# Post-hoc Stochastic Concept Bottleneck Models Source: [Post-hoc Stochastic Concept Bottleneck Models]() Collection index: [llms.txt]() Data updated: 2026-03-18T05:00:04.466Z Authors: Wiktor Jan Hoffmann, Sonia Laguna, Moritz Vandenhirtz, Emanuele Palumbo, Julia E. Vogt Published: 2025-10-09T13:42:54.000Z ## 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 CBMs under interventions, while remaining far more efficient than retraining a similar stochastic model from scratch. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Concept Prediction on CUB (test)](): Concept Prediction; CUB (test); Mean Concept AUC: 98.59. - [Concept Classification on Caltech-UCSD Birds-200 2011 (test)](): Concept Classification; Caltech-UCSD Birds-200 2011 (test); Concept Accuracy: 94.9285. - [Image Classification on Caltech-UCSD Birds (CUB-200-2011) (test)](): Image Classification; Caltech-UCSD Birds (CUB-200-2011) (test); Accuracy: 68.3983. - [Image Classification on CUB (test)](): Image Classification; CUB (test); Accuracy: 68.6611. ## Original sources and implementation [Original paper]() [PDF]()