The Mathematics of Generative Models

Welcome to our cutting-edge course on the mathematical foundations of AI generative models. This course is designed for advanced students and professionals who want to delve deep into the theoretical underpinnings of modern AI systems.

Course Duration: 12 weeks

Prerequisites: Linear Algebra, Calculus, Probability Theory

Module 1: Probability Theory and Statistical Learning

1.1 Fundamentals of Probability Theory

Review of probability distributions, conditional probability, and Bayes' theorem.

1.2 Maximum Likelihood Estimation

Deriving likelihood functions and optimization techniques.

Module 2: Neural Network Foundations

2.1 Feedforward Neural Networks

Architecture, activation functions, and backpropagation.

2.2 Convolutional Neural Networks

Convolution operations, pooling, and their applications in generative models.

Module 3: Generative Adversarial Networks (GANs)

3.1 GAN Architecture and Loss Functions

Mathematical formulation of generator and discriminator networks.

3.2 Wasserstein GANs and Gradient Penalties

Advanced GAN techniques and stability improvements.

Interactive Exercise: GAN Loss Function Optimization



Module 4: Variational Autoencoders (VAEs)

4.1 Variational Inference

KL divergence, ELBO, and reparameterization trick.

4.2 Latent Variable Models

Mathematical foundations of VAE architectures.

Module 5: Transformers and Attention Mechanisms

5.1 Self-Attention and Multi-Head Attention

Mathematical formulation of attention mechanisms.

5.2 Transformer Architecture

Positional encoding, layer normalization, and feed-forward networks.

← Advanced Topics in Generative AI Practical Applications of Generative Models →