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| | __NOTOC__ | | __NOTOC__ |
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| − | = Fall 2020 = | + | = Spring 2021 = |
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| | <b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted. | | <b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted. |
| | <b>We usually end for questions at 3:20 PM.</b> | | <b>We usually end for questions at 3:20 PM.</b> |
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| − | <b> IMPORTANT: </b> In Fall 2020 the seminar is being run online. | + | <b> IMPORTANT: </b> In Spring 2021 the seminar is being run online. [https://uwmadison.zoom.us/j/91828707031?pwd=YUJXMUJkMDlPR0VRdkRCQVJtVndIdz09 ZOOM LINK] |
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| | If you would like to sign up for the email list to receive seminar announcements then please join [https://groups.google.com/a/g-groups.wisc.edu/forum/#!forum/probsem our group]. | | If you would like to sign up for the email list to receive seminar announcements then please join [https://groups.google.com/a/g-groups.wisc.edu/forum/#!forum/probsem our group]. |
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| − | == September 17, 2020, [https://www.math.tamu.edu/~bhanin/ Boris Hanin] (Princeton and Texas A&M) == | + | == January 28, 2021, == |
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| − | '''Pre-Talk:'''
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| − | Title: '''Neural Networks for Probabilists'''
| + | == February 4, 2021, == |
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| − | Abstract: Deep neural networks are a centerpiece in modern machine learning. They are also fascinating probabilistic models, about which much remains unclear. In this pre-talk I will define neural networks, explain how they are used in practice, and give a survey of the big theoretical questions they have raised. If time permits, I will also explain how neural networks are related to a variety of classical areas in probability and mathematical physics, including random matrix theory, optimal transport, and combinatorics of hyperplane arrangements.
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| − | '''Talk:'''
| + | == February 11, 2021, == |
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| − | Title: '''Effective Theory of Deep Neural Networks'''
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| − | Abstract: Deep neural networks are often considered to be complicated "black boxes," for which a full systematic analysis is not only out of reach but also impossible. In this talk, which is based on ongoing joint work with Sho Yaida and Daniel Adam Roberts, I will make the opposite claim. Namely, that deep neural networks with random weights and biases are exactly solvable models. Our approach applies to networks at finite width n and large depth L, the regime in which they are used in practice. A key point will be the emergence of a notion of "criticality," which involves a finetuning of model parameters (weight and bias variances). At criticality, neural networks are particularly well-behaved but still exhibit a tension between large values for n and L, with large values of n tending to make neural networks more like Gaussian processes and large values of L amplifying higher cumulants. Our analysis at initialization has many consequences also for networks during after training, which I will discuss if time permits.
| + | == February 18, 2021, == |
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| − | == September 24, 2020, [https://people.ucd.ie/neil.oconnell Neil O'Connell] (Dublin) ==
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| − | == October 1, 2020, [https://marcusmichelen.org/ Marcus Michelen], [https://mscs.uic.edu/ UIC] == | + | == February 25, 2021, [https://math.mit.edu/directory/profile.php?pid=2121 Roger Van Peski] (MIT) == |
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| − | Title: '''Roots of random polynomials near the unit circle'''
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| − | Abstract: It is a well-known (but perhaps surprising) fact that a polynomial with independent random coefficients has most of its roots very close to the unit circle. Using a probabilistic perspective, we understand the behavior of roots of random polynomials exceptionally close to the unit circle and prove several limit theorems; these results resolve several conjectures of Shepp and Vanderbei. We will also discuss how our techniques provide a heuristic, probabilistic explanation for why random polynomials tend to have most roots near the unit circle. Based on joint work with Julian Sahasrabudhe.
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| − | == October 8, 2020, [http://sites.harvard.edu/~sus977/index.html Subhabrata Sen], [https://statistics.fas.harvard.edu/ Harvard] ==
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| − | Title: '''TBA'''
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| − | Abstract: TBA
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| − | == November 12, 2020, [http://stanford.edu/~ajdunl2/ Alexander Dunlap], [https://cims.nyu.edu/ NYU Courant Institute] ==
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| − | Title: '''TBA'''
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| − | Abstract: TBA
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| | [[Past Seminars]] | | [[Past Seminars]] |
