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<div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255)"><div class="gmail_default" style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;text-align:start;text-indent:0px;text-decoration-style:initial;text-decoration-color:initial"><font color="#000000" face="arial, helvetica, sans-serif">When: <b style="font-weight:400"> </b>   Tuesday, May 22nd <span class="gmail-m_-4721497507425796220gmail-m_-1288128789894450374gmail-m_-1216822548864914938m_1430452980776983890gmail-m_1031910664862358996gmail-m_8778633083237298896gmail-m_-8347358208690191418gmail-m_6958947101002467454gmail-m_4240741644540508174gmail-m_-7649362550103587767m_3439038168464703931gmail-m_7186661958014209082gmail-m_-4881373329697077770gmail-m_-2141744242196855365gmail-m_1163836401633243615gmail-m_2148237477730121328gmail-m_-6691959996525573090gmail-m_1517372298344856049gmail-m_491069367152086750gmail-m_-8327640324523575189gmail-m_2420618808463760418gmail-m_7960197898027616883gmail-m_8692226636264124041gmail-m_2794822896869921223gmail-m_7508998950622620526gmail-m_-7153355664495542534gmail-il" style="font-weight:400">at</span> <span style="font-weight:400;background-color:rgb(255,255,255)"><b>11:00 am</b></span></font></div><div class="gmail_default" style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;font-weight:400;text-align:start;text-indent:0px;text-decoration-style:initial;text-decoration-color:initial"><font color="#000000" face="arial, helvetica, sans-serif"><br></font></div><div class="gmail_default" style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;text-align:start;text-indent:0px;text-decoration-style:initial;text-decoration-color:initial"><font color="#000000" face="arial, helvetica, sans-serif">Where:    <span class="gmail-m_-4721497507425796220gmail-m_-1288128789894450374gmail-m_-1216822548864914938m_1430452980776983890gmail-m_1031910664862358996gmail-m_8778633083237298896gmail-m_-8347358208690191418gmail-m_6958947101002467454gmail-m_4240741644540508174gmail-m_-7649362550103587767m_3439038168464703931gmail-m_7186661958014209082gmail-m_-4881373329697077770gmail-m_-2141744242196855365gmail-m_1163836401633243615gmail-m_2148237477730121328gmail-m_-6691959996525573090gmail-m_1517372298344856049gmail-m_491069367152086750gmail-m_-8327640324523575189gmail-m_2420618808463760418gmail-m_7960197898027616883gmail-m_8692226636264124041gmail-m_2794822896869921223gmail-m_7508998950622620526gmail-m_-7153355664495542534gmail-m_8421504075585210435gmail-m_3262824545120381495gmail-m_-1141671822915777344gmail-m_-7219251726624328345gmail-m_-8588148075564318222gmail-m_-8767966813928691312gmail-m_-1542318334608687154gmail-m_5717104778280916634gmail-m_4845490158781220632gmail-m_5124567205141626540gmail-m_3209361100497750746gmail-m_2953668934074478317gmail-m_-3155518689668024534m_9067904842688472155gmail-m_3071693547520408192gmail-il" style="font-weight:400"><span class="gmail-m_-4721497507425796220gmail-m_-1288128789894450374gmail-m_-1216822548864914938m_1430452980776983890gmail-m_1031910664862358996gmail-m_8778633083237298896gmail-m_-8347358208690191418gmail-m_6958947101002467454gmail-m_4240741644540508174gmail-m_-7649362550103587767m_3439038168464703931gmail-m_7186661958014209082gmail-m_-4881373329697077770gmail-m_-2141744242196855365gmail-m_1163836401633243615gmail-m_2148237477730121328gmail-m_-6691959996525573090gmail-m_1517372298344856049gmail-m_491069367152086750gmail-m_-8327640324523575189gmail-m_2420618808463760418gmail-m_7960197898027616883gmail-m_8692226636264124041gmail-m_2794822896869921223gmail-m_7508998950622620526gmail-m_-7153355664495542534gmail-il"><span class="gmail-m_-4721497507425796220gmail-m_-1288128789894450374gmail-m_-1216822548864914938m_1430452980776983890gmail-m_1031910664862358996gmail-m_8778633083237298896gmail-m_-8347358208690191418gmail-m_6958947101002467454gmail-il">TTIC</span></span></span>, 6045 S Kenwood Avenue, 5th Floor, Room 526</font></div><div class="gmail_default" style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;font-weight:400;text-align:start;text-indent:0px;text-decoration-style:initial;text-decoration-color:initial"><font face="arial, helvetica, sans-serif"><br></font></div><div style="text-align:start;text-indent:0px;text-decoration-style:initial;text-decoration-color:initial"><font color="#000000" style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px"><font face="arial, helvetica, sans-serif">Who:       </font></font><span style="font-size:12.8px">Yasaman Bahri, Google Brain</span></div><div style="text-align:start;text-indent:0px;text-decoration-style:initial;text-decoration-color:initial"><span style="font-size:12.8px"><br></span></div><br class="gmail-m_-4721497507425796220gmail-m_-1288128789894450374gmail-Apple-interchange-newline">Title:<span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:small;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;font-weight:400">        </span><span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;font-weight:400;text-align:start;text-indent:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">Wide, Deep Neural Networks are Gaussian Processes</span></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255)"><br></div><span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255)">Abstract: One means of better understanding seemingly complicated models such as deep neural networks is to connect them to other objects we already understand. For instance, Gaussian processes are well-studied models with well-controlled analytic properties. In his seminal work, Radford Neal suggested thinking about inference in function space, rather than parameter space, and in doing so established a correspondence between single-layer fully-connected neural networks with an i.i.d prior over parameters and certain Gaussian processes (GPs), in the limit of infinite network width. The correspondence was, however, restricted to a single-hidden layer.</span><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255)"><span style="font-size:12.8px"><br></span></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255)"><span style="font-size:12.8px">We develop this line of work and build an exact correspondence between deep, infinitely wide neural networks and Gaussian processes. Algorithmically, this mapping also enables a route towards Bayesian inference with deep neural networks, without needing to instantiate a network, which we implement on MNIST and CIFAR-10. We compare to the performance of finite-width networks trained with standard stochastic optimization. We find that performance increases as finite-width trained networks are made wider and more similar to a GP, and thus that GP predictions typically outperform those of finite-width networks. </span></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255)"><span style="font-size:12.8px"><br></span></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255)"><span style="font-size:12.8px">Time permitting, I will also give some brief highlights of our related work, studying the propagation of signals through random neural networks. This analysis informs initializations for training ultra-deep networks with tens of thousands of layers.</span></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255)"><span style="font-size:12.8px"><br></span></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255)"><span style="font-size:12.8px"><span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">Links: </span><div dir="auto" style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Jeffrey Pennington and Yasaman Bahri. “Geometry of Neural Network Loss Surfaces via Random Matrix Theory.” ICML 2017.<span> </span><a href="http://proceedings.mlr.press/v70/pennington17a" target="_blank" style="color:rgb(17,85,204)">http://proceedings.mlr.p<wbr>ress/v70/pennington17a</a></div><div dir="auto" style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><br></div><div dir="auto" style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Jaehoon Lee*, Yasaman Bahri*, Roman Novak, Samuel S. Schoenholz, Jeffrey Pennington, Jascha Sohl-Dickstein. “Deep Neural Networks as Gaussian Processes.” ICLR 2018.<span> </span><a href="https://arxiv.org/abs/1711.00165" target="_blank" style="color:rgb(17,85,204)">https://arxiv.org/abs/17<wbr>11.00165</a>. </div><div dir="auto" style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><br></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Bio: Yasaman Bahri is a researcher at Google Brain working on deep learning. The goal of her research is to advance a scientific, principled understanding of deep learning, with an eye towards theoretical analysis informed by careful empirical work. She got a PhD in Theoretical Condensed Matter physics from UC Berkeley, specializing in many body physics; working on symmetry-protected topological phases, many-body localization, non-Fermi liquids, and topological mechanics. She is also interested in the connections between condensed matter, theoretical physics and machine learning. </div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><br></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><br></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Host:<span> </span><a href="mailto:mesrob@ttic.edu" target="_blank" style="color:rgb(17,85,204)">Mesrob Ohannessian</a></div><br class="gmail-m_-4721497507425796220gmail-m_-1288128789894450374gmail-Apple-interchange-newline"></span></div><br class="gmail-Apple-interchange-newline">

