CBX-Bench: A Human-Aligned MLLM Council for Benchmarking Concept Bottleneck Model Explanations

Concept Bottleneck Models (CBMs) are designed to make visual classification interpretable by expressing predictions through human-understandable concepts. Although interpretability is the central motivation for CBMs, they are still largely evaluated as predictive models by downstream classification accuracy, supplemented by isolated qualitative examples. This highlights a pressing need for quantitative measures, a challenge complicated by the infeasibility of ground-truth concept annotation at scale and the open nature of concept lists due to a lack of consensus. To fill this gap, we develop a multimodal large language model (MLLM) council that, given an image and its CBM explanation, produces an explanation quality score. To ground and validate the council, we first conduct a human study to establish a ground-truth reference for CBM explanation quality: for an image, annotators compare explanations from two of LF-CBM, VLG-CBM, and CBM-Suite and choose the more useful one, or mark them as equally good or equally bad, yielding 2700 judgments over 900 image-comparison items on CUB-200, ImageNet-100, and Places365. Against this human reference, our five-model council, consisting of open-weight MLLMs, recovers over 70% of strict human preference rankings, rising to 83% on items where human annotators unanimously agree. Building on this validated council, we introduce CBX-Bench, a public benchmark and leaderboard: authors of new CBMs can submit their model's explanations, and CBX-Bench scores them with the council and maintains dataset-level rankings of explanation quality. CBX-Bench thus provides a human-aligned, scalable evaluation of CBM explanations beyond accuracy and isolated qualitative examples. The benchmark is available at https://github.com/meric-karadag/cbx-bench.