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SUMMARY:Quantum advantage for learning periodic neurons with non-uniform d
 ata - Laura Lewis\, Caltech
DTSTART:20250220T141500Z
DTEND:20250220T151500Z
UID:TALK228622@talks.cam.ac.uk
CONTACT:Laurens Lootens
DESCRIPTION:Applying quantum computers to machine learning tasks is an exc
 iting potential direction to explore in search of quantum advantage. Theor
 etical frameworks such as the quantum probably approximately correct (PAC)
  and quantum statistical query (QSQ) models have been proposed to study qu
 antum algorithms for learning classical functions. Despite numerous works 
 investigating quantum advantages in these models\, we nevertheless only un
 derstand it at two extremes: either exponential quantum advantages for uni
 form input distributions or no advantage for potentially adversarial distr
 ibutions. In this work\, we make progress towards filling the gap between 
 these two regimes by designing an efficient quantum algorithm for learning
  periodic neurons in the QSQ model over a broad range of non-uniform distr
 ibutions\, which includes Gaussian\, generalized Gaussian\, and logistic d
 istributions. To our knowledge\, our work is also the first result in quan
 tum learning theory for classical functions that explicitly considers real
 -valued functions. Recent advances in classical learning theory prove that
  learning periodic neurons is hard for any classical gradient-based algori
 thm\, giving us an exponential quantum advantage over such algorithms. The
 re is also strong evidence that the problem remains hard for classical sta
 tistical query algorithms and even general classical algorithms learning u
 nder small amounts of noise.
LOCATION:MR2
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