Chapter 9: Neural Networks
Build the foundation of modern deep learning from first principles. Understand how perceptrons combine into multi-layer networks, how activation functions enable non-linear learning, how backpropagation efficiently computes gradients, and how optimizers navigate the loss landscape.
Chapter Overview
Neural networks are universal function approximators—with enough neurons, they can learn to represent any continuous function. This remarkable capability, combined with efficient training via backpropagation, sparked the deep learning revolution.
The basic unit is the perceptron: a weighted sum of inputs passed through a non-linear activation function. Individual perceptrons can only learn linear boundaries, but stacking them into layers creates Multi-Layer Perceptrons (MLPs) that learn arbitrarily complex patterns.
The key insight that made training deep networks practical is backpropagation: by applying the chain rule of calculus, we can efficiently compute how the loss changes with respect to every weight in the network. This transforms learning from an intractable search problem into gradient descent optimization.
Modern neural networks wouldn't work without careful engineering: activation functions prevent vanishing gradients, weight initialization ensures healthy signal flow, and adaptive optimizers like Adam automatically tune learning rates per parameter.
Understanding these fundamentals is essential before moving to specialized architectures like CNNs, RNNs, and Transformers. The same principles—forward passes, loss functions, gradients, and optimization—apply throughout deep learning.
This chapter covers:
- Perceptrons & MLPs: From single neurons to deep multi-layer networks with universal approximation capability
- Activation Functions: Non-linear functions that enable learning complex patterns and their properties
- Backpropagation: The algorithm that makes deep learning tractable by efficiently computing gradients
- Optimizers: Methods for navigating loss landscapes, from basic SGD to adaptive algorithms like Adam
Chapter Roadmap
Click any topic to jump in
Perceptrons & MLPs
Single neurons to multi-layer networks — weighted sums, activation functions, and the universal approximation theorem.
Activation and gradient computation
Activation Functions
Non-linear functions that enable learning complex patterns — ReLU, sigmoid, softmax, and the vanishing gradient problem.
Backpropagation
The chain rule applied to neural networks — efficiently computing gradients from output to input for weight updates.
Optimizers
Navigating loss landscapes with SGD, momentum, and Adam — adaptive learning rates and convergence strategies.
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