Abstract: Contemporary generative models used in the context of unsupervised learning have primarily been designed around the construction of a map between two probability distributions that transform samples from the first into samples from the second. Advances in this domain have been governed by the introduction of algorithms or inductive biases that make learning this…

Abstract: Energy-based models are a recent class of probabilistic generative models wherein the distribution being learned is parametrized up to a constant of proportionality (i.e. a partition function). Fitting such models using maximum likelihood (i.e. finding the parameters which maximize the probability of the observed data) is computationally challenging, as evaluating the partition function involves a high dimensional…

Abstract: The Paley graph is a classical number-theoretic construction of a graph that is believed to behave "pseudorandomly" in many regards. Accurately bounding the clique number of the Paley graph is a long-standing open problem in number theory, with applications to several other questions about the statistics of finite fields. I will present recent results…