Linear equivalence
Linear equivalence
$\text{multilayered FFNN, all neurons use linear} f_{a}s$ $\text{EQUIVALENT TO}$ $\text{singlelayer NN, all neurons linear}$
Need for nonlinearities

multilayer network using solely linear neurons

lacks the expressive power gained from nonlinear activations,

reducing its capabilities to that of a simpler, singlelayer network.

Linear activation functions don't introduce the complexity needed for neural networks to learn and represent intricate patterns

therefore use deep NNs when your data IS NOT linearly separable/ CANNOT be modeled using a linear model