Abstract

Generative priors are effective tools to combat the curse of dimensionality, and enable efficient learning that otherwise will be ill-posed, in data science. This talk starts with the classical low-rank prior, by discussing how the trick of preconditioning boosts the learning speed of gradient descent without compensating generalization in overparameterized low-rank models, unveiling the phenomenon of implicit regularization. The talk next discusses non-asymptotic theory towards understanding the data generation process of diffusion models in discrete time, assuming access to reasonable estimates of the score functions.