LIPIcs.CCC.2015.567.pdf
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A Polylogarithmic PRG for Degree 2 Threshold Functions in the Gaussian Setting
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30th Conference on Computational Complexity (CCC 2015)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Computational Complexity Conference (CCC) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2015-06-06
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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)
https://doi.org/10.4230/LIPIcs.CCC.2015.567
https://doi.org/10.4230/LIPIcs.CCC.2015.567
Abstract
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.
Keywords
- polynomial threshold function
- pseudorandom generator
- Gaussian distribution
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