## A Structure Theorem for Poorly Anticoncentrated Gaussian Chaoses and Applications to the Study of Polynomial Threshold Functions

- Daniel M. Kane
- 2012 IEEE 53rd Annual Symposium on Foundations of…
- 2012

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@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} }

- Published 2010 in STOC
DOI:10.1145/1806689.1806763

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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