Generative modelling
In the wake of models like Dall-E and ChatGPT, generative models have had a massive impact on text and image applications. The goal of this class is to present their mathematical and algorithmical foundations.
New site for the class
Program for 2025
- 10/09/25 Class cancelled
- 11/09/25 Introduction to GenAI, MLE, Bayes + Base Models, Mixtures of Gaussian, EM (notes by Y. Dziki)
- 17/09/25 Maximum a posteriori vs max likelihood, PCA, PPCA, VAE notes by M. Ottavy
- at home: LAB 1 : simple generative models: PCA, mixture of Gaussian, pretrained models, VAE
- 18/09/25 [postponed due to ENS being closed] GAN/WGAN
- 24/09/25 Flow matching notes by H. Martel, blog post on Flow Matching
- 25/09/25 Lab on Flow Matching
- 01/10/25 GANS (material 1, material 2, material 3)
- 02/10/25 WGAN + Lab WGAN
- 08/10/25 Diffusion 1/2
- 09/10/25 Introduction to sequence modelling: tokenizers, bigram models, autoregressive models, Transformers
- 15/10/25 Diffusion 2/2 (links with flow matching, conditional generation)
- 16/10/25 Metrics (FID/rec/recall/density), conditional generation, classifier/classifier-free guidance, OT, Reflow
- 17/10/25 Project progress evaluation
- 22/10/25 Lab transformers
- 23/10/25 No class (work on Lab)
- 05/11/25 Discrete models
- 06/11/25 Discrete models + lab DDPM/DDIM
- 12/11/25 Project defense 1/2
- 13/11/25 Project defense 2/2
Validation in 2025
- weekly homeworks + quizzes + 3 Labs in python
- paper presentation and extension of a selected research article and the associated code applied on real data.
Prerequisite
- probabilities (densities, change of variable formula)
- linear algebra (PSD matrices, eigenvalue decomposition, spectral theorem)
- calculus (gradient, Hessian, Jacobian, chain rule, ordinary differential equations)