This interactive demo illustrates how a combination of linear transformation and non-linearity can transform data in a way that linear transformations alone cannot. Observe how the data, initially not linearly separable in the input space (X), becomes separable after passing through a linear layer (Y) and then a non-linear activation (Z).

This provides intuition for why layers with non-linear activations are powerful: they can map data into a new space where complex patterns become simpler (potentially linearly separable), making them learnable by subsequent layers.