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<span style="font-size: 14pt;"><b>"The mathematical foundations of deep learning: from rating impossibility to practical existence theorems"</b></span>
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<div class="ContentPasted0"><span style="font-size: 14pt;"><b>Simone Brugiapaglia</b></span>,</div>
<div class="ContentPasted0">Department of Mathematics and Statistics,</div>
<div class="ContentPasted0">Concordia University</div>
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<div class="ContentPasted0"><i>NOTE: Please feel free to forward/share this invitation with other groups/disciplines that might be interested in this talk/topic.</i>
<b>All are welcome to attend. </b></div>
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<div class="ContentPasted0"><b>https://fsu.zoom.us/j/94273595552 </b></div>
<div class="ContentPasted0">Meeting # <b>942 7359 5552 </b></div>
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<div class="ContentPasted0"><b>Wednesday, Nov 9th</b>, 2022, Schedule: </div>
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<div class="ContentPasted0">* 3:00 to 3:30 PM Eastern Time (US and Canada) </div>
<div class="ContentPasted0">Nespresso & Teatime (in 417 DSL Commons) </div>
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<div class="ContentPasted0">* <b>3:30 to 4:30 PM</b> Eastern Time (US and Canada)
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<div class="ContentPasted0"><b>Colloquium</b> - Attend F2F (in 499 DSL) or Virtually (via Zoom)
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<div class="ContentPasted0"><b>Abstract: </b></div>
<div class="ContentPasted0">Deep learning is having a profound impact on scientific research. Yet, while deep neural networks continue to show impressive performance in a wide variety of fields, including scientific computing, their mathematical foundations
are far from being well established. In this talk, we will present recent developments in this area by illustrating two case studies.</div>
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<div class="ContentPasted0">First, motivated by applications in cognitive science, we will present “rating impossibility" theorems. These theorems identify frameworks where neural networks are provably unable to generalize outside the training set while performing
the seemingly simple task of learning identity effects, i.e. classifying pairs of objects as identical or not.</div>
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<div class="ContentPasted0">Second, motivated by applications in scientific computing, we will illustrate “practical existence" theorems. These theorems combine universal approximation results for deep neural networks with compressed sensing and high-dimensional
polynomial approximation theory. As a result, they yield sufficient conditions on the network architecture, the training strategy, and the number of samples able to guarantee accurate approximation of smooth functions of many variables.</div>
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Time permitting, we will also discuss work in progress and open questions in this research area.
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