<br><div class="gmail_extra"><br clear="all"><div><div class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><font face="arial, helvetica, sans-serif">Mary C. Marre</font><div><font face="arial, helvetica, sans-serif">Administrative Assistant</font></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6"><b>Toyota Technological Institute</b></font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6">6045 S. Kenwood Avenue</font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6">Room 504</font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6">Chicago, IL  60637</font></i></div><div><i><font face="arial, helvetica, sans-serif">p:(773) 834-1757</font></i></div><div><i><font face="arial, helvetica, sans-serif">f: (773) 357-6970</font></i></div><div><b><i><a href="mailto:mmarre@ttic.edu" target="_blank"><font face="arial, helvetica, sans-serif">mmarre@ttic.edu</font></a></i></b></div></div></div></div></div></div></div></div></div></div>
<br><div class="gmail_quote">On Mon, May 21, 2018 at 4:37 PM, Mary Marre <span dir="ltr"><<a href="mailto:mmarre@ttic.edu" target="_blank">mmarre@ttic.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">

<div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255)"><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;text-align:start;text-indent:0px;text-decoration-style:initial;text-decoration-color:initial"><font color="#000000" face="arial, helvetica, sans-serif">When: <b style="font-weight:400"> </b>   Tuesday, May 22nd <span class="m_-4721497507425796220gmail-m_-1288128789894450374gmail-m_-1216822548864914938m_1430452980776983890gmail-m_1031910664862358996gmail-m_8778633083237298896gmail-m_-8347358208690191418gmail-m_6958947101002467454gmail-m_4240741644540508174gmail-m_-7649362550103587767m_3439038168464703931gmail-m_7186661958014209082gmail-m_-4881373329697077770gmail-m_-2141744242196855365gmail-m_1163836401633243615gmail-m_2148237477730121328gmail-m_-6691959996525573090gmail-m_1517372298344856049gmail-m_491069367152086750gmail-m_-8327640324523575189gmail-m_2420618808463760418gmail-m_7960197898027616883gmail-m_8692226636264124041gmail-m_2794822896869921223gmail-m_7508998950622620526gmail-m_-7153355664495542534gmail-il" style="font-weight:400">at</span> <span style="font-weight:400;background-color:rgb(255,255,255)"><b>11:00 am</b></span></font></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;font-weight:400;text-align:start;text-indent:0px;text-decoration-style:initial;text-decoration-color:initial"><font color="#000000" face="arial, helvetica, sans-serif"><br></font></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;text-align:start;text-indent:0px;text-decoration-style:initial;text-decoration-color:initial"><font color="#000000" face="arial, helvetica, sans-serif">Where:    <span class="m_-4721497507425796220gmail-m_-1288128789894450374gmail-m_-1216822548864914938m_1430452980776983890gmail-m_1031910664862358996gmail-m_8778633083237298896gmail-m_-8347358208690191418gmail-m_6958947101002467454gmail-m_4240741644540508174gmail-m_-7649362550103587767m_3439038168464703931gmail-m_7186661958014209082gmail-m_-4881373329697077770gmail-m_-2141744242196855365gmail-m_1163836401633243615gmail-m_2148237477730121328gmail-m_-6691959996525573090gmail-m_1517372298344856049gmail-m_491069367152086750gmail-m_-8327640324523575189gmail-m_2420618808463760418gmail-m_7960197898027616883gmail-m_8692226636264124041gmail-m_2794822896869921223gmail-m_7508998950622620526gmail-m_-7153355664495542534gmail-m_8421504075585210435gmail-m_3262824545120381495gmail-m_-1141671822915777344gmail-m_-7219251726624328345gmail-m_-8588148075564318222gmail-m_-8767966813928691312gmail-m_-1542318334608687154gmail-m_5717104778280916634gmail-m_4845490158781220632gmail-m_5124567205141626540gmail-m_3209361100497750746gmail-m_2953668934074478317gmail-m_-3155518689668024534m_9067904842688472155gmail-m_3071693547520408192gmail-il" style="font-weight:400"><span