{"id":49073,"date":"2024-08-26T10:37:56","date_gmt":"2024-08-26T14:37:56","guid":{"rendered":"https:\/\/engineering.jhu.edu\/ams\/?post_type=tribe_events&#038;p=49073"},"modified":"2025-06-24T10:32:50","modified_gmt":"2025-06-24T14:32:50","slug":"ams-weekly-seminar-molei-tao","status":"publish","type":"tribe_events","link":"https:\/\/engineering.jhu.edu\/ams\/event\/ams-weekly-seminar-molei-tao\/","title":{"rendered":"AMS Weekly Seminar | Molei Tao"},"content":{"rendered":"<p><strong>Location:\u00a0<\/strong>Gilman 50<\/p>\n<p><strong>When:<\/strong> April 17th at 1:30 p.m.<\/p>\n<p><strong>Title:\u00a0<\/strong><span>Optimization, Sampling, and Generative Modeling in Non-Euclidean Spaces<\/span><\/p>\n<p style=\"font-weight: 400;\"><strong>Abstract:\u00a0<\/strong><span>Machine learning in non-Euclidean spaces have been rapidly attracting attention in recent years, and this talk will give some examples of progress on its mathematical and algorithmic foundations. A sequence of developments that eventually lead to the generative modeling of data on Lie groups will be reported. Such a problem occurs, for example, in the Gen-AI design of molecules.<\/span><\/p>\n<p><span>More precisely, I will begin with variational optimization, which, together with delicate interplays between continuous- and discrete-time dynamics, enables the construction of momentum-accelerated algorithms that optimize functions defined on manifolds. Selected applications, such as a generic improvement of Transformer, and a low-dim. approximation of high-dim. optimal transport distance, will be described. Then I will turn the optimization dynamics into an algorithm that samples from probability distributions on Lie groups. This sampler provably converges, even without log-concavity condition or its common relaxations. Finally, I will describe how this sampler can lead to a structurally-pleasant diffusion generative model that allows users to, given training data that follow any latent statistical distribution on a Lie group manifold, generate more data exactly on the same manifold that follow the same distribution. If time permits, applications such as molecule design and generative innovation of quantum processes will be briefly discussed.<\/span><\/p>\n<p><strong>Zoom link:<\/strong> <a href=\"https:\/\/wse.zoom.us\/j\/93287142219?pwd=z9fqWnRMzmzS0SGijRiie5yN3kHRSZ.1\">https:\/\/wse.zoom.us\/j\/93287142219?pwd=z9fqWnRMzmzS0SGijRiie5yN3kHRSZ.1<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Location:\u00a0Gilman 50 When: April 17th at 1:30 p.m. Title:\u00a0Optimization, Sampling, and Generative Modeling in Non-Euclidean Spaces Abstract:\u00a0Machine learning in non-Euclidean spaces have been rapidly attracting attention in recent years, and&hellip;<\/p>\n","protected":false},"author":69,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_relevanssi_hide_post":"","_relevanssi_hide_content":"","_relevanssi_pin_for_all":"","_relevanssi_pin_keywords":"","_relevanssi_unpin_keywords":"","_relevanssi_related_keywords":"","_relevanssi_related_include_ids":"","_relevanssi_related_exclude_ids":"","_relevanssi_related_no_append":"","_relevanssi_related_not_related":"","_relevanssi_related_posts":"","_relevanssi_noindex_reason":"","_tribe_events_status":"","_tribe_events_status_reason":"","footnotes":""},"tags":[],"tribe_events_cat":[260],"class_list":["post-49073","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-seminars-and-endowed-lectures","cat_seminars-and-endowed-lectures"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>AMS Weekly Seminar | Molei Tao | Department of Applied Mathematics and Statistics<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/engineering.jhu.edu\/ams\/event\/ams-weekly-seminar-molei-tao\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"AMS Weekly Seminar | Molei Tao | Department of Applied Mathematics and Statistics\" \/>\n<meta property=\"og:description\" content=\"Location:\u00a0Gilman 50 When: April 17th at 1:30 p.m. Title:\u00a0Optimization, Sampling, and Generative Modeling in Non-Euclidean Spaces Abstract:\u00a0Machine learning in non-Euclidean spaces have been rapidly attracting attention in recent years, and&hellip;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/engineering.jhu.edu\/ams\/event\/ams-weekly-seminar-molei-tao\/\" \/>\n<meta property=\"og:site_name\" content=\"Department of Applied 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