May 01, 2026, Webb Hall 1100

Many applications throughout data science require methods that are appropriate for problems or data of any size. In machine learning, we are given training data from which we wish to learn algorithms capable of solving problems of any size. In particular, the learned algorithm must generalize to inputs of sizes that are not present in the training set. For example, algorithms for processing graphs or point clouds must generalize to inputs with any number of nodes or points. A second challenge pertaining to any-dimensionality arises in applications such as game theory or network statistics in which we wish to characterize solutions to problems of growing size. Examples include computing values of games with any number of players, or proving moment inequalities for random vectors and graphs of any size. From an optimization perspective, this amounts to deriving bounds that hold for entire sequences of problems of growing dimensionality. We present a unified framework to tackle such any-dimensional problems based on relating and comparing problems of different sizes. Our methodology leverages the recently-identified phenomenon of representation stability. We illustrate the resulting framework for any-dimensional problems in several applications. (Joint work with Eitan Levin)

Venkat Chandrasekaran is on the faculty at Caltech in Computing and Mathematical Sciences and in Electrical Engineering. He received a Ph.D. in Electrical Engineering from MIT (2011) and undergraduate degrees in Mathematics and in Electrical Engineering from Rice University (2005). His research interests lie in optimization and the information sciences.