Abstract. We prove asymptotically optimal bounds on the Gaussian noise sensitivity of degree-d polynomial threshold functions. These bounds translate into optimal bounds on the Gau...
We give explicit constructions of epsilon nets for linear threshold functions on the binary cube and on the unit sphere. The size of the constructed nets is polynomial in the dime...
We give a “regularity lemma” for degree-d polynomial threshold functions (PTFs) over the Boolean cube {−1, 1}n . Roughly speaking, this result shows that every degree-d PTF ...
Ilias Diakonikolas, Rocco A. Servedio, Li-Yang Tan...