Abstract This talk will introduce three new tools for summarizing a probability distribution more effectively than independent sampling or standard Markov chain Monte Carlo thinning: Given an initial n point summary (for example, from independent sampling or a Markov chain), kernel thinning finds a subset of only square-root n points with comparable worst-case integration error…

Abstract: When training neural networks with gradient methods and small weight initialisation, peculiar learning curves are observed: the training initially shows minimal progress, which is then followed by a sudden transition where a new "feature" is rapidly learned. This pattern is commonly known as incremental learning. In this talk, I will demonstrate that we can comprehensively understand this phenomenon within the…

Abstract: Schrödinger studied in the 1930s a thought experiment about hot gas in which a cloud of particles evolves in time from an initial distribution to another one, possibly quite different from the initial one. He posed the problem of determining the most likely evolution among the many possible ones, a problem now known as…