The correct exponent for the Gotsman–Linial Conjecture

@article{Kane2013TheCE,
  title={The correct exponent for the Gotsman–Linial Conjecture},
  author={Daniel M. Kane},
  journal={2013 IEEE Conference on Computational Complexity},
  year={2013},
  pages={56-64}
}
We prove new bounds on the average sensitivity of polynomial threshold functions. In particular, we show that for f, a degree-d polynomial threshold function in n variables that $$\mathbb{AS}(f) \leq \sqrt{n}(\log(n))^{O(d log(d))}2^{O(d^2 log(d))}.$$ AS ( f ) ≤ n ( log ( n ) ) O ( d l o g ( d ) ) 2 O ( d 2 l o g ( d ) ) . This bound amounts to a significant improvement over previous bounds, and in particular, for fixed d gives the same asymptotic exponent of n as the one predicted by the… CONTINUE READING
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