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Progress in contemporary generative modeling for continuous-valued data has been driven by the development of algorithms, such as score-based diffusion, that are built on dynamical transport of measure. I will describe a project of research with my collaborators to build a general paradigm for dynamical generative modeling which we call stochastic interpolants. Crucially, these methods rely on access to large amounts of data from the target distribution. In that regard, a dual problem to this one is learning to sample from a target distribution only through access to the unnormalized density and its gradient. In the latter half of this talk, I will describe recent results in learning samplers for this problem built on dynamical transport and Jarzynski’s equality in non-equilibrium thermodynamics. Interestingly, the learning algorithms for these samplers do not require backpropagation through the simulation of the dynamical system. 

Please join us for pre-Colloquium Tea

This is a continuation of the lecture from Oct 23, 90 minutes. 

We use the Selberg zeta function to study the limit behavior of resonances of a degenerating family of Kleinian Schottky groups. We prove that, after a suitable rescaling, the Selberg zeta functions converge to the Ihara zeta function of a limiting finite graph associated with the relevant non-Archimedean Schottky group acting on the Berkovich projective line. Moreover, our techniques can be used to obtain effective statements. One key idea is to introduce an intermediate zeta function that captures Archimedean and non-Archimedean information (while the Selberg resp. Ihara zeta function concerns only Archimedean resp. non-Archimedean properties). This is a joint work with Jialun Li, Carlos Matheus, and Zhongkai Tao.