Polynomial Threshold Functions, Hyperplane Arrangements, and Random Tensors

SIAM Journal on Mathematics of Data Science ◽

10.1137/19m1257792 ◽

2019 ◽

Vol 1 (4) ◽

pp. 699-729 ◽

Author(s):

Pierre Baldi ◽

Roman Vershynin

Keyword(s):

Hyperplane Arrangements ◽

Threshold Functions ◽

Polynomial Threshold Functions

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New degree bounds for polynomial threshold functions

Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03 ◽

10.1145/780542.780592 ◽

2003 ◽

Author(s):

Ryan O'Donnell ◽

Rocco A. Servedio

Keyword(s):

Threshold Functions ◽

Degree Bounds ◽

Polynomial Threshold Functions

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Bounding the average sensitivity and noise sensitivity of polynomial threshold functions

Proceedings of the 42nd ACM symposium on Theory of computing - STOC '10 ◽

10.1145/1806689.1806763 ◽

2010 ◽

Author(s):

Ilias Diakonikolas ◽

Prahladh Harsha ◽

Adam Klivans ◽

Raghu Meka ◽

Prasad Raghavendra ◽

...

Keyword(s):

Noise Sensitivity ◽

Average Sensitivity ◽

Threshold Functions ◽

Polynomial Threshold Functions

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On XOR lemmas for the weight of polynomial threshold functions

Information and Computation ◽

10.1016/j.ic.2019.104439 ◽

2019 ◽

Vol 269 ◽

pp. 104439 ◽

Author(s):

Kazuyuki Amano ◽

Shoma Tate

Keyword(s):

Threshold Functions ◽

Polynomial Threshold Functions

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Extremal properties of polynomial threshold functions

18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings. ◽

10.1109/ccc.2003.1214406 ◽

2004 ◽

Author(s):

R. O'Donnell ◽

R.A. Servedio

Keyword(s):

Threshold Functions ◽

Polynomial Threshold Functions ◽

Extremal Properties

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A structure theorem for poorly anticoncentrated polynomials of Gaussians and applications to the study of polynomial threshold functions

The Annals of Probability ◽

10.1214/16-aop1097 ◽

2017 ◽

Vol 45 (3) ◽

pp. 1612-1679 ◽

Author(s):

Daniel Kane

Keyword(s):

Structure Theorem ◽

Threshold Functions ◽

Polynomial Threshold Functions

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The Gaussian Surface Area and Noise Sensitivity of Degree-d Polynomial Threshold Functions

2010 IEEE 25th Annual Conference on Computational Complexity ◽

10.1109/ccc.2010.27 ◽

2010 ◽

Author(s):

Daniel M. Kane

Keyword(s):

Surface Area ◽

Noise Sensitivity ◽

Threshold Functions ◽

Polynomial Threshold Functions ◽

Gaussian Surface

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Harmonic Analysis of Polynomial Threshold Functions

SIAM Journal on Discrete Mathematics ◽

10.1137/0403015 ◽

1990 ◽

Vol 3 (2) ◽

pp. 168-177 ◽

Author(s):

Jehoshua Bruck

Keyword(s):

Harmonic Analysis ◽

Threshold Functions ◽

Polynomial Threshold Functions

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Pseudorandom generators for polynomial threshold functions

Proceedings of the 42nd ACM symposium on Theory of computing - STOC '10 ◽

10.1145/1806689.1806749 ◽

2010 ◽

Author(s):

Raghu Meka ◽

David Zuckerman

Keyword(s):

Pseudorandom Generators ◽

Threshold Functions ◽

Polynomial Threshold Functions

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Hardness Results for Agnostically Learning Low-Degree Polynomial Threshold Functions

Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms ◽

10.1137/1.9781611973082.123 ◽

2011 ◽

Author(s):

Ilias Diakonikolas ◽

Ryan O'Donnell ◽

Rocco A. Servedio ◽

Yi Wu

Keyword(s):

Degree Polynomial ◽

Threshold Functions ◽

Polynomial Threshold Functions

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Average Sensitivity and Noise Sensitivity of Polynomial Threshold Functions

SIAM Journal on Computing ◽

10.1137/110855223 ◽

2014 ◽

Vol 43 (1) ◽

pp. 231-253 ◽

Author(s):

Ilias Diakonikolas ◽

Prasad Raghavendra ◽

Rocco A. Servedio ◽

Li-Yang Tan

Keyword(s):

Noise Sensitivity ◽

Average Sensitivity ◽

Threshold Functions ◽

Polynomial Threshold Functions

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