Why is multi-layer network crucial?

Single layer networks vs Non-linearity:

Single layer networks (perceptrons) can only solve linearly separable problems. Many real-world problem are non-linearly separable, requiring multi-layer networks to create more complex decision boundaries

Non-linearly separable examples are:

• Image recognition: The difference between cats and dogs isn't a simple linear boundary in pixel space.
• Natural language processing: The meaning of sentences often depends on complex, non-linear relationships between words.
• Financial predictions: Stock market trends often involve non-linear relationships between multiple factors.

Advantage of 2-layer networks:

Two layer networks can transform non-linearly separable input data into a new feature space where the problem becomes linearly separable. This is achieved through the hidden layer's nonlinear activation functions.

How hidden layers transform non-linearly separable inputs into linearly separable features?

Hidden layers apply non-linear transformation to the input data, effectively projecting it into higher dimensional space. In this new space, previously non-linearly separable data points may become linearly separable.

Detailed vs Condensed representations of neural network

1. Detailed representations show individual neurons & connections
2. while condensed representations group neurons into layers. Condensed representations are often more practical for visualizing & discussing larger networks.