Concept Bottleneck Models (CBMs) promote interpretability by grounding predictions in human-understandable concepts. However, existing CBMs typically fix their task predictor to a single linear or Boolean expression, 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 experts and the functional form of each expert, exposing an underexplored region of the 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 under user-specified operator vocabularies. Empirical evaluation demonstrates that varying the mixture size and functional form provides a robust framework for navigating the accuracy-interpretability trade-off, adapting to different user and task needs.
@article{arxiv.2602.02886,
title = {Mixture of Concept Bottleneck Experts},
author = {Francesco De Santis and Gabriele Ciravegna and Giovanni De Felice and Arianna Casanova and Francesco Giannini and Michelangelo Diligenti and Mateo Espinosa Zarlenga and Pietro Barbiero and Johannes Schneider and Danilo Giordano},
journal= {arXiv preprint arXiv:2602.02886},
year = {2026}
}