Abstract
Concept bottleneck models (CBMs) are neural classifiers that allow to explain their decisions via high-level concepts, potentially enabling understanding, steering and debugging. However, their explanations are often derived heuristically. Building on formal explainability, we argue they should also be faithful, i.e., not misreport which concepts actually matter. We show that, for widespread CBM architectures, including recent VLM-based variants, faithful explanations must include all concepts in the bottleneck, compromising interpretability when this is large. This result applies to both heuristic and faithful-by-construction formal explanations. To encourage the existence of compact faithful explanations, we suggest i) modeling concepts probabilistically as binary or categorical random variables (rather than logits), and ii) employing per-concept training-time sparsification via group lasso (rather than regular elastic net). We also extend algorithms from formal explainability to CBMs, and show they outperform natural heuristics in terms of guarantees and explanation size. Overall, our work warns against naive interpretability claims and provides formal conditions and practical strategies for ensuring CBMs are as interpretable as advertised.
Keywords
Publication details
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- Open access
- Green open access
Cite this article
APA 7
Teso, S., Marconato, E., Azzolin, S., & Vergari, A. (2026). When Are Concept Bottleneck Model Explanations Faithful and Compact? https://omanscience.com/en/articles/when-are-concept-bottleneck-model-explanations-faithful-and-compact
MLA 9
Teso, Stefano, et al. "When Are Concept Bottleneck Model Explanations Faithful and Compact?" https://omanscience.com/en/articles/when-are-concept-bottleneck-model-explanations-faithful-and-compact.
Chicago (author–date)
Teso, Stefano, Emanuele Marconato, Steve Azzolin, and Antonio Vergari. 2026. "When Are Concept Bottleneck Model Explanations Faithful and Compact?" https://omanscience.com/en/articles/when-are-concept-bottleneck-model-explanations-faithful-and-compact.
Harvard
Teso, S., Marconato, E., Azzolin, S. and Vergari, A. (2026) 'When Are Concept Bottleneck Model Explanations Faithful and Compact?', Available at: https://omanscience.com/en/articles/when-are-concept-bottleneck-model-explanations-faithful-and-compact.
Vancouver
Teso S, Marconato E, Azzolin S, Vergari A. When Are Concept Bottleneck Model Explanations Faithful and Compact? https://omanscience.com/en/articles/when-are-concept-bottleneck-model-explanations-faithful-and-compact
IEEE
S. Teso, E. Marconato, S. Azzolin, and A. Vergari, "When Are Concept Bottleneck Model Explanations Faithful and Compact?," https://omanscience.com/en/articles/when-are-concept-bottleneck-model-explanations-faithful-and-compact.