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.
Dec 16, 2026
Concept extraction methods, including sparse autoencoders and transcoders, seek symbolic concepts within learned representations. This work studies their theoretical guarantees by treating concept extraction as a generative-model identification problem. A general identifiability theorem reduces the analysis to characterizing the intersection of two sets. Applying the framework to several common methods simplifies existing arguments and provides a foundation for designing concept extraction approaches with provable guarantees.
Apr 27, 2026
This chapter introduces causal representation learning as an inverse problem: recovering a latent causal model from the observations it generates. It reviews how interventions on latent variables can make this recovery possible, covering identifiability results for parametric and nonparametric models under interventions on one or multiple variables. The chapter also discusses practical algorithms that connect these theoretical results to representation learning.
Mar 20, 2026
Jul 21, 2023