class="m_-4721497507425796220gmail-m_-1288128789894450374gmail-m_-1216822548864914938m_1430452980776983890gmail-m_1031910664862358996gmail-m_8778633083237298896gmail-m_-8347358208690191418gmail-m_6958947101002467454gmail-m_4240741644540508174gmail-m_-7649362550103587767m_3439038168464703931gmail-m_7186661958014209082gmail-m_-4881373329697077770gmail-m_-2141744242196855365gmail-m_1163836401633243615gmail-m_2148237477730121328gmail-m_-6691959996525573090gmail-m_1517372298344856049gmail-m_491069367152086750gmail-m_-8327640324523575189gmail-m_2420618808463760418gmail-m_7960197898027616883gmail-m_8692226636264124041gmail-m_2794822896869921223gmail-m_7508998950622620526gmail-m_-7153355664495542534gmail-il"><span class="m_-4721497507425796220gmail-m_-1288128789894450374gmail-m_-1216822548864914938m_1430452980776983890gmail-m_1031910664862358996gmail-m_8778633083237298896gmail-m_-8347358208690191418gmail-m_6958947101002467454gmail-il">TTIC</span></span></span>, 6045 S Kenwood Avenue, 5th Floor, Room 526</font></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;font-weight:400;text-align:start;text-indent:0px;text-decoration-style:initial;text-decoration-color:initial"><font face="arial, helvetica, sans-serif"><br></font></div><div style="text-align:start;text-indent:0px;text-decoration-style:initial;text-decoration-color:initial"><font color="#000000" style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px"><font face="arial, helvetica, sans-serif">Who:       </font></font><span style="font-size:12.8px">Yasaman Bahri, Google Brain</span></div><div style="text-align:start;text-indent:0px;text-decoration-style:initial;text-decoration-color:initial"><span style="font-size:12.8px"><br></span></div><br class="m_-4721497507425796220gmail-m_-1288128789894450374gmail-Apple-interchange-newline">Title:<span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:small;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;font-weight:400">        </span><span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;font-weight:400;text-align:start;text-indent:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">Wide, Deep Neural Networks are Gaussian Processes</span></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255)"><br></div><span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Abstract: One means of better understanding seemingly complicated models such as deep neural networks is to connect them to other objects we already understand. For instance, Gaussian processes are well-studied models with well-controlled analytic properties. In his seminal work, Radford Neal suggested thinking about inference in function space, rather than parameter space, and in doing so established a correspondence between single-layer fully-connected neural networks with an i.i.d prior over parameters and certain Gaussian processes (GPs), in the limit of infinite network width. The correspondence was, however, restricted to a single-hidden layer.</span><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><span style="font-size:12.8px"><br></span></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><span style="font-size:12.8px">We develop this line of work and build an exact correspondence between deep, infinitely wide neural networks and Gaussian processes. Algorithmically, this mapping also enables a route towards Bayesian inference with deep neural networks, without needing to instantiate a network, which we implement on MNIST and CIFAR-10. We compare to the performance of finite-width networks trained with standard stochastic optimization. We find that performance increases as finite-width trained networks are made wider and more similar to a GP, and thus that GP predictions typically outperform those of finite-width networks. </span></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><span style="font-size:12.8px"><br></span></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><span style="font-size:12.8px">Time permitting, I will also give some brief highlights of our related work, studying the propagation of signals through random neural networks. This analysis informs initializations for training ultra-deep networks with tens of thousands of layers.