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