For an n-variate degree-2 real polynomial p, we prove that E x~ D [sig (p (x))] Is determined
up to an additive ε as long as D is a k-wise Independent distribution over {-1, 1} n for 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).

Let x be a random vector coming from any k-wise independent distribution over {-1, 1}^ n.
For an n-variate degree-2 polynomial p, we prove that E [sgn (p (x))] is determined up to an
additive epsilon for k= poly (1/epsilon). This answers an open question of Diakonikolas et
al.(FOCS 2009). Using standard constructions of k-wise independent distributions, we obtain
a broad class of explicit generators that epsilon-fool the class of degree-2 threshold
functions with seed length log (n)* poly (1/epsilon). Our approach is quite robust: it easily …