Mathematical Foundations of Generative AI (BSDA5002) in IITM BS: Syllabus

Mathematical Foundations of Generative AI (BSDA5002) is a 4 credit elective at the degree level of the IITM BS in Data Science. The handbook places it at level 5. It has no formal prerequisite. The course explains the probability and learning methods behind models that generate data: GANs, VAEs, diffusion models and large language models.

The course is taught by Prathosh A P, Assistant Professor in the Division of EECS at IISc Bangalore.

Handbook check. The course page leaves the course type blank. The handbook's course table lists it as a BD/BP elective. Both agree on 4 credits and no prerequisite.

What you learn in Mathematical Foundations of Generative AI

The page says you will study the theory and also implement the models in frameworks such as PyTorch. The 12 weeks fall into five blocks.

• Weeks 1 and 2: the idea of a generative model. What it means to learn a probability distribution with a deep network. Then learning by minimising a divergence between the model and the data.
• Weeks 3 and 4: GANs. How a generator and a discriminator are trained against each other. Then Wasserstein GANs and where GANs are used.
• Weeks 5 and 6: VAEs. Generating data through variational auto-encoding. Then improvements to VAEs, including VQ-VAE.
• Weeks 7 to 9: diffusion models. How denoising diffusion models are set up, their different forms and how to implement them. Then conditional diffusion and score-based models.
• Weeks 10 to 12: autoregressive models and LLMs. Autoregressive models as the base of language models. Then sampling, inference and quantisation, and aligning LLMs with reinforcement learning methods such as PPO and DPO.

The suggested book is Generative Deep Learning (O'Reilly, 2023), along with recent papers and surveys.

How the course is assessed

The course page points to the standard course structure on the programme's Academics page. It does not list a separate assessment plan. The page mentions lectures and assignments as the way you get hands-on practice.

Where it counts

• Minor in Generative AI. It is one of three courses, with Large Language Models (BSDA5004) and Deep Learning Practice (BSDA5013). See the Generative AI minor.
• BS level stream rule. It is level 5 and tagged BD/BP. The handbook does not say which stream a BD/BP course counts for, so ask support before you rely on it for either. See the BS degree level.
• Terms. The DS course table (updated 18 March 2026) marks it for May 2026, September 2026 and January 2027.

The handbook says level 5 courses are more complex than level 3 and level 4 courses, with the same credits and fee as level 4.

Who finds it hard and how to prepare

The name says "mathematical" for a reason. If the probability in Statistics 2 or Machine Learning Techniques felt weak, the first weeks will feel heavy. Divergence shows up in week 2, and probability runs through every later block.

• Revise probability first: conditional probability, expectation, Bayes' rule and the normal distribution in more than one dimension.
• Learn what KL divergence measures and practise computing it for two simple distributions.
• Take Deep Learning (BSCS3004) before this course, even though it is not required. You need to be at ease with networks, loss functions and training loops.
• Write a small GAN and a small VAE in PyTorch on a toy dataset. Seeing them fail teaches as much as the lectures.
• For each model family, keep one page with its objective, how it is trained and one weakness.

What to take before and after

Statistics 2, Machine Learning Techniques and Deep Learning give the best base. After this course, Large Language Models (BSDA5004) goes deeper into transformers and LLM training. Deep Learning Practice (BSDA5013) is the hands-on course in the same minor.

Common questions

Is this the same as the diploma course on DL and GenAI?

No. Introduction to DL and GenAI (BSDA2001) is a diploma level course that alternates theory and practice weeks. This is a level 5 degree course focused on the maths behind the same families of models.

Can I take it without Deep Learning?

Neither the course page nor the handbook lists a prerequisite. Without Deep Learning it will be much harder, because deep networks are part of the course from week 1.

Does it cover GPT style models?

Yes, in the last three weeks. It covers autoregressive models, LLM sampling and inference, quantisation and alignment with PPO and DPO.