Concept frustration: Aligning human concepts and machine representations

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.

Toward using GANs in astrophysical Monte-Carlo simulations

Accurate modelling of spectra produced by X-ray sources requires the use of Monte-Carlo simulations. These simulations need to evaluate physical processes, such as those occurring in accretion processes around compact objects by sampling a number of different probability distributions. This is computationally time-consuming and could be sped up if replaced by neural networks. We demonstrate, on an example of the Maxwell-J\"uttner distribution that describes the speed of relativistic electrons, that the generative adversarial network (GAN) is capable of statistically replicating the distribution. The average value of the Kolmogorov-Smirnov test is 0.5 for samples generated by the neural network, showing that the generated distribution cannot be distinguished from the true distribution.