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Statistics Seminar Speaker: Enric Boix, 11/09/2022

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Wednesday Nov 09 2022

Statistics Seminar Speaker: Enric Boix, 11/09/2022

4:15pm @ G01 Biotechnology
In Statistics Seminars

Enric Boix is a 5th year PhD student at MIT, working on the theory of deep learning and optimal transport. He has been named a Siebel Scholar, an NSF Graduate Research Fellow, and an Apple AI/ML scholar.

Talk: The Merged-Staircase property

Abstract: Which functions f : {+1,-1}^d \to \R can neural networks learn when trained with SGD? In this talk, we will consider functions that depend only on a small number of coordinates. We will study the dynamics of two-layer neural networks in the mean-field parametrization, trained by O(d) samples of SGD. Our main result will be to characterize a hierarchical property, the "merged-staircase property"— that is both necessary and nearly sufficient for learning in this setting. We will further show that non-linear training is necessary: for this class of functions, linear methods on any feature map (e.g., the NTK) are not capable of learning efficiently. The key tools are a new “dimension-free” dynamics approximation result that applies to functions defined on a latent space of low-dimension, and a proof of global convergence based on polynomial identity testing.

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