Mixture of Concept Bottleneck Experts

Francesco De Santis, Gabriele Ciravegna, Giovanni De Felice, Arianna Casanova, Francesco Giannini, Michelangelo Diligenti, Johannes Schneider, Danilo Giordano, Mateo Espinosa Zarlenga, Pietro Barbiero
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:23407-23431, 2026.

Abstract

Concept Bottleneck Models (CBMs) promote interpretability by grounding predictions in human-understandable concepts. However, existing CBMs typically constrain their task predictor to a single expression whose functional form is set a priori, limiting both predictive accuracy and adaptability to diverse user needs. We propose Mixture of Concept Bottleneck Experts (M-CBEs), a framework that generalizes existing CBMs along two dimensions: the number of expressions, referred to as experts, employed by the task predictor to map concepts to the task, and the functional form each expression takes, thus exposing an underexplored region of this design space. We investigate this region by instantiating two novel models: Linear M-CBE, which learns a finite set of linear expressions, and Symbolic M-CBE, which leverages symbolic regression to discover expert functions from data subject to user-specified operator vocabularies. Empirical evaluation demonstrates that varying the number of expressions and their functional form provides a robust framework for navigating the accuracy-interpretability trade-off.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-de-santis26a, title = {Mixture of Concept Bottleneck Experts}, author = {De Santis, Francesco and Ciravegna, Gabriele and De Felice, Giovanni and Casanova, Arianna and Giannini, Francesco and Diligenti, Michelangelo and Schneider, Johannes and Giordano, Danilo and Espinosa Zarlenga, Mateo and Barbiero, Pietro}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {23407--23431}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/de-santis26a/de-santis26a.pdf}, url = {https://proceedings.mlr.press/v306/de-santis26a.html}, abstract = {Concept Bottleneck Models (CBMs) promote interpretability by grounding predictions in human-understandable concepts. However, existing CBMs typically constrain their task predictor to a single expression whose functional form is set a priori, limiting both predictive accuracy and adaptability to diverse user needs. We propose Mixture of Concept Bottleneck Experts (M-CBEs), a framework that generalizes existing CBMs along two dimensions: the number of expressions, referred to as experts, employed by the task predictor to map concepts to the task, and the functional form each expression takes, thus exposing an underexplored region of this design space. We investigate this region by instantiating two novel models: Linear M-CBE, which learns a finite set of linear expressions, and Symbolic M-CBE, which leverages symbolic regression to discover expert functions from data subject to user-specified operator vocabularies. Empirical evaluation demonstrates that varying the number of expressions and their functional form provides a robust framework for navigating the accuracy-interpretability trade-off.} }
Endnote
%0 Conference Paper %T Mixture of Concept Bottleneck Experts %A Francesco De Santis %A Gabriele Ciravegna %A Giovanni De Felice %A Arianna Casanova %A Francesco Giannini %A Michelangelo Diligenti %A Johannes Schneider %A Danilo Giordano %A Mateo Espinosa Zarlenga %A Pietro Barbiero %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-de-santis26a %I PMLR %P 23407--23431 %U https://proceedings.mlr.press/v306/de-santis26a.html %V 306 %X Concept Bottleneck Models (CBMs) promote interpretability by grounding predictions in human-understandable concepts. However, existing CBMs typically constrain their task predictor to a single expression whose functional form is set a priori, limiting both predictive accuracy and adaptability to diverse user needs. We propose Mixture of Concept Bottleneck Experts (M-CBEs), a framework that generalizes existing CBMs along two dimensions: the number of expressions, referred to as experts, employed by the task predictor to map concepts to the task, and the functional form each expression takes, thus exposing an underexplored region of this design space. We investigate this region by instantiating two novel models: Linear M-CBE, which learns a finite set of linear expressions, and Symbolic M-CBE, which leverages symbolic regression to discover expert functions from data subject to user-specified operator vocabularies. Empirical evaluation demonstrates that varying the number of expressions and their functional form provides a robust framework for navigating the accuracy-interpretability trade-off.
APA
De Santis, F., Ciravegna, G., De Felice, G., Casanova, A., Giannini, F., Diligenti, M., Schneider, J., Giordano, D., Espinosa Zarlenga, M. & Barbiero, P.. (2026). Mixture of Concept Bottleneck Experts. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:23407-23431 Available from https://proceedings.mlr.press/v306/de-santis26a.html.

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