Deep Learning
Neural Networks — The Foundation of Modern AI
Discover how neural networks form the backbone of modern AI systems, enabling machines to learn complex patterns from data.
- Universal function approximation — learn any mapping from inputs to outputs
- Backpropagation — efficient gradient computation for training
- Deep architectures — stack layers for hierarchical feature learning
The brain is a computer made of meat, and it is very good at being a brain.
Neural Networks Fundamentals
Neural networks learn complex patterns by stacking simple computational units (neurons) in layers. At the mathematical core, a neural network is a parameterized nonlinear function that is optimized via gradient-based methods.
The Perceptron
The perceptron is the atomic unit of neural computation. Given input vector , weights , and bias :
Activation Functions
Activation functions introduce nonlinearity, enabling networks to approximate arbitrary functions. Without them, a multi-layer network collapses to a single linear transformation.
Multi-Layer Perceptron (MLP)
An MLP stacks layers of neurons to form a deep network. Each layer computes an affine transformation followed by a nonlinear activation:
where and is the input.
Backpropagation
Backpropagation computes the gradient of the loss with respect to every parameter via the chain rule applied recursively from output to input.
Gradient Descent Variants
Weight Initialization
PyTorch Implementation
Key Takeaways
What to Learn Next
-> Convolutional Neural Networks Learn how CNNs process visual data with parameter sharing.
-> RNNs and LSTMs Explore networks designed for sequential data.
-> Training Deep Networks Master optimizers, batch norm, and regularization.
-> Transformers Learn the architecture that replaced RNNs.
-> Weight Initialization Understand Xavier, He, and modern initialization.
-> Optimizers for Deep Learning SGD, Adam, AdamW, and beyond.