Add to ORKGAbstract: We give a “regularity lemma ” for degree-d polynomial threshold functions (PTFs) over the Boolean cube {−1,1}n. Roughly speaking, this result shows that every degree-d PTF can be decomposed into a constant number of subfunctions such that almost all of the subfunctions are close to being regular PTFs. Here a “regular ” PTF is a PTF sign(p(x)) where the influence of each variable on the polynomial p(x) is a small fraction of the total influence of p
© Richard Ryan Williams; licensed under Creative Commons License CC-BY 33rd Computational Complexity...
Abstract: We give the first nontrivial upper bounds on the average sensitivity and noise sensitivity...
Dzindzalieta D, Götze F. HALF-SPACES WITH INFLUENTIAL VARIABLE. THEORY OF PROBABILITY AND ITS APPLIC...
AbstractIn this paper we give new extremal bounds on polynomial threshold function (PTF) representat...
A simple way to generate a Boolean function is to take the sign of a real polynomial in $n$ variable...
Linear threshold functions (for real and Boolean inputs) have received much attention, for they are ...
Abstract. We consider Boolean exact threshold functions defined by linear equations, and in general ...
A simple way to generate a Boolean function in n variables is to take the sign of some polynomial. S...
Abstract. The analysis of linear threshold Boolean functions has recently attracted the attention of...
AbstractLinear threshold functions (for real and Boolean inputs) have received much attention, for t...
We give new upper and lower bounds on the degree of real multivariate polynomials whi h sign-represe...
Linear threshold functions (for real and Boolean inputs) have received much attention, for they are ...
Abstract—We prove two main results on how arbitrary linear threshold functions f(x) = sign(w · x − ...
For $S \subseteq \{0,1\}^n$ a Boolean function $f \colon S \to \{-1,1\}$ is a polynomial threshold f...
AbstractThe notion of a threshold function as a Boolean function for which there is a hyperplane in ...
© Richard Ryan Williams; licensed under Creative Commons License CC-BY 33rd Computational Complexity...
Abstract: We give the first nontrivial upper bounds on the average sensitivity and noise sensitivity...
Dzindzalieta D, Götze F. HALF-SPACES WITH INFLUENTIAL VARIABLE. THEORY OF PROBABILITY AND ITS APPLIC...
AbstractIn this paper we give new extremal bounds on polynomial threshold function (PTF) representat...
A simple way to generate a Boolean function is to take the sign of a real polynomial in $n$ variable...
Linear threshold functions (for real and Boolean inputs) have received much attention, for they are ...
Abstract. We consider Boolean exact threshold functions defined by linear equations, and in general ...
A simple way to generate a Boolean function in n variables is to take the sign of some polynomial. S...
Abstract. The analysis of linear threshold Boolean functions has recently attracted the attention of...
AbstractLinear threshold functions (for real and Boolean inputs) have received much attention, for t...
We give new upper and lower bounds on the degree of real multivariate polynomials whi h sign-represe...
Linear threshold functions (for real and Boolean inputs) have received much attention, for they are ...
Abstract—We prove two main results on how arbitrary linear threshold functions f(x) = sign(w · x − ...
For $S \subseteq \{0,1\}^n$ a Boolean function $f \colon S \to \{-1,1\}$ is a polynomial threshold f...
AbstractThe notion of a threshold function as a Boolean function for which there is a hyperplane in ...
© Richard Ryan Williams; licensed under Creative Commons License CC-BY 33rd Computational Complexity...
Abstract: We give the first nontrivial upper bounds on the average sensitivity and noise sensitivity...
Dzindzalieta D, Götze F. HALF-SPACES WITH INFLUENTIAL VARIABLE. THEORY OF PROBABILITY AND ITS APPLIC...