The Rough High-Dimensional Landscape Problem
Coordinators: Giulio Biroli, Chiara Cammarota, Patrick Charbonneau, and Andrea Montanari
Scientific Advisors: Gérard Ben Arous, Jean-Philippe Bouchaud, David Donoho, and Daniel S. Fisher
What do glassy materials and machine learning have in common? Although these two topics evolve in different research spheres, they both contend with a rough high-dimensional landscape resulting from their inherent disorder. The properties of complex landscapes and of the dynamics within them are actually central to a wide set of disparate fields, including computer science and information theory, statistical and high-energy physics, high-dimensional probability and statistics as well as biology and ecology.
Our consideration of these problems has often been erroneous; our intuition is faulty for very high dimensions. However, recent formal advances have galvanized different communities into a flurry of activity. In particular, substantial progress has been made in the development of new methods and models in both statistical physics (e.g., in the study of jamming and glasses) and computer science and statistics (e.g., in machine learning and high-dimensional statistics).
This program will bring together established and upcoming computer scientists, probabilists and mathematicians with statistical physicists and glass and disordered system researchers, as well as scientists from other interdisciplinary areas, to unify the concepts and methods recently developed by different communities. This program should trigger further advances in the characterization of universal features of complex high-dimensional landscapes and in the resolution of the specific challenges encountered in the various research areas for which such landscapes are relevant.