{"683284":{"#nid":"683284","#data":{"type":"event","title":"Machine Learning Seminar Series Fall 2025 | Do Neural Networks Generalize Well? Low Norm Solutions vs. Flat Minima","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003EDo Neural Networks Generalize Well? Low Norm Solutions vs. Flat Minima\u003C\/strong\u003E\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003EAbstract: \u003C\/strong\u003EThis talk investigates the fundamental differences between low-norm and flat solutions of shallow ReLU networks training problems, particularly in high-dimensional settings. We show that global minima with small weight norms exhibit strong generalization guarantees that are dimension-independent. In contrast, local minima that are \u201cflat\u201d can generalize poorly as the input dimension increases. We attribute this gap to a phenomenon we call neural shattering, where neurons specialize to extremely sparse input regions, resulting in activations that are nearly disjoint across data points. This forces the network to rely on large weight magnitudes, leading to poor generalization. Our theoretical analysis establishes an exponential separation between flat and low-norm minima. In particular, while flatness does imply some degree of generalization, we show that the corresponding convergence rates necessarily deteriorate exponentially with input dimension. These findings suggest that flatness alone does not fully explain the generalization performance of neural networks.\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003EBio: \u003C\/strong\u003ERahul Parhi is an Assistant Professor in the Department of Electrical and Computer Engineering at the University of California, San Diego. Prior to joining UCSD, he was a Postdoctoral Researcher at the \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), where he worked from 2022 to 2024. He completed his PhD in Electrical Engineering at the University of Wisconsin-Madison in 2022. His research interests lie at the interface between functional and harmonic analysis and data science.\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\u003Cp\u003EZoom link: \u003Ca href=\u0022https:\/\/gatech.zoom.us\/j\/93991261775?pwd=PCAJs5vTANpLGiCcKyyBR50hMuV432.1\u0022 rel=\u0022noopener noreferrer\u0022 target=\u0022_blank\u0022 title=\u0022https:\/\/gatech.zoom.us\/j\/93991261775?pwd=PCAJs5vTANpLGiCcKyyBR50hMuV432.1\u0022\u003Ehttps:\/\/gatech.zoom.us\/j\/93991261775?pwd=PCAJs5vTANpLGiCcKyyBR50hMuV432.1\u003C\/a\u003E\u003Cbr\u003E\u003Cstrong\u003EMeeting ID:\u003C\/strong\u003E 939 9126 1775\u0026nbsp;\u003Cbr\u003E\u003Cstrong\u003EPasscode:\u003C\/strong\u003E 914902\u003C\/p\u003E","summary":"","format":"limited_html"}],"field_subtitle":"","field_summary":[{"value":"\u003Cp\u003E\u003Cstrong\u003EAll Seminars Held on Wednesdays 12pm - 1pm\u003C\/strong\u003E\u003C\/p\u003E","format":"limited_html"}],"field_summary_sentence":[{"value":" Featuring Rahul Parhi -   Assistant Professor, Electrical and Computer Engineering @ UC San Diego"}],"uid":"27863","created_gmt":"2025-07-25 17:22:57","changed_gmt":"2025-08-27 18:29:22","author":"Christa Ernst","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2025-09-10T12:00:00-04:00","event_time_end":"2025-09-10T13:00:00-04:00","event_time_end_last":"2025-09-10T13:00:00-04:00","gmt_time_start":"2025-09-10 16:00:00","gmt_time_end":"2025-09-10 17:00:00","gmt_time_end_last":"2025-09-10 17:00:00","rrule":null,"timezone":"America\/New_York"},"location":"CODA Building 9th floor Atrium \u0026 Virtual","extras":[],"related_links":[{"url":"https:\/\/sparsity.ucsd.edu\/rahul\/","title":"Speaker Website"}],"groups":[{"id":"1278","name":"College of Sciences"},{"id":"545781","name":"Institute for Data Engineering and Science"},{"id":"142761","name":"IRIM"}],"categories":[],"keywords":[{"id":"9167","name":"machine learning"},{"id":"654","name":"College of Computing"},{"id":"187023","name":"go-data"},{"id":"191138","name":"artificial neural networks"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1795","name":"Seminar\/Lecture\/Colloquium"}],"invited_audience":[{"id":"78761","name":"Faculty\/Staff"},{"id":"177814","name":"Postdoc"},{"id":"78771","name":"Public"},{"id":"174045","name":"Graduate students"},{"id":"78751","name":"Undergraduate students"}],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}