The deep learning approach learns a trainable non-linear mapping function φ from x to a representation φ(x) which can be used as an input to a linearly separable classification problem. The general form of this trainable mapping we consider is: ŷ = W φ(x) + b φ(x) = g(W'x + b') where g is a non-linear function. Why do we need non-linear mappings such as g() in this formulation?