[2510.08219] Post-hoc Stochastic Concept Bottleneck Models

Computer Science > Machine Learning arXiv:2510.08219 (cs) [Submitted on 9 Oct 2025 (v1), last revised 3 Mar 2026 (this version, v3)] Title:Post-hoc Stochastic Concept Bottleneck Models Authors:Wiktor Jan Hoffmann, Sonia Laguna, Moritz Vandenhirtz, Emanuele Palumbo, Julia E. Vogt View a PDF of the paper titled Post-hoc Stochastic Concept Bottleneck Models, by Wiktor Jan Hoffmann and 4 other authors View PDF HTML (experimental) Abstract:Concept Bottleneck Models (CBMs) are interpretable models that predict the target variable through high-level human-understandable concepts, allowing users to intervene on mispredicted concepts to adjust the final output. While recent work has shown that modeling dependencies between concepts can improve CBM performance, especially under interventions, such approaches typically require retraining the entire model, which may be infeasible when access to the original data or compute is limited. In this paper, we introduce Post-hoc Stochastic Concept Bottleneck Models (PSCBMs), a lightweight method that augments any pre-trained CBM with a multivariate normal distribution over concepts by adding only a small covariance-prediction module, without retraining the backbone model. We propose two training strategies and show on real-world data that PSCBMs consistently match or improve both concept and target accuracy over standard CBMs at test time. Furthermore, we show that due to the modeling of concept dependencies, PSCBMs perform much better than C...