STOR 89X (Spring 2026): GASPp

Generative AI, Statistical and Probabilistic (p)rinciples

Instructor: Shankar Bhamidi
Meeting time: Tue–Thu, 11:00–12:15
Location: Hanes 107

Note on course logistics: Official course materials, announcements, submissions, and grades will be handled via UNC Canvas.
This public website provides a lightweight “front door” with links to slides/notes/readings (e.g., via Dropbox) and a running schedule.

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Course overview

This course explores Generative AI through the lens of probability and statistics, with a particular emphasis on identifying—or questioning—the existence of coherent statistical and probabilistic principles underlying modern generative models.

The course title GASPp reflects this goal:

• GASP: Generative AI, Statistical and probabilistic …
• p (lower case): principles — an open question (still emerging vs. clean/unified)

This is an intentionally exploratory, research-oriented course. Roughly two-thirds of the semester will focus on building foundational understanding of:

• Large Language Models (LLMs)
• Diffusion models
• Related optimization and representation-learning frameworks

The course is not implementation-heavy; the emphasis is on understanding, intuition, reading research papers critically, and identifying research directions.

Official syllabus

More details can be found here

Major acknowledgement

I can only convey my understanding of the material, much of which I learnt from the material in the Resources. In particular I need to mention the wonderful resources developed by Prof. Cosma Shalizi and Prof. Ambuj Tewari. I am largely following in the shadow of these giants.

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Learning goals

By the end of the semester, students should:

• Be fluent in the conceptual and mathematical language of modern generative models.
• Understand how probability/statistics/stochastic-process ideas interact with (and often fail to explain) these models.
• Be able to read, dissect, and present current research papers.
• Identify a concrete research direction or question with the potential to evolve into a paper.

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Quick links

• Schedule (main, living schedule + materials links). This is probably the most important part of this webpage
• Resources (books, notes, online courses)
• Policies & Projects (expectations, proposal, final project)

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Announcements

• Brief course updates here; Canvas remains the source of truth for logistics!

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Schedule (living)

Official announcements/submissions are via Canvas. This part of the page is the “living” schedule with links (e.g., Dropbox) to slides, notes, and readings. If the links below do not work, this folder link to all the lectures should hopefully be more stable.

Date	Topic	Materials
2026-01-08 (Thu)	Intro to course. Class expectations. BPE Tokenization.	Slides: Lecture 1, P1-49 Reading: notes
2026-01-13 (Tue)	Vector semantics and representation learning. Classification and inevitability of logistic regression.	Slides: Lecture 1, slides 49 - 114 Reading: notes
2026-01-15 (Thu)	Word2vec and node2vec. Toy models. Start of information theory	Slides: Lecture 1, slides 114 - end, Lecture 2, slides 1-9 Reading: notes
2026-01-20 (Tue)	Basics of information theory	Slides: Lecture 2, Slides 9-41, Reading: notes
2026-01-22 (Thu)	Data processing inequality, Information theory and MLE and LDP. Entropy rates for stochastic processes	Slides: Lecture 2, associated slides,
2026-01-27 (Tue)	Classes cancelled owing to snow day.
2026-01-29 (Thu)	Ergodic sequences and entropy. Convexity of KL. Information geometry (maximization of Entropy, ELBO)	Slides: Lecture 2, associated slides, Reading: notes
2026-02-03 (Tue)	N-gram models and their use	Slides: Lecture 3
2026-02-05 (Thu)	Finished N-gram models. Started Neural networks. Origin story.	Slides: Lecture 3, Lecture 4, Slides 1-20
2026-02-10 (Tue)	Neural networks, Kolmogarov and Arnold. Baby implementation in Logistic regression	Lecture 4, Slides 21-45
2026-02-12 (Thu)	Neural networks and Stochastic gradient descent, Back propogation. Noise contrastive estimation	Lectue 4, slides 45-86
2026-02-17 (Tue)	Basics of Stochastic gradient descent	Lecture 4, slides 95-115
2026-02-19 (Thu)	Convergence a.s for stochastic gradient descent, state of the art for high dimensional stochastic gradient descent	Lecture 4 till the end
2026-02-24 (Tue)	Enter the transformer	Lecture 5
2026-02-26 (Thu)
2026-03-03 (Tue)
2026-03-05 (Thu)
2026-03-10 (Tue)
2026-03-12 (Thu)

Detailed reading

2026-01-08 reading

Material covered in the lecture

• Lecture 1, slides 1-49.
• Jurafsky and Martin, Chapter 2, Sec 2.1, 2.2, 2.4

Suggested reading and additional resources

• Machine learning street talk Podcast with Chris Bishop. Some key takeaways:

  • Fundamental importance of probability theory: Across the podcast, Bishop emphasizes that probability theory is the foundational language of machine learning because the subject is inherently about learning from data under uncertainty. He argues that once you take uncertainty seriously and want a quantitative framework, you are naturally led to probability, and he presents it as the conceptual bedrock for how to think about modeling, prediction, and learning. In that spirit, he’s direct about advice to students: he recommends they invest seriously in learning probability, and he says you can’t really work in machine learning without understanding it. He also acknowledges that modern practice often relies on scalable approximations, point estimates and stochastic gradient methods, yet he treats probability theory as the guiding framework that explains what those procedures are trying to do and how to interpret their outputs, including uncertainty and generalization. He highlights probability theory as a unifying lens across seemingly different methods, noting that algorithms like hidden Markov models and Kalman filters can be derived from the same basic probability rules and graphical factorization ideas. Stepping back, Bishop suggests that part of the maturation of the field has been a shift toward a more probabilistic and statistical perspective, with probability theory providing a durable bedrock for clear thinking even as models and compute continue to evolve.
  • Mysteries of stochastic gradient descent: Bishop points out that modern deep learning overturns a core statistical intuition: in earlier machine learning and in classical statistics, fitting models with far more parameters than data points seems obviously unreasonable. Bishop notes that, nevertheless, overparameterized neural networks often drive the training error to zero while the test error continues to improve. Bishop argues that this behavior suggests generalization is not explained simply by “minimize a loss and reach a global optimum.” Because there are many global minima with zero training error, some that overfit and others that generalize. Bishop emphasizes that the training dynamics, especially the implicit bias of stochastic gradient descent, appear to play a central role in selecting good solutions. Bishop concludes that explaining why these systems work so well remains an important open research problem.
  • Magic of information theory: Bishop also highlights what feels like the “magic of information theory”: when neural networks are trained to compress human language—i.e., to represent and predict it efficiently, they unexpectedly acquire the ability to behave like “reasoning engines.” He frames this as a genuine surprise to the field: a compression-driven objective can produce emergent reasoning capability rather than merely better text prediction.

