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<p class="MsoNormal"><i><span style="font-size:12.0pt;font-family:Helvetica;color:#8B0102"> </span></i><o:p></o:p></p>
<p class="MsoNormal"><i><span style="font-size:12.0pt;font-family:Helvetica;color:#8B0102">UNIVERSITY OF CHICAGO</span></i><o:p></o:p></p>
<p class="MsoNormal"><i><span style="font-size:12.0pt;font-family:Helvetica;color:#8B0102">COMPUTER SCIENCE DEPARTMENT</span></i><o:p></o:p></p>
<p class="MsoNormal"><i><span style="font-size:12.0pt;font-family:Helvetica;color:#8B0102">PRESENTS</span></i><o:p></o:p></p>
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<p class="MsoNormal"><b><span style="font-size:12.0pt;font-family:Helvetica">Haotian Jiang, PhD</span></b><o:p></o:p></p>
<p class="MsoNormal"><b><span style="font-size:11.0pt;font-family:Helvetica">Assistant Professor, University of Chicago</span></b><o:p></o:p></p>
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<p class="MsoNormal"><b><span style="font-size:11.0pt;color:black">Tuesday, </span>
</b><b><span style="font-size:11.0pt">October 1<span style="color:black">, 202</span>4<span style="color:black"> at 3:30pm</span></span></b><o:p></o:p></p>
<p class="MsoNormal"><b><span style="font-size:11.0pt;color:black;background:yellow">Location: Kent 102</span></b><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> </span><b><i><u><span style="font-size:14.0pt">Title:</span></u></i></b><i><span style="font-size:14.0pt"> </span></i><span style="font-size:12.0pt">Tensor Concentration Inequalities: A Geometric Approach</span><o:p></o:p></p>
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<p class="MsoNormal"><b><i><u><span style="font-size:14.0pt">Abstract:</span></u></i></b><span style="font-size:11.0pt"> </span><span style="font-size:12.0pt">Matrix Concentration inequalities, commonly used in the forms of Matrix Chernoff Bounds or the Non-Commutative
Khintchine Inequality, are central to a wide range of applications in computer science and mathematics. However, they fall short in many applications where tensor versions of these inequalities are required. </span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">In this work, we study concentration inequalities for the $\ell_p$-injective norms of sums of independent tensors. We obtain the first such inequalities beyond Rudelson's classical work on rank-1 tensors,
and our tensor concentration inequalities are tight in certain regimes of $p$ and the order of the tensors. Our results are obtained via a geometric argument based on estimating the covering numbers for the natural stochastic processes corresponding to tensor injective norms. </span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">We also discuss applications and connections of our inequalities to various other problems, e.g. tensor PCA, locally-decodable codes, and natural models for random tensors and their tensor extensions. </span><o:p></o:p></p>
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<p><span style="color:black"> </span><b><i><span style="font-size:14.0pt;color:black">Bio:
</span></i></b><span style="color:black">Haotian Jiang is an Assistant Professor of computer science. Previously, he was a Postdoctoral Researcher at Microsoft Research, Redmond. In December 2022, he obtained his PhD from the Paul G. Allen School of Computer
Science & Engineering at the University of Washington under the supervision of Yin Tat Lee. He is broadly interested in theoretical computer science and applied mathematics. His primary area of expertise is the design and analysis of algorithms for continuous
and discrete optimization problems, and algorithm design through the lens of discrepancy theory. His work on optimization has been recognized by a Best Student Paper Award in SODA 2021.</span><o:p></o:p></p>
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<p style="margin-bottom:12.0pt"><b><span style="font-family:Helvetica;color:black">Host:<span class="apple-converted-space"> A</span></span></b><span class="apple-converted-space"><b><span style="font-family:Helvetica">lexander Razborov</span></b></span><br>
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