Concept Modulation Models: A Unified Framework for Identifiability and Extrapolation

Concept modulation models connect identifiability and extrapolation in conditional generative models. Attributes determine modulators, which govern latent concepts and ultimately observed features. The framework uses attribute potentials to characterize both the latent transformations compatible with observed data and the conditions under which agreement extends to unseen attributes. This provides algebraic extrapolation criteria and a common basis for several existing results in nonlinear ICA, causal representation learning, and perturbation modeling.