McCulloch-Pitts Model

The McCulloch-Pitts model maps the input $\{x_1, x_2,\cdots, x_i \cdots, x_N \}$ into a scalar $y\in\{1,-1\}$,

$$ y = \operatorname{sign}( w\cdot x - b). $$

Since $w\cdot x - b = 0$ is a hyperplane, the McCulloch-Pitts model separates the state space using this hyperplane. The shift $b$ determines the interception, and $w$ decides the slope.