Homework: Linear separability and hidden layers

John Alderete, Simon Fraser University

Goal: explain a problem posed by some Boolean functions for single layer

perceptrons $($networks with just one set of weights to train$).$

Part $1.$ Boolean functions in two dimensions

Boolean functions

Task: represent the target functions for "and", inclusive $"$or$",$ "not and" and exclusive

$"$or$"$ in the $2$D Cartesian coordinate system below. Separate the regions that yield $"1"$

from those that yield $"0".$ Lable the chart appropriately.

Question: which functions can be drawn with a single straight line, and which

cannot be$?$