{"id":55686,"date":"2026-02-09T13:26:28","date_gmt":"2026-02-09T18:26:28","guid":{"rendered":"https:\/\/engineering.jhu.edu\/ams\/?post_type=tribe_events&#038;p=55686"},"modified":"2026-03-09T12:37:03","modified_gmt":"2026-03-09T16:37:03","slug":"ams-weekly-seminar-sayan-banerjee","status":"publish","type":"tribe_events","link":"https:\/\/engineering.jhu.edu\/ams\/event\/ams-weekly-seminar-sayan-banerjee\/","title":{"rendered":"AMS Weekly Seminar | Sayan Banerjee"},"content":{"rendered":"<p><strong>Location: <\/strong>Shaffer 3<\/p>\n<p><strong>When:<\/strong> April 2nd at 1:30 p.m.<\/p>\n<p><strong>Title: <\/strong><span>Stationary States and Phase Transitions in Noisy Mean-Field Transformers<\/span><\/p>\n<p><span><strong>Abstract: <\/strong><\/span><span>Mean-field limits of attention-based models\u2014such as noisy Transformer architectures\u2014lead naturally to McKean\u2013Vlasov equations on the circle. Understanding their stationary states is key to explaining phase transitions, symmetry breaking, and the emergence of structured multi-mode patterns in these systems.<\/span><span><br \/>\n<\/span><span><br \/>\n<\/span><span>We develop a Fourier-based framework for analyzing stationary solutions of such equations. The central observation is an exact equivalence between the stationary McKean\u2013Vlasov equation and an infinite-dimensional quadratic system for its Fourier coefficients. This reformulation converts the problem from a nonlinear PDE in function space to an explicit algebraic system in sequence space, allowing detailed analysis of bifurcations from the uniform state.<\/span><span><br \/>\n<\/span><span><br \/>\n<\/span><span>We derive analytic criteria describing when and how stationary solutions <\/span><span>emerge<\/span><span>, including supercritical and subcritical bifurcations involving multiple interacting modes, and connect these mechanisms to discontinuous (<\/span><span>first-order<\/span><span>) phase transitions. At the global level, we characterize the geometry of the free-energy landscape and <\/span><span>identify<\/span><span>phase transitions with non-differentiability of the minimal free energy.<\/span><span><br \/>\n<\/span><span><br \/>\n<\/span><span>Specializing to the Noisy Mean-Field Transformer model, we show how increasing the inverse temperature parameter \u03b2 produces a rich family of approximate multi-mode stationary states (interpretable as metastable configurations) and drives a sharp transition from continuous to discontinuous phase behavior.<\/span><\/p>\n<p class=\"s6\"><span>Based on joint work with Krishnakumar Balasubramanian and Philippe Rigollet.<\/span><\/p>\n<p><strong>Zoom link:<\/strong> https:\/\/wse.zoom.us\/j\/92366532431<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Location: Shaffer 3 When: April 2nd at 1:30 p.m. Title: Stationary States and Phase Transitions in Noisy Mean-Field Transformers Abstract: Mean-field limits of attention-based models\u2014such as noisy Transformer architectures\u2014lead naturally&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-55686","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 v27.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>AMS Weekly Seminar | Sayan Banerjee | 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-sayan-banerjee\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"AMS Weekly Seminar | Sayan Banerjee | Department of Applied Mathematics and Statistics\" \/>\n<meta property=\"og:description\" content=\"Location: Shaffer 3 When: April 2nd at 1:30 p.m. Title: Stationary States and Phase Transitions in Noisy Mean-Field Transformers Abstract: Mean-field limits of attention-based models\u2014such as noisy Transformer architectures\u2014lead naturally&hellip;\" \/>\n<meta property=\"og:url\" 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