</span></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><span style="font-size:12.8px"><br></span></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><span style="font-size:12.8px"><span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">Links: </span><div dir="auto" style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Jeffrey Pennington and Yasaman Bahri. “Geometry of Neural Network Loss Surfaces via Random Matrix Theory.” ICML 2017.<span> </span><a href="http://proceedings.mlr.press/v70/pennington17a" style="color:rgb(17,85,204)" target="_blank">http://proceedings.mlr.p<wbr>ress/v70/pennington17a</a></div><div dir="auto" style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><br></div><div dir="auto" style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Jaehoon Lee*, Yasaman Bahri*, Roman Novak, Samuel S. Schoenholz, Jeffrey Pennington, Jascha Sohl-Dickstein. “Deep Neural Networks as Gaussian Processes.” ICLR 2018.<span> </span><a href="https://arxiv.org/abs/1711.00165" style="color:rgb(17,85,204)" target="_blank">https://arxiv.org/abs/17<wbr>11.00165</a>. </div><div dir="auto" style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><br></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Bio: Yasaman Bahri is a researcher at Google Brain working on deep learning. The goal of her research is to advance a scientific, principled understanding of deep learning, with an eye towards theoretical analysis informed by careful empirical work. She got a PhD in Theoretical Condensed Matter physics from UC Berkeley, specializing in many body physics; working on symmetry-protected topological phases, many-body localization, non-Fermi liquids, and topological mechanics. She is also interested in the connections between condensed matter, theoretical physics and machine learning. </div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><br></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><br></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Host:<span> </span><a href="mailto:mesrob@ttic.edu" style="color:rgb(17,85,204)" target="_blank">Mesrob Ohannessian</a></div><br class="m_-4721497507425796220gmail-m_-1288128789894450374gmail-Apple-interchange-newline"></span></div><br class="m_-4721497507425796220gmail-Apple-interchange-newline">

<br><div class="gmail_extra"><br clear="all"><div><div class="m_-4721497507425796220gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><font face="arial, helvetica, sans-serif">Mary C. Marre</font><div><font face="arial, helvetica, sans-serif">Administrative Assistant</font></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6"><b>Toyota Technological Institute</b></font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6">6045 S. Kenwood Avenue</font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6">Room 504</font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6">Chicago, IL  60637</font></i></div><div><i><font face="arial, helvetica, sans-serif">p:(773) 834-1757</font></i></div><div><i><font face="arial, helvetica, sans-serif">f: (773) 357-6970</font></i></div><div><b><i><a href="mailto:mmarre@ttic.edu" target="_blank"><font face="arial, helvetica, sans-serif">mmarre@ttic.edu</font></a></i></b></div></div></div></div></div></div></div></div></div></div>
<br><div class="gmail_quote">On Wed, May 16, 2018 at 11:20 AM, Mary Marre <span dir="ltr"><<a href="mailto:mmarre@ttic.edu" target="_blank">mmarre@ttic.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">

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<div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;text-align:start;text-indent:0px;text-decoration-style:initial;text-decoration-color:initial"><font color="#000000" face="arial, helvetica, sans-serif">When: <b style="font-weight:400"> </b>   Tuesday, May 22nd <span class="m_-4721497507425796220m_-1288128789894450374gmail-m_-1216822548864914938m_1430452980776983890gmail-m_1031910664862358996gmail-m_8778633083237298896gmail-m_-8347358208690191418gmail-m_6958947101002467454gmail-m_4240741644540508174gmail-m_-7649362550103587767m_3439038168464703931gmail-m_7186661958014209082gmail-m_-4881373329697077770gmail-m_-2141744242196855365gmail-m_1163836401633243615gmail-m_2148237477730121328gmail-m_-6691959996525573090gmail-m_1517372298344856049gmail-m_491069367152086750gmail-m_-8327640324523575189gmail-m_2420618808463760418gmail-m_7960197898027616883gmail-m_8692226636264124041gmail-m_2794822896869921223gmail-m_7508998950622620526gmail-m_-7153355664495542534gmail-il" style="font-weight:400">at</span> <span