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DTSTAMP:20261006T103517
DTSTART;TZID=America/Detroit:20261014T160000
DTEND;TZID=America/Detroit:20261014T170000
SUMMARY:Lecture / Discussion:Exponential Rank Bounds for Random Matrices
DESCRIPTION:A basic question in random matrix theory is how likely a matrix is to have a large rank. For many classical models\, this probability decays extremely quickly\, but the strongest results often rely on the entries being identically distributed. In this talk\, I will discuss how to obtain the same exponential scale for matrices with fully independent\, non-identically distributed entries under only a uniform anti-concentration assumption and explain the main ideas that make this possible.
UID:153344-21915672@events.umich.edu
URL:https://events.umich.edu/event/153344
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 4088
CONTACT:
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BEGIN:VEVENT
DTSTAMP:20261006T105312
DTSTART;TZID=America/Detroit:20261021T160000
DTEND;TZID=America/Detroit:20261021T170000
SUMMARY:Lecture / Discussion:Small Moments of the Sensitivity of Polynomial Threshold Functions
DESCRIPTION:Abstract: Polynomial threshold functions (PTFs) are a central class of Boolean functions with important roles in learning theory and approximation. A fundamental question is to understand the complexity of their behavior under small perturbations of the input. On the Boolean cube\, this is captured by notions such as sensitivity\, average sensitivity\, and Boolean surface area. In this talk\, we revisit a recursive approach used to derive bounds for the average sensitivity and Boolean surface area of PTFs and obtain a polylogarithmic bound for small moments of their sensitivity. We will also explore the interplay between Fourier expansion and induction on scales from harmonic analysis\, random averaging from probability\, and decision trees and regularization from combinatorics.
UID:153329-21915644@events.umich.edu
URL:https://events.umich.edu/event/153329
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 4088
CONTACT:
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