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DTSTART;TZID=America/New_York:20260211T120000
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SUMMARY:CMSA Q&A Seminar: James Eldred Pascoe\, Drexel University
DESCRIPTION:CMSA Q&A Seminar \nSpeaker: James Eldred Pascoe\, Drexel University \nTitle: (What is) The tracial fundamental group and free universal monodromy? \nAbstract: We introduce the tracial fundamental group to classify the analytic continuation of functions that are locally behave like the trace of natural matrix valued functions. While globally defined natural matrix-valued functions (known as free noncommutative functions\, which roughly locally are defined by noncommutative power series) satisfy universal monodromy\, we show that these tracial free functions exhibit a rigid but nontrivial structure governed by the aforementioned group. We prove that the tracial fundamental group is always a torsion-free\, divisible abelian group\, standing in sharp contrast to the non-abelian fundamental groups of classical domains.
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_21126/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:CMSA Q&A Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Q-A-Seminar-2.11.2026.docx-scaled.png
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DTSTART;TZID=America/New_York:20260211T140000
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SUMMARY:ReLU and Softplus neural nets as zero-sum\, turn-based\, stopping games
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Yiannis Vlassopoulos\, Athena Research Center \nTitle: ReLU and Softplus neural nets as zero-sum\, turn-based\, stopping games \nAbstract: Neural networks are for the most part treated as black boxes. In an effort to begin elucidating the mathematical structure they encode\, we will explain how ReLU neural nets can be interpreted as zero-sum turn-based\, stopping games. The game runs in the opposite direction to the net. The input to the net is the terminal reward of the game\, the output of the net is the value of the game at its initial states. The bias at each neuron is used to define the reward and the weights are used to define state-transition probabilities. One player –Max– is trying to maximize reward and the other –Min-\, to minimize it. Every neuron gives rise to two game states\, one where Max plays and one where Min plays. In fact running the ReLU net is equivalent to the Shapley-Bellman backward recursion for the value of the game. As a corollary of this construction we get a path integral expression for the output of the net\, given input. Moreover using the fact that the Shapley operator is monotonic (with respect to the coordinate-wise order) we get bounds for the output of the net\, given bounds for the input. Adding an entropic regularization to the ReLU net game allows us to interpret Softplus neural nets as games in an analogous fashion.\nThis is joint work with Stéphane Gaubert. \n 
URL:https://cmsa.fas.harvard.edu/event/newtech_21126/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-2.11.2026.docx-1-scaled.png
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