style="font-weight:400;background-color:rgb(255,255,255)"><b>11:00 am</b></span></font></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;font-weight:400;text-align:start;text-indent:0px;text-decoration-style:initial;text-decoration-color:initial"><font color="#000000" face="arial, helvetica, sans-serif"><br></font></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;text-align:start;text-indent:0px;text-decoration-style:initial;text-decoration-color:initial"><font color="#000000" face="arial, helvetica, sans-serif">Where:    <span class="m_-4721497507425796220m_-1288128789894450374gmail-m_-1216822548864914938m_1430452980776983890gmail-m_1031910664862358996gmail-m_8778633083237298896gmail-m_-8347358208690191418gmail-m_6958947101002467454gmail-m_4240741644540508174gmail-m_-7649362550103587767m_3439038168464703931gmail-m_7186661958014209082gmail-m_-4881373329697077770gmail-m_-2141744242196855365gmail-m_1163836401633243615gmail-m_2148237477730121328gmail-m_-6691959996525573090gmail-m_1517372298344856049gmail-m_491069367152086750gmail-m_-8327640324523575189gmail-m_2420618808463760418gmail-m_7960197898027616883gmail-m_8692226636264124041gmail-m_2794822896869921223gmail-m_7508998950622620526gmail-m_-7153355664495542534gmail-m_8421504075585210435gmail-m_3262824545120381495gmail-m_-1141671822915777344gmail-m_-7219251726624328345gmail-m_-8588148075564318222gmail-m_-8767966813928691312gmail-m_-1542318334608687154gmail-m_5717104778280916634gmail-m_4845490158781220632gmail-m_5124567205141626540gmail-m_3209361100497750746gmail-m_2953668934074478317gmail-m_-3155518689668024534m_9067904842688472155gmail-m_3071693547520408192gmail-il" style="font-weight:400"><span class="m_-4721497507425796220m_-1288128789894450374gmail-m_-1216822548864914938m_1430452980776983890gmail-m_1031910664862358996gmail-m_8778633083237298896gmail-m_-8347358208690191418gmail-m_6958947101002467454gmail-m_4240741644540508174gmail-m_-7649362550103587767m_3439038168464703931gmail-m_7186661958014209082gmail-m_-4881373329697077770gmail-m_-2141744242196855365gmail-m_1163836401633243615gmail-m_2148237477730121328gmail-m_-6691959996525573090gmail-m_1517372298344856049gmail-m_491069367152086750gmail-m_-8327640324523575189gmail-m_2420618808463760418gmail-m_7960197898027616883gmail-m_8692226636264124041gmail-m_2794822896869921223gmail-m_7508998950622620526gmail-m_-7153355664495542534gmail-il"><span class="m_-4721497507425796220m_-1288128789894450374gmail-m_-1216822548864914938m_1430452980776983890gmail-m_1031910664862358996gmail-m_8778633083237298896gmail-m_-8347358208690191418gmail-m_6958947101002467454gmail-il">TTIC</span></span></span>, 6045 S Kenwood Avenue, 5th Floor, Room 526</font></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;font-weight:400;text-align:start;text-indent:0px;text-decoration-style:initial;text-decoration-color:initial"><font face="arial, helvetica, sans-serif"><br></font></div><div style="text-align:start;text-indent:0px;text-decoration-style:initial;text-decoration-color:initial"><font color="#000000" style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px"><font face="arial, helvetica, sans-serif">Who:       </font></font><span style="font-size:12.8px">Yasaman Bahri, Google Brain</span></div><div style="text-align:start;text-indent:0px;text-decoration-style:initial;text-decoration-color:initial"><span style="font-size:12.8px"><br></span></div><br class="m_-4721497507425796220m_-1288128789894450374gmail-Apple-interchange-newline">

Title:<span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:small;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;font-weight:400">        </span><span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;font-weight:400;text-align:start;text-indent:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">Wide, Deep Neural Networks are Gaussian Processes</span></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;font-weight:400;text-align:start;text-indent:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><br></div><span style="font-size:12.8px">Abstract: One means of better understanding seemingly complicated models such as deep neural networks is to connect them to other objects we already understand. For instance, Gaussian processes are well-studied models with well-controlled analytic properties. In his seminal work, Radford Neal suggested thinking about inference in function space, rather than parameter space, and in doing so established a correspondence between single-layer fully-connected neural networks with an i.i.d prior over parameters and certain Gaussian processes (GPs), in the limit of infinite network width. The correspondence was, however, restricted to a single-hidden layer.