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UID:www.tcs.tifr.res.in/event/1753
DTSTAMP:20260722T081038Z
SUMMARY:Convex Basins in Single-Index Model Loss Landscapes: Applications t
 o Robust Recovery under Strong Adversarial Corruption
DESCRIPTION:Speaker: Santanu Das (TIFR)\n\nAbstract: \nWe study the problem
  of robustly learning Gaussian Single Index Models (SIMs) in the presence 
 of heavy-tailed noise and a constant fraction of adversarially corrupted c
 ovariates and responses. Prior work on robust recovery has considered sett
 ings such as linear regression (Pensia et al.\, JASA 2024)\, strictly mono
 tonic link functions (Awasthi et al.\, NeurIPS 2022)\, and phase retrieval
  (Buna and Rebeschini\, AISTATS 2025). However\, these techniques do not e
 xtend to generic asymmetric non-monotonic link functions such as GeLU and 
 Swish\, which arise naturally as scalar primitives in modern gated neural 
 architectures. We close this gap by giving the first robust recovery algor
 ithm with near-linear sample and time complexity for generic non-monotonic
  link functions\, thereby establishing the first robust recovery guarantee
 s for a broad family of nonlinear SIMs for which no guarantees were previo
 usly known. Our central contribution is a new structural understanding of 
 the Gaussian squared-loss landscape under adversarial contamination. Cruci
 ally\, we prove that for a broad class of nonlinear non-monotonic SIMs\, a
  dimension-independent\, constant-radius convex basin exists around the gr
 ound truth and is efficiently reachable via robust spectral initialization
  even under adversarial contamination. Prior works fail to establish both 
 guarantees simultaneously\, thereby either breaking down under adversarial
  contamination or failing to handle generic non-monotonic link functions. 
 Together\, these structural insights yield a principled warm start for rob
 ust gradient descent that provably converges to a final estimation error o
 f O(σ√ε) in Õ(nd) time with Õ(d) samples\, where ε is the contamina
 tion fraction.\n
URL:https://www.tcs.tifr.res.in/web/events/1753
DTSTART;TZID=Asia/Kolkata:20260724T160000
DTEND;TZID=Asia/Kolkata:20260724T170000
LOCATION:A-201 (STCS Seminar Room)
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