A linear threshold function is a Boolean function obtained by thresholding 
on 
, with real coefficients 
.
The output is 1 when this expression is nonnegative
and 
otherwise (O'Donnell 2021, §5.1). For example, thresholding 
returns the value taken by a majority of its three
coordinates. Linear threshold functions are polynomial
threshold functions represented by polynomials
of total degree at most 1.
Linear Threshold Function
See also
Boolean Function, Polynomial Threshold FunctionExplore with Wolfram|Alpha
References
O'Donnell, R. Analysis of Boolean Functions. 21 May 2021. https://arxiv.org/abs/2105.10386.Cite this as:
Weisstein, Eric W. "Linear Threshold Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LinearThresholdFunction.html