Aligning human-interpretable concepts with the internal representations learned by modern machine learning systems remains a central challenge for interpretable AI. We introduce a geometric framework for comparing supervised human concepts with unsupervised intermediate representations extracted from foundation model embeddings. Motivated by the role of conceptual leaps in scientific discovery, we formalise the notion of concept frustration: a contradiction that arises when an unobserved concept induces relationships between known concepts that cannot be made consistent within an existing ontology. We develop task-aligned similarity measures that detect concept frustration between supervised concept-based models and unsupervised representations derived from foundation models, and show that the phenomenon is detectable in task-aligned geometry while conventional Euclidean comparisons fail. Under a linear-Gaussian generative model we derive a closed-form expression for Bayes-optimal concept-based classifier accuracy, decomposing predictive signal into known-known, known-unknown and unknown-unknown contributions and identifying analytically where frustration affects performance. Experiments on synthetic data and real language and vision tasks demonstrate that frustration can be detected in foundation model representations and that incorporating a frustrating concept into an interpretable model reorganises the geometry of learned concept representations, to better align human and machine reasoning. These results suggest a principled framework for diagnosing incomplete concept ontologies and aligning human and machine conceptual reasoning, with implications for the development and validation of safe interpretable AI for high-risk applications.

To increase the trustworthiness of deep neural networks, it is critical to improve the understanding of how they make decisions. This paper introduces a novel unsupervised concept-based model for image classification, named Learnable Concept-Based Model (LCBM) which models concepts as random variables within a Bernoulli latent space. Unlike traditional methods that either require extensive human supervision or suffer from limited scalability, our approach employs a reduced number of concepts without sacrificing performance. We demonstrate that LCBM surpasses existing unsupervised concept-based models in generalization capability and nearly matches the performance of black-box models. The proposed concept representation enhances information retention and aligns more closely with human understanding. A user study demonstrates the discovered concepts are also more intuitive for humans to interpret. Finally, despite the use of concept embeddings, we maintain model interpretability by means of a local linear combination of concepts.

With the increasing demands for accountability, interpretability is becoming an essential capability for real-world AI applications. However, most methods utilize post-hoc approaches rather than training the interpretable model. In this article, we propose a novel interpretable model based on the concept bottleneck model (CBM). CBM uses concept labels to train an intermediate layer as the additional visible layer. However, because the number of concept labels restricts the dimension of this layer, it is difficult to obtain high accuracy with a small number of labels. To address this issue, we integrate supervised concepts with unsupervised ones trained with self-explaining neural networks (SENNs). By seamlessly training these two types of concepts while reducing the amount of computation, we can obtain both supervised and unsupervised concepts simultaneously, even for large-sized images. We refer to the proposed model as the concept bottleneck model with additional unsupervised concepts (CBM-AUC). We experimentally confirmed that the proposed model outperformed CBM and SENN. We also visualized the saliency map of each concept and confirmed that it was consistent with the semantic meanings.