Fast Quantum Algorithms for Learning Linear Threshold Functions

Linear threshold functions are $f_{w,θ}(x)=\text{sign}(\langle x,w \rangle -θ)$, where the weight vector $w\in\mathbb{R}^n$ is a unit vector, $θ\in\mathbb R$ is a threshold, and typically $x\in\mathbb{R}^n$ or $x\in\{-1,1\}^n$. When $θ=0$, the LTF is called homogeneous, and we write $f_w:=f_{w,0}$.