A Polylogarithmic PRG for Degree 2 Threshold Functions in the Gaussian Setting

Author Daniel M. Kane

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Daniel M. Kane

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Daniel M. Kane. A Polylogarithmic PRG for Degree 2 Threshold Functions in the Gaussian Setting. In 30th Conference on Computational Complexity (CCC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 33, pp. 567-581, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


We construct and analyze a new pseudorandom generator for degree 2 polynomial threshold functions with respect to the Gaussian measure. In particular, we obtain one whose seed length is polylogarithmic in both the dimension and the desired error, a substantial improvement over existing constructions. Our generator is obtained as an appropriate weighted average of pseudorandom generators against read once branching programs. The analysis requires a number of ideas including a hybrid argument and a structural result that allows us to treat our degree 2 threshold function as a function of a number of linear polynomials and one approximately linear polynomial.
  • polynomial threshold function
  • pseudorandom generator
  • Gaussian distribution


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