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DTSTART;TZID=America/New_York:20220202T140000
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SUMMARY:Neural diffusion PDEs\, differential geometry\, and graph neural networks
DESCRIPTION:Speaker: Michael Bronstein\, University of Oxford and Twitter \nTitle: Neural diffusion PDEs\, differential geometry\, and graph neural networks \nAbstract: In this talk\, I will make connections between Graph Neural Networks (GNNs) and non-Euclidean diffusion equations. I will show that drawing on methods from the domain of differential geometry\, it is possible to provide a principled view on such GNN architectural choices as positional encoding and graph rewiring as well as explain and remedy the phenomena of oversquashing and bottlenecks.
URL:https://cmsa.fas.harvard.edu/event/2-2-2022-new-technologies-in-mathematics/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-02.02.2022-2-1583x2048-1.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220209T140000
DTEND;TZID=America/New_York:20220209T150000
DTSTAMP:20240517T193404Z
CREATED:20230808T181534Z
LAST-MODIFIED:20240517T193404Z
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SUMMARY:Toward Demystifying Transformers and Attention
DESCRIPTION:Speaker: Ben Edelman\, Harvard Computer Science \nTitle: Toward Demystifying Transformers and Attention \nAbstract: Over the past several years\, attention mechanisms (primarily in the form of the Transformer architecture) have revolutionized deep learning\, leading to advances in natural language processing\, computer vision\, code synthesis\, protein structure prediction\, and beyond. Attention has a remarkable ability to enable the learning of long-range dependencies in diverse modalities of data. And yet\, there is at present limited principled understanding of the reasons for its success. In this talk\, I’ll explain how attention mechanisms and Transformers work\, and then I’ll share the results of a preliminary investigation into why they work so well. In particular\, I’ll discuss an inductive bias of attention that we call sparse variable creation: bounded-norm Transformer layers are capable of representing sparse Boolean functions\, with statistical generalization guarantees akin to sparse regression.
URL:https://cmsa.fas.harvard.edu/event/2-9-2022-new-technologies-in-mathematics-seminar/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-02.09.2022-1553x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220216T140000
DTEND;TZID=America/New_York:20220216T150000
DTSTAMP:20240515T205523Z
CREATED:20230808T181915Z
LAST-MODIFIED:20240515T205523Z
UID:10001205-1645020000-1645023600@cmsa.fas.harvard.edu
SUMMARY:Bootstrapping hyperbolic manifolds
DESCRIPTION:Speaker: James Bonifacio\, Cambridge DAMTP \nTitle: Bootstrapping hyperbolic manifolds \nAbstract: Hyperbolic manifolds are a class of Riemannian manifolds that are important in mathematics and physics\, playing a prominent role in topology\, number theory\, and string theory. Associated with a given hyperbolic metric is a sequence of numbers corresponding to the discrete eigenvalues of the Laplace-Beltrami operator. While these eigenvalues usually cannot be calculated exactly\, they can be found numerically and must also satisfy various bounds. In this talk\, I will discuss a new approach for finding numerical bounds on the eigenvalues of closed hyperbolic manifolds using general consistency conditions and semidefinite programming\, inspired by the approach of the conformal bootstrap from physics. Although these bootstrap bounds follow from seemingly trivial consistency conditions\, they are surprisingly strong and are sometimes almost saturated by actual manifolds; for example\, one such bound implies that the first nonzero eigenvalue of a closed hyperbolic surface must be less than 3.83890\, and this is very close to being saturated by a particular genus-2 surface called the Bolza surface. I will show how to derive this and other bounds and will discuss some possible future directions for this approach.
URL:https://cmsa.fas.harvard.edu/event/2-16-2022-new-technologies-in-mathematics-seminar/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-02.16.2022-1553x2048-1.png
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