L¹ polynomial regression achieves Õ(n^{O(log(1/ε)/σ)}) for smoothed agnostic halfspace learning, with nearly matching SQ lower bound n^{Ω(log(1+σ/ε²)/σ)}.
Spielman and Shang-Hua Teng , title =
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Smoothed analysis shows the expected SOS rank of unweighted minimum knapsack is O(sqrt(n) log(n/sigma)) after Gaussian perturbation of q, though linear rank occurs when q is exponentially close to an integer.
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A Near-optimal SQ Lower Bound for Smoothed Agnostic Learning of Boolean Halfspaces
L¹ polynomial regression achieves Õ(n^{O(log(1/ε)/σ)}) for smoothed agnostic halfspace learning, with nearly matching SQ lower bound n^{Ω(log(1+σ/ε²)/σ)}.
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On the Distribution of Unweighted Minimum Knapsack Instances with Large SOS Rank
Smoothed analysis shows the expected SOS rank of unweighted minimum knapsack is O(sqrt(n) log(n/sigma)) after Gaussian perturbation of q, though linear rank occurs when q is exponentially close to an integer.