Events
Statistics & Data Science Seminar
Learning From Gaussian Data: Single and Multi-Index Models
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Speaker: Alex Damian (Kempner at Harvard) Kempner Research Fellow Kempner Institute, Harvard University Monday, September 15, 2025 3:30PM - 4:30PM 3:30pm Pre-talk meet and greet teatime in 1307
4:00-5:00pm Talk in 1327 and via Webcast: https://yale.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=f535f143-1393-4f69-a787-b3450114ea41 |
Abstract: In this work we consider generic Gaussian Multi-index models, in which the labels only depend on the (Gaussian) d-dimensional inputs through their projection onto a low-dimensional subspace, and we study efficient agnostic estimation procedures for this hidden subspace. We introduce the generative leap exponent k*, a natural extension of the generative exponent from [DPVLB24] to the multi-index setting. We first show that a sample complexity of n= Θ(d^{1∨k*/2}) is necessary in the class of algorithms captured by the Low-Degree-Polynomial framework. We then establish that this sample complexity is also sufficient, by giving an agnostic sequential estimation procedure (that is, requiring no prior knowledge of the multi-index model) based on a spectral U-statistic over appropriate Hermite tensors. We further compute the generative leap exponent for several examples including piecewise linear functions (deep ReLU networks with bias).
Speaker bio: Alex Damian is a Research Fellow at the Kempner Institute at Harvard University, where he studies the mathematical foundations of deep learning. His work centers on optimization dynamics and representation learning, with the goal of understanding how algorithms such as stochastic gradient descent and Adam navigate high-dimensional loss landscapes and shape the representations that neural networks learn. He earned his Ph.D. in Applied and Computational Mathematics from Princeton University, advised by Jason D. Lee, and his B.S. in Mathematics from Duke University. His research has been supported by an NSF Graduate Research Fellowship and a Jane Street Graduate Research Fellowship.
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- Statistics & Data Science Seminar
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