Multi-Layer Neural Networks
Stack dense layers into multi-layer perceptrons, using hidden layers and representation learning to combine raw features into abstract concepts.
Lessons in this Topic
Limitations of Single-Layer Networks
Explore why single-layer linear networks cannot learn compound feature interactions or solve non-linearly separable classification problems.
Hidden Layers and Network Geometry
Insert intermediate hidden layers between inputs and outputs to create hierarchical geometric transformations across multi-layer perceptrons.
Representation Learning Foundations
Trace how successive hidden layers automatically transform low-level input features into high-level abstract representations inside the network.
The Rectified Linear Unit Activation
Apply the piecewise linear ReLU function to introduce non-linearity while preserving identity gradients for positive activation values in neurons.
The Complete MLP Forward Pass Math
Formulate the end-to-end forward pass equation chaining matrix transformations, biases, and activations from input vector to final predictions.
Multi-Layer Networks In Practice
Master multi-layer forward passes, hidden representations, composite activations, and dimension tracking through complete manual calculations.