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DTSTART;TZID=America/New_York:20251017T120000
DTEND;TZID=America/New_York:20251017T130000
DTSTAMP:20260501T082711
CREATED:20250827T141359Z
LAST-MODIFIED:20251010T180544Z
UID:10003766-1760702400-1760706000@cmsa.fas.harvard.edu
SUMMARY:DMFT\, Two Point Correlations of Resolvents\, and Applications to Machine Learning Theory
DESCRIPTION:Member Seminar \nSpeaker: Blake Bordelon \nTitle: DMFT\, Two Point Correlations of Resolvents\, and Applications to Machine Learning Theory \nAbstract: Machine learning algorithms evolve the parameters of a model in a high dimensional and disordered loss landscape. To characterize the effects of random initialization of model parameters\, randomly sampled training data\, and the effect of SGD noise\, it often is useful to invoke ideas from random matrix theory and the physics of disordered systems. In this seminar\, I describe a general idea\, known as dynamical mean field theory (DMFT) which describes the evolution of a disordered dynamical system in infinite dimensions. I will briefly describe simple examples of interest to theoretical neuroscientists and machine learning theorists. For linear dynamical systems\, I will show that this method characterizes the typical case trajectory in terms of two point correlations of resolvent matrices evaluated at different frequencies. This bispectral object can account for puzzling effects such as late time divergence of gradient descent at the interpolation threshold (when parameters = dataset size) despite the Jacobian of the dynamics having real and non-positive eigenvalues. I will then describe a novel two point correlation result for general free products of the form M = O B O^T A for O sampled from the Haar measure. I will use this result to characterize the exact asymptotics of the performance of a linear transformer trained to perform in-context linear regression on “generic” (randomly rotated) covariance matrices.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-101725/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-10.17.25-scaled.png
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DTSTART;TZID=America/New_York:20251017T130000
DTEND;TZID=America/New_York:20251017T160000
DTSTAMP:20260501T082711
CREATED:20250930T134721Z
LAST-MODIFIED:20251014T133421Z
UID:10003800-1760706000-1760716800@cmsa.fas.harvard.edu
SUMMARY:Freedman Seminar: Michael Freedman\, CMSA & Bowen Yang\, CMSA
DESCRIPTION:Freedman Seminar \nSpeaker: Michael Freedman\, Harvard CMSA \nTitle: Sullivan’s work on Lipschitz structures \nAbstract: I’ll begin with an elementary\, but now little known\, piece of PL topology: engulfing. John Stalling used it to give an alternative proof of the high dimensional Poincare conjecture. Then I’ll explain Dennis Sullivan’s enhancement of Kirby’s torus trick (which relies on engulfing.) I’ll note an open question regarding Lipschitz structures on 4-manifolds. \n  \nSpeaker: Bowen Yang\, CMSA \nTitle: Quantum Cellular Automata and Algebraic L-Theory \nAbstract: Quantum cellular automata (QCAs) are models of reversible quantum dynamics that preserve locality; they can be thought of as quantum analogues of classical cellular automata\, but with much richer structure. I will describe a classification of the Clifford subclass of QCAs using methods from algebraic L-theory. The main result identifies the group of Clifford QCAs\, up to natural equivalences\, with L-theory homology of the underlying space. This gives a conceptual explanation of previously observed periodic patterns in lattice models and extends the picture to more general spaces. I will outline the ideas behind the construction and indicate how the framework connects topology\, operator algebras\, and quantum information. If time permits\, I will also comment on what is known — and unknown — about the general (non-Clifford) case.
URL:https://cmsa.fas.harvard.edu/event/freedman_101725/
LOCATION:Virtual
CATEGORIES:Freedman Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Freedman-Seminar-10.17.25.docx-1-scaled.png
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