Measuring What Matters: Synthetic Benchmarks for Concept Bottleneck Models

Human decision-making interprets the world through high-level concepts, such as recognizing a bird by its belly color. To bridge the gap between opaque deep learning representations and human understanding, Post-Hoc Concept Bottleneck Models (post-hoc CBMs) project latent features onto interpretable concept spaces using auxiliary datasets or vision-language models. However, relying on target task accuracy as the primary measure of post-hoc CBM success obscures whether the learned concepts are semantically meaningful or merely predictive artifacts. For example, random concept projections can achieve competitive accuracy despite being semantically meaningless. In this work, we analyze the learned projections directly and identify two failure cases: First, for concept projections learned from auxiliary data, covariate shifts can lead to unfaithful concept representations for the target task. In particular, we provide an upper bound on the error introduced by this shift. Second, systematic label noise in surrogate concept labels generated by vision-language models leads to unfaithful projections. After formalizing these failure modes, we introduce novel metrics that decouple concept faithfulness from predictive accuracy. Our empirical results across real-world and synthetic benchmarks confirm that these metrics identify unfaithful behaviors that standard accuracy-based evaluation fails to detect.

Concept Bottleneck Models (CBMs) are a relevant tool for explainable Artificial Intelligence because they make their predictions through human-interpretable symbols. However, high task accuracy does not guarantee that these symbols are detected faithfully: jointly trained CBMs may encode task-specific shortcuts in the bottleneck, making their explanations unreliable. In this paper, we study concept-detection reliability by swapping independently trained concept detectors and classification heads that share the same symbolic vocabulary. We use the resulting performance degradation, concept-level metrics, and symbol-wise uncertainty estimates to identify concepts that are especially prone to spurious firing. Finally, we propose a reliability-aware training strategy in which a shared concept detector is optimized with multiple classification heads and penalized for relying on globally or instance-wise unreliable symbols. On CUB-200-2011 with full concept supervision, detectors and heads are almost freely interchangeable (swap drop below one accuracy point, relative retention above $99\%$, and no concept detected below chance), whereas on a controlled synthetic task we show that, as the concept-supervision weight is reduced, models keep near-perfect task accuracy while swapped accuracy and agreement with the ground-truth concepts collapse to chance. Our reliability-aware training substantially mitigates this leakage, roughly doubling swap accuracy in the leaky regime.

Concept-bottleneck models (CBMs) are neural classifiers that compute predictions from high-level concepts extracted from the input. CBMs ensure stakeholders can understand the concepts -- and the predictions they entail -- by learning these from concept-level annotations, which are however seldom available. Recent CBM architectures work around this issue by obtaining annotations from Vision-Language Models (VLMs). While greatly broadening applicability, doing so can yield lower quality concepts and therefore less interpretable models. We strike for a middle ground by introducing Vision-plus-Human-guided CBM (VH-CBM), a hybrid approach that exploits both VLMs and a small amount of dense annotations. VH-CBM employs a Gaussian Process in the VLM's embedding space, which captures useful global information about the target domain, to propagate the expert's supervision to any target data point. Our empirical evaluation shows how VH-CBM predicts more accurate concepts than VLM-guided CBMs even when annotating as little as 1% of the data, while sporting better concept calibration and supporting active learning.