Bounding the average sensitivity and noise sensitivity of polynomial threshold functions

@inproceedings{Diakonikolas2010BoundingTA,
  title={Bounding the average sensitivity and noise sensitivity of polynomial threshold functions},
  author={Ilias Diakonikolas and Prahladh Harsha and Adam R. Klivans and Raghu Meka and Prasad Raghavendra and Rocco A. Servedio and Li-Yang Tan},
  booktitle={STOC},
  year={2010}
}
We give the first non-trivial upper bounds on the average sensitivity and noise sensitivity of degree-d polynomial threshold functions (PTFs). These bounds hold both for PTFs over the Boolean hypercube {-1,1}n and for PTFs over Rn under the standard n-dimensional Gaussian distribution N(0,In). Our bound on the Boolean average sensitivity of PTFs represents progress towards the resolution of a conjecture of Gotsman and Linial [17], which states that the symmetric function slicing the middle d… CONTINUE READING
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