On Learning Sparse High-Dimensional Functions with Gradient Descent

Abstract：

Neural Networks are hailed for their ability to discover useful low-dimensional features out of complex high-dimensional data. Over the recent years, the class of sparse (or 'multi-index') functions has emerged as a model with both practical motivations and rich structure, enabling a quantitative mathematical theory of 'feature learning'. In this talk, I will review recent progress on this front, by describing (i) the ability of gradient-descent algorithms to efficiently learn the multi-index class over Gaussian data,  (ii) Computational lower bounds, and, time permitting, (iii) the robustness of such GD algorithms to non-Gaussian data. Joint work with Loucas Pillaud-Vivien, Alberto Bietti, Aaron Zweig and Alex Damian

Zoom：

Link: https://zoom.us/j/84492465027?pwd=ZUNUS3g5elYwUjlRa0tOS1VjZG5ZQT09

ID：844 9246 5027

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Brief bio:

Joan Bruna is an Associate Professor at Courant Institute, New York University (NYU), in the Department of Computer Science, Department of Mathematics (affiliated) and the Center for Data Science. He belongs to the CILVR group and to the Math and Data groups. From 2015 to 2016, he was Assistant Professor of Statistics at UC Berkeley and part of BAIR (Berkeley AI Research). Before that, he worked at FAIR (Facebook AI Research) in New York. Prior to that, he was a postdoctoral researcher at Courant Institute, NYU. He completed his PhD in 2013 at Ecole Polytechnique, France. Before his PhD he was a Research Engineer at a semi-conductor company, developing real-time video processing algorithms. Even before that, he did a MsC at Ecole Normale Superieure de Cachan in Applied Mathematics (MVA) and a BA and MS at UPC (Universitat Politecnica de Catalunya, Barcelona) in both Mathematics and Telecommunication Engineering. For his research contributions, he has been awarded a Sloan Research Fellowship (2018), a NSF CAREER Award (2019), a best paper award at ICMLA (2018) and the IAA Outstanding Paper Award.