</span><div><span style="font-size:12.8px"><br></span></div><div><span style="font-size:12.8px">We develop this line of work and build an exact correspondence between deep, infinitely wide neural networks and Gaussian processes. Algorithmically, this mapping also enables a route towards Bayesian inference with deep neural networks, without needing to instantiate a network, which we implement on MNIST and CIFAR-10. We compare to the performance of finite-width networks trained with standard stochastic optimization. We find that performance increases as finite-width trained networks are made wider and more similar to a GP, and thus that GP predictions typically outperform those of finite-width networks. </span></div><div><span style="font-size:12.8px"><br></span></div><div><span style="font-size:12.8px">Time permitting, I will also give some brief highlights of our related work, studying the propagation of signals through random neural networks. This analysis informs initializations for training ultra-deep networks with tens of thousands of layers.</span></div><div><span style="font-size:12.8px"><br></span></div><div><span style="font-size:12.8px"><span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">Links: </span><div dir="auto" style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Jeffrey Pennington and Yasaman Bahri. “Geometry of Neural Network Loss Surfaces via Random Matrix Theory.” ICML 2017.<span> </span><a href="http://proceedings.mlr.press/v70/pennington17a" style="color:rgb(17,85,204)" target="_blank">http://proceedings.mlr.p<wbr>ress/v70/pennington17a</a></div><div dir="auto" style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><br></div><div dir="auto" style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Jaehoon Lee*, Yasaman Bahri*, Roman Novak, Samuel S. Schoenholz, Jeffrey Pennington, Jascha Sohl-Dickstein. “Deep Neural Networks as Gaussian Processes.” ICLR 2018.<span> </span><a href="https://arxiv.org/abs/1711.00165" style="color:rgb(17,85,204)" target="_blank">https://arxiv.org/abs/17<wbr>11.00165</a>. </div><div dir="auto" style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><br></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Bio: Yasaman Bahri is a researcher at Google Brain working on deep learning. The goal of her research is to advance a scientific, principled understanding of deep learning, with an eye towards theoretical analysis informed by careful empirical work. She got a PhD in Theoretical Condensed Matter physics from UC Berkeley, specializing in many body physics; working on symmetry-protected topological phases, many-body localization, non-Fermi liquids, and topological mechanics. She is also interested in the connections between condensed matter, theoretical physics and machine learning. </div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><br></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><br></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Host: <a href="mailto:mesrob@ttic.edu" target="_blank">Mesrob Ohannessian</a></div><br class="m_-4721497507425796220m_-1288128789894450374gmail-Apple-interchange-newline">

</span></div><br clear="all"><div><div class="m_-4721497507425796220m_-1288128789894450374gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><font face="arial, helvetica, sans-serif">Mary C. Marre</font><div><font face="arial, helvetica, sans-serif">Administrative Assistant</font></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6"><b>Toyota Technological Institute</b></font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6">6045 S. Kenwood Avenue</font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6">Room 504</font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6">Chicago, IL  60637</font></i></div><div><i><font face="arial, helvetica, sans-serif">p:(773) 834-1757</font></i></div><div><i><font face="arial, helvetica, sans-serif">f: (773) 357-6970</font></i></div><div><b><i><a href="mailto:mmarre@ttic.edu" target="_blank"><font face="arial, helvetica, sans-serif">mmarre@ttic.edu</font></a></i></b></div></div></div></div></div></div></div></div></div></div>
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