New Framework Unifies Identifiability and Extrapolation in Latent Variable Models

This paper introduces Concept Modulation Models (CMMs), a novel theoretical framework designed to unify the understanding of identifiability and extrapolation within conditional latent variable models. These models are structured such that observed attributes influence modulators, which in turn induce latent concept laws, ultimately generating observed features. CMMs extend transition-based identifiability to conditional settings by demonstrating how feature agreement across observed attributes constrains latent concept transitions. This is expressed through "attribute potentials," which are log-density ratios between attribute-conditioned concept laws. These potentials are central to both identifiability and extrapolation. The framework provides algebraic criteria for extrapolation, indicating that agreement at unseen attributes holds if transported attribute-potential identities extend to those attributes. This work consolidates various existing identifiability and extrapolation results under a common potential-based proof object, offering a more generalized approach to reliable generalization in AI systems.