<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /></head><body style='font-size: 10pt; font-family: Verdana,Geneva,sans-serif'>
<p style="font-family: Verdana, Geneva, sans-serif; font-size: 13.333333015441895px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none; caret-color: #ffffff; color: #ffffff;"><span style="caret-color: #ffffff; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-size: 12pt; font-family: times new roman, times, serif;">Dear colleagues and PDE friends,</span><br style="caret-color: #ffffff; color: #ffffff; font-family: monospace; font-size: 13.333333015441895px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" /><span style="caret-color: #ffffff; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-size: 12pt; font-family: times new roman, times, serif;"> </span><br style="caret-color: #ffffff; color: #ffffff; font-family: monospace; font-size: 13.333333015441895px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" /><span style="color: #000000; font-family: times new roman, times, serif; font-size: 12pt;"><span style="caret-color: #ffffff; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">We have the pleasure to announce the next session of our CMM PDE seminar with a talk<span class="v1JtukPc"> given by</span></span><span style="caret-color: #ffffff; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;"><strong><span style="font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -moz-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none; caret-color: #000000;"> <strong>Prof. <span class="JtukPc"><span id="rAECCd" aria-level="1">Mircea Petrache (Puc)</span></span></strong></span></strong></span><span style="caret-color: #ffffff; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;"><span class="v1JtukPc"><span id="v1rAECCd"><strong> </strong>be held</span></span></span><span style="caret-color: #ffffff; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;"><strong> tomorrow Tuesday, November 21st at 12:00 hs </strong>(Santiago time) in the <strong>Sala John Von Neumann</strong></span><span style="caret-color: #ffffff; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;"> (seventh floor), Beauchef 851.<br /></span></span></p>
<div class="v1rcmBody" style="font-family: Verdana, Geneva, sans-serif; font-size: 10pt; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none; caret-color: #ffffff; color: #ffffff;"><span style="color: #000000; font-family: times new roman, times, serif; font-size: 12pt;"><span style="caret-color: #ffffff; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;"></span></span>
<div style="caret-color: #ffffff; color: #ffffff; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;"><span style="color: #000000; font-family: times new roman, times, serif; font-size: 12pt;"><strong>Title: </strong>Approximate and partial symmetries in Deep Learning</span></div>
<div style="caret-color: #ffffff; color: #ffffff; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;"><span style="color: #000000; font-family: times new roman, times, serif; font-size: 12pt;"> </span></div>
<div style="caret-color: #ffffff; color: #ffffff; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;"><span style="color: #000000; font-family: times new roman, times, serif; font-size: 12pt;"><span style="caret-color: #000000;"></span></span>
<div style="font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none; caret-color: #000000; color: #000000; font-family: 'trebuchet ms', sans-serif;"><span style="color: #000000; font-family: times new roman, times, serif; font-size: 12pt;"><strong>Abstract: </strong>The image of a rotated cat still represents a cat: while this simple rule seems obvious to a human, it is not obvious to neural networks, which separately "learn" each new rotation of the same image. This applies to different groups of symmetries for images, graphs, texts, and other types of data. Implementing "equivariant" neural networks that respect symmetries, reduces the number of learned parameters, and helps improve their generalization properties outside the training set. On the other hand, in networks that "identify too much", that is, where we impose too many symmetries, the error begins to increase, due to not respecting the data. In work with S. Trivedi, (NeurIPS 2023), we quantify this tradeoff, which allows to define the optimal amount of symmetries in learning models. I will give an introduction to classical learning theory bounds, and our extension of the ideas to the study of "partial/approximate equivariance". In passing, I'll describe some possible directions for working with partial symmetries in specific tasks.</span></div>
</div>
<div style="caret-color: #ffffff; color: #ffffff; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;">
<div style="color: #000000; caret-color: #000000;">
<p><span style="color: #000000; font-family: times new roman, times, serif; font-size: 12pt;"><span style="caret-color: #ffffff; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">The link to access the zoom meeting:</span></span><span style="font-size: 12pt;"><span style="color: #000000; font-family: times new roman, times, serif;"><span style="caret-color: #ffffff; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;"><span style="caret-color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -moz-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none; display: inline !important; float: none;"> <a href="https://reuna.zoom.us/j/5602423930">https://reuna.zoom.us/j/5602423930</a><a href="https://reuna.zoom.us/j/5602423930"> </a></span></span></span></span><span style="font-size: 12pt;"><span style="color: #000000; font-family: times new roman, times, serif;"><span style="caret-color: #ffffff; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;"><span style="caret-color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -moz-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none; display: inline !important; float: none;"></span></span></span></span></p>
</div>
</div>
</div>
<div class="v1rcmBody" style="font-family: Verdana, Geneva, sans-serif; font-size: 10pt; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none; caret-color: #ffffff; color: #ffffff;">
<p><span style="caret-color: #ffffff; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: times new roman, times, serif; font-size: 12pt;">You can find more information about the seminar and future sesions in the seminar web page:</span><br style="caret-color: #ffffff; color: #ffffff; font-family: monospace; font-size: 13.333333015441895px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" /><span style="caret-color: #ffffff; color: #0000ff; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: times new roman, times, serif; font-size: 12pt;"><a style="color: #0000ff;" href="https://eventos.cmm.uchile.cl/pdeseminar/" target="_blank" rel="noopener noreferrer">https://eventos.cmm.uchile.cl/pdeseminar/<span style="background-color: #3598db;"></span></a></span></p>
<p><span style="caret-color: #ffffff; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; color: #000000; font-family: 'times new roman', times, serif; font-size: 12pt;" data-mce-fragment="1">Best wishes,</span><br style="caret-color: #ffffff; color: #ffffff; font-size: 13.333333px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: monospace;" data-mce-fragment="1" /><span style="caret-color: #ffffff; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; color: #000000; font-family: 'times new roman', times, serif; font-size: 12pt;" data-mce-fragment="1"> </span><br style="caret-color: #ffffff; color: #ffffff; font-size: 13.333333px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: monospace;" data-mce-fragment="1" /><span style="caret-color: #ffffff; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; color: #000000; font-family: 'times new roman', times, serif; font-size: 12pt;" data-mce-fragment="1">Rayssa Caju and María Eugenia Martínez.</span></p>
</div>
</body></html>