Probability Seminar

Universal approximation of measure-to-measure operators by transformers. Abstract: Scientific data increasingly takes the form of evolving point cloud ensembles, interacting particles, or varying-size collections of sensor measurements, rather than fixed-dimensional data representations. This motivates the approximation of mappings from one probability measure to another. This talk centers on measure-to-measure transformer architectures that act directly on particle representations of distributional data. Toward analyzing the capabilities and limitations of such architectures, the talk presents recent approximation, stability, and discretization theory that underpin their computational cost and accuracy. A running example throughout the talk is the amortized estimation of conditional distributions. Joint work with Frank Cole and Takashi Furuya.