• Andrej Karpathy on Dwarkesh podcast: deep thinker and expert in this general area. One thing I am still wrapping my head around are his views on reinforcement learning and its role in training LLMs. I know very little about this general area. His take is as follows: Karpathy argues that reinforcement learning plays only a limited and deeply flawed role in the development of large language models. His core critique is that RL relies on an extremely weak learning signal: a single scalar reward assigned after a long trajectory of actions, which is then indiscriminately propagated backward across every step. This creates noisy credit assignment, where incorrect reasoning steps are reinforced as long as the final outcome happens to be correct. He describes this as “sucking supervision through a straw” and views it as a statistically inefficient and conceptually misguided approach. In contrast to humans, who reflect selectively, revise mistakes, and attribute credit unevenly, RL blindly upweights entire trajectories. As a result, RL does not capture how reasoning or learning actually works and produces brittle improvements rather than genuine gains in intelligence. At the same time, Karpathy emphasizes that imitation learning and pretraining were far more surprising and impactful breakthroughs than reinforcement learning. Fine-tuning pretrained models on human demonstrations quickly transformed autocomplete systems into useful assistants while preserving their knowledge. Reinforcement learning, such as RLHF, provides incremental benefits like preference shaping and modest hill climbing when correct answers exist, but it does not solve reasoning, planning, or continual learning. Attempts to improve RL through process-based supervision run into severe problems because automated judges are gameable and lead to adversarial behavior, where models exploit reward models without improving correctness. Karpathy believes progress will require fundamentally new training paradigms involving reflection, selective credit assignment, memory, and distillation, rather than simply scaling RL, and he does not see reinforcement learning as the main path toward general intelligence. I guess only time will tell where we stand on these debates. While the above podcast goes into lots of other topics, in the specific setting of reinforcement learning, it seems to follow a previous podcast by another great researcher Richard Sutton. I have not had the time to dive into this second podcast yet.

2026-01-13 reading

Material covered in the lecture

• Lecture 1, slides 49 - 114

Suggested reading and additional resources

• Chapter 5
• Neural Word Embedding as Implicit Matrix Factorization by Omer Levy, Yoav Goldberg

2026-01-16 reading

Material covered in the lecture

• Lecture 1, slides 114 - end
• Lecture 2, slides 1-9

Suggested reading and additional resources

• Lectures 1,2 from Prof. Shalizi’s course
• Chapter 2 of Cover and Thomas’s book on information theory

2026-01-20 reading

Material covered in the lecture

Suggested reading and additional resources

• Related to the lecture material:
• Related to the proposed open problems: Node2vec, Random walks on configuration model, Entropic time and cutoff and Salez’s lecture notes

2026-01-29 reading

Material covered in the lecture

Suggested reading and additional resources

• Related to the lecture material: Chapter 3,4 and 11 from Cover and Thomas

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Spring 2026 — Tentative plan at the start of the semester (subject to change)

Date	Topic	Materials
2026-01-08 (Thu)	Intro to course. Class expectations.	Slides: link · Notes: link
2026-01-13 (Tue)	BPE / N-grams / vector semantics / representation learning	Slides: link · Reading: link
2026-01-15 (Thu)	Information theory: cross-entropy loss and MLE	Slides: link · Reading: link
2026-01-20 (Tue)	AEP, ergodic theory, Shannon–McMillan–Breiman	Slides: link · Reading: link
2026-01-22 (Thu)	Markov chains for text; stochastic gradient descent	Slides: link · Reading: link
2026-01-27 (Tue)	SGD in low and high dimensions	Slides: link · Reading: link
2026-01-29 (Thu)	SGD continued: neural networks	Slides: link · Reading: link
2026-02-03 (Tue)	Transformers, attention	Slides: link · Reading: link
2026-02-05 (Thu)	Transformers, attention (cont.)	Slides: link · Reading: link
2026-02-10 (Tue)	Transformers and interacting particle systems	Slides: link · Reading: link
2026-02-12 (Thu)	Prompting as conditioning; RLHF	Slides: link · Reading: link
2026-02-17 (Tue)	Influence functions; superconcentration; propagation of chaos	Slides: link · Reading: link
2026-02-19 (Thu)	Interlude: graph rep learning; spectral clustering	Slides: link · Reading: link
2026-02-24 (Tue)	Interlude: graph neural networks	Slides: link · Reading: link
2026-02-26 (Thu)	Latent variables I: K-means and EM	Slides: link · Reading: link
2026-03-03 (Tue)	Latent variables II: VI & ELBO; score matching	Slides: link · Reading: link
2026-03-05 (Thu)	GANs and autoencoders	Slides: link · Reading: link
2026-03-10 (Tue)	GANs and autoencoders II	Slides: link · Reading: link
2026-03-12 (Thu)	Diffusion models I	Slides: link · Reading: link

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