior from a data split) and a prior, and correct its proposals with a split-sample Metropolis-Hastings accept/reject step based on partial Bayes factors, inside a Metropolis-within-Gibbs sampler with multiple-try proposals and batched LLM concept annotation.
Key results
- On CUB-Birds family tasks, BC-LLM reached 0.680 accuracy and 0.874 AUC in-distribution, outperforming LLM+CBM (0.640, 0.810) and Human+CBM (0.658, 0.835), and ResNet50 (0.664 accuracy, 0.853 AUC).
- On the SFGH readmission task, BC-LLM augmented a tabular model from AUC 0.60 to 0.64 and received an average clinician relevance rating of 2.5 versus at most 2.1 for comparators.
- On simulated MIMIC outcomes, BC-LLM with 400 observations performed on par with the oracle human-concept CBM.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use BC-LLM instead of LLM+CBM | CUB-Birds family tasks · CUB-Birds family tasks, in-distribution | accuracy: 0.640 -> 0.680 | Helped |
| Use BC-LLM instead of ResNet | CUB-Birds family tasks · CUB-Birds family tasks, in-distribution | accuracy: 0.664 -> 0.680 | Helped |
| Use BC-LLM instead of LLM+CBM | CUB-Birds family tasks · CUB-Birds family tasks, in-distribution | AUC: 0.810 -> 0.874 | Helped |
| Use BC-LLM instead of LLM+CBM | CUB-Birds family tasks · CUB-Birds family tasks, in-distribution | Brier: 0.452 -> 0.428 | Helped |
| Use BC-LLM instead of LLM+CBM | CUB-Birds family tasks · CUB-Birds family tasks, OOD | entropy: 0.663 -> 0.865 | Helped |
| Use BC-LLM instead of LLM+CBM | CUB-Birds with Claude 3.5 Haiku · CUB-Birds, Claude 3.5 Haiku | accuracy: 0.583 -> 0.665 | Helped |
| Use BC-LLM instead of LLM+CBM | CUB-Birds with Claude 3.5 Haiku · CUB-Birds, Claude 3.5 Haiku | Brier: 0.507 -> 0.443 | Helped |
| Use BC-LLM instead of LLM+CBM | fMoW image classification · fMoW USA images | accuracy: 0.311 -> 0.357 | Helped |
| Use BC-LLM instead of LLM+CBM | Imagenette classification · Imagenette | accuracy: 0.902 -> 0.987 | Helped |
| Add four clinical-note concepts to the original tabular model | Readmission risk model · Readmission risk, heart failure patients | AUC: 0.60 -> 0.64 | Helped |
| Use Claude 3.5 Haiku instead of GPT-4o-mini (ablation) | BC-LLM · CUB-Birds | accuracy | No clear effect |
| Use a simpler, vaguer Step 0 prompt (ablation) | BC-LLM · MIMIC simulated outcomes | predictive performance | No clear effect |
Surprising findings
- Soft CBMs performed worse than BC-LLM once concepts were constrained to be fully interpretable.
- The Boosting LLM+CBM baseline performed near chance on the all-200-species CUB task in the appendix table.
Limitations
- Designed for small interpretable CBMs (K typically at most 20); scaling to many concepts is slow.
- Theoretical guarantees rely on regularity conditions and asymptotic Laplace approximation; LLM partial posteriors may not be consistent with a prior.
- The MIMIC experiment uses simulated outcomes and the clinical experiment uses PHI data that cannot be released.
Experimental setup
Datasets: CUB-Birds MIMIC-IV clinical notes Zuckerberg San Francisco General Hospital discharge notes (PHI) fMoW Imagenette ImageNetV2
Benchmarks: CUB-Birds (37 family tasks) MIMIC-IV simulated outcomes SFGH heart failure readmission fMoW Imagenette
Metrics: accuracy AUC Brier score entropy (OOD) concept precision concept recall clinician relevance rating
Baselines: Human+CBM LLM+CBM Boosting LLM+CBM LLM+CBM (No keyphrases) ResNet50 Human(Oracle)+CBM
Builds on: concept bottleneck models Metropolis-within-Gibbs multiple-try Metropolis-Hastings Bayesian variable selection
Closest papers by meaning
- Stochastic Concept Bottleneck Models (NeurIPS 2024 · similarity 0.91)
- VLG-CBM: Training Concept Bottleneck Models with Vision-Language Guidance (NeurIPS 2024 · similarity 0.91)
- Energy-Based Concept Bottleneck Models: Unifying Prediction, Concept Intervention, and Probabilistic Interpretations (ICLR 2024 · similarity 0.91)
- Hybrid Concept Bottleneck Models (CVPR 2025 · similarity 0.90)
- Concepts Worth Having: Refining VLM-Guided Concept Bottleneck Models with Minimal Annotations (NeurIPS 2026 · similarity 0.89)
- Concept Bottleneck Large Language Models (ICLR 2025 · similarity 0.89)
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