Relatore:
Minh Ha Quang
- RIKEN Center for Advanced Intelligence Project (AIP), Tokyo, JAPAN
martedì 24 marzo 2026
alle ore
16.30
CV3 T.06 (presenza ed on line)
ABSTRACT:
Scaling laws describe how learning performance improves with data, compute, or training time, and have become a central theme in modern deep learning. We study this phenomenon in a canonical nonlinear model: phase retrieval with anisotropic Gaussian inputs whose covariance spectrum follows a power law. Unlike the isotropic case, where dynamics collapse to a two-dimensional system, anisotropy yields a qualitatively new regime in which an infinite hierarchy of coupled equations governs the evolution of the summary statistics. We develop a tractable reduction that reveals a three-phase trajectory: (i) fast escape from low alignment, (ii) slow convergence of the summary statistics, and (iii) spectral-tail learning in low-variance directions. From this decomposition, we derive explicit scaling laws for the mean-squared error, showing how spectral decay dictates convergence times and error curves. Experiments confirm the predicted phases and exponents. These results provide the first rigorous characterization of scaling laws in nonlinear regression with anisotropic data, highlighting how anisotropy reshapes learning dynamics.
SHORT BIO:
Prof. Minh Ha Quang is the Leader of the Functional Analytic Learning Team at RIKEN. His current research interests focus on machine learning and statistical methodologies using theories and techniques from Functional Analysis and related mathematical fields. In particular, he has been working on theories and methods involving reproducing kernel Hilbert spaces (RKHS), Riemannian geometry, Matrix and Operator Theory, Information Geometry, and Optimal Transport, especially in the Infinite-Dimensional setting. Prof. Minh Ha Quang received his PhD in mathematics from Brown University (Providence, RI, USA) and wrote his dissertation under the supervision of Stephen Smale. Before joining RIKEN, he was a researcher at the Pattern Analysis and Computer Vision group at the Italian Institute of Technology (Istituto Italiano di Tecnologia) in Genoa (Genova), Italy. Prior to Italy, he was a postdoctoral researcher at the University of Vienna, Austria, and the Humboldt University of Berlin, Germany.
Meeting ID: 872 7910 9947
