Nisha Chandramoorthy — Toward Physical Generative Models

In any generative model, the generated samples have a different distribution than the data distribution, due to inevitable learning errors. This discrepancy, and metrics for evaluating the generated samples, are hard to characterize in high dimensions, motivating the need to understand how learning errors affect the reproducibility of certain "features" of the generated distributions. A first question is whether generative models produce "physical" samples, i.e., samples whose support is close to that of the true target distribution, despite algorithmic errors. A second question concerns what we term a lazy generative model: given samples from the target, we apply an arbitrary random dynamical system such that the distribution at finite time is approximately Gaussian. In principle, this noising process cannot be exactly inverted to recover target samples—but under what conditions can we approximately recover samples from a nearby distribution? Joint work with Adriaan de Clercq (UChicago) and Georg Gottwald (U Sydney).