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Fourier Entropy-Influence Conjecture for Random Linear Threshold Functions

  • Sourav Chakraborty
  • Sushrut Karmalkar
  • Srijita Kundu
  • Satyanarayana V. Lokam
  • Nitin Saurabh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10807)

Abstract

The Fourier-Entropy Influence (FEI) Conjecture states that for any Boolean function \(f:\{+1,-1\}^n \rightarrow \{+1,-1\}\), the Fourier entropy of f is at most its influence up to a universal constant factor. While the FEI conjecture has been proved for many classes of Boolean functions, it is still not known whether it holds for the class of Linear Threshold Functions. A natural question is: Does the FEI conjecture hold for a “random” linear threshold function? In this paper, we answer this question in the affirmative. We consider two natural distributions on the weights defining a linear threshold function, namely uniform distribution on \([-1,1]\) and Normal distribution.

Notes

Acknowledgments

We thank the reviewers for helpful comments that improved the presentation of the paper.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Chennai Mathematical InstituteChennaiIndia
  2. 2.Centrum Wiskunde InformatikaAmsterdamNetherlands
  3. 3.University of TexasAustinUSA
  4. 4.Centre for Quantum TechnologiesSingaporeSingapore
  5. 5.Microsoft ResearchBangaloreIndia
  6. 6.Charles UniversityPragueCzech Republic

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