arXiv:2603.29654v1 Announce Type: cross Abstract: 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.

arXiv:2504.14094v3 Announce Type: replace-cross Abstract: Concept-based Models aim to improve interpretability by predicting high-level intermediate concepts, representing a promising approach for deployment in high-risk scenarios. However, they are known to suffer from information leakage, whereby models exploit unintended information encoded within the learned concepts. We introduce an information-theoretic framework to rigorously characterise and quantify leakage, and define two complementary measures: the concepts-task leakage (CTL) and interconcept leakage (ICL) scores. We show that these measures are strongly predictive of model behaviour under interventions and outperform existing alternatives. Using this framework, we identify the primary causes of leakage and, as a case study, analyse how it manifests in Concept Embedding Models, revealing interconcept and alignment leakage in addition to the concepts-task leakage present by design. Finally, we present a set of practical guidelines for designing concept-based models to reduce leakage and ensure interpretability.