  Concept bottleneck models (CBMs) have emerged as critical tools in domains
where interpretability is paramount. These models rely on predefined textual
descriptions, referred to as concepts, to inform their decision-making process
and offer more accurate reasoning. As a result, the selection of concepts used
in the model is of utmost significance. This study proposes
\underline{\textbf{C}}onceptual \underline{\textbf{L}}earning via
\underline{\textbf{E}}mbedding \underline{\textbf{A}}pproximations for
\underline{\textbf{R}}einforcing Interpretability and Transparency, abbreviated
as CLEAR, a framework for constructing a CBM for image classification. Using
score matching and Langevin sampling, we approximate the embedding of concepts
within the latent space of a vision-language model (VLM) by learning the scores
associated with the joint distribution of images and concepts. A concept
selection process is then employed to optimize the similarity between the
learned embeddings and the predefined ones. The derived bottleneck offers
insights into the CBM's decision-making process, enabling more comprehensive
interpretations. Our approach was evaluated through extensive experiments and
achieved state-of-the-art performance on various benchmarks. The code for our
experiments is available at https://github.com/clearProject/CLEAR/tree/main
