Bounded Independence Fools Degree-2 Threshold Functions
Ilias Diakonikolas, Daniel M. Kane, Jelani Nelson · 2010
For an n-variate degree-2 real polynomial p, we prove that Ex~D[sig(p(x))] Is determined up to an additive ε as long as D is a k-wise Independent distribution over {-1, 1}nfor k = poly(1/ε). This gives a broad class of explicit pseudorandom generators against degree-2 boolean threshold functions, and answers an open question of Diakonikolas et al. (FOCS 2009).