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BEGIN:VEVENT
UID:www.tcs.tifr.res.in/event/1677
DTSTAMP:20260209T062627Z
SUMMARY:What Kinds of Functions Do Neural Networks Learn? Low-Norm vs. Flat
  Solutions
DESCRIPTION:Speaker: Rahul Parhi (University of California\, San Diego (UCS
 D))\n\nAbstract: \nThis talk investigates the fundamental differences betw
 een low-norm and flat solutions of shallow ReLU networks training problems
 \, particularly in high-dimensional settings. We sharply characterize the 
 regularity of the functions learned by neural networks in these two regime
 s. This enables us to show that global minima with small weight norms exhi
 bit strong generalization guarantees that are dimension-independent. In co
 ntrast\, local minima that are "flat" can generalize poorly as the input d
 imension increases. We attribute this gap to a phenomenon we call neural s
 hattering\, where neurons specialize to extremely sparse input regions\, r
 esulting in activations that are nearly disjoint across data points. This 
 forces the network to rely on large weight magnitudes\, leading to poor ge
 neralization. Our analysis establishes an exponential separation between f
 lat and low-norm minima. In particular\, while flatness does imply some de
 gree 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 per
 formance of neural networks.\n \nShort Bio: Rahul Parhi is an Assistant P
 rofessor at the University of California\, San Diego. Prior to joining UCS
 D\, he was a Postdoctoral Researcher at the École Polytechnique Fédéral
 e de Lausanne (EPFL)\, where he worked from 2022 to 2024. He completed his
  PhD at the University of Wisconsin-Madison in 2022. His research is focus
 ed on the mathematical foundations of neural networks\, and its connection
 s with functional/harmonic analysis\, approximation theory\, and statistic
 s.\n
URL:https://www.tcs.tifr.res.in/web/events/1677
DTSTART;TZID=Asia/Kolkata:20260211T150000
DTEND;TZID=Asia/Kolkata:20260211T160000
LOCATION:HBA Foyer
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