Course description

Large language models generalize in ways we did not design and fail in ways we did not anticipate. This course is about understanding why.

This course will take an empirical approach to unpacking this question: building language models from scratch to develop hands-on fluency, then using that fluency to ask scientific questions about generalization. What does compute-optimal training actually mean? What do data quality, repetition, and domain diversity do to what a model learns? When and why does chain-of-thought help? And more.

Students will learn to build transformers from scratch, fit scaling laws, build data pipelines, and run fine-tuning experiments---not as engineering exercises, but as instruments for forming and testing hypotheses. By the end, students will be equipped to read the frontier literature critically, design experiments, and pursue research questions in one of the most consequential but incompletely understood areas of science.

Prerequisites

Machine learning, linear algebra, probability, and proficiency in Python and PyTorch.

Logistics

Lectures: Mondays, 2:45–4:45pm
Instructor: Pratyusha Sharma
Teaching Assistant: Jiahan Li
Contact: p.sharma@nyu.edu, jl17319@nyu.edu
Office Hours: Tuesday 9am–10am [Pratyusha Sharma], Friday 1pm-2pm [Jiahan Li]

Schedule

Schedule is tentative and will be updated as the semester progresses.

#	Date	Topic	Papers
1	Sept 14	Framing the Course. LLMs as scientific objects; generalization as the organizing question.
2	Sept 21	Optimization. Guest lecture by John Langford.	Adam. Muon. Dion.
3	Sept 28	Scaling Laws	Kaplan scaling law. Hoffman scaling law. Data constrained scaling. Beating power law scaling [Bonus].
4	Oct 5	Training Dynamics.	Grokking. Double descent. Edge of stability.
—	Oct 12	Fall Break — no class
5	Oct 14 (Legislative Monday)	Post-Hoc Phenomena.	Lottery ticket hypothesis. Linear mode connectivity. LASER / Better sub networks.
6	Oct 19	Data.	Fineweb. Data mixing. Dataset difficulty.
7	Oct 26	Generalization.	Lazy vs rich. Emergence. Sharpness aware minimization.
8	Nov 2	In-context learning.	Influence of data. Induction heads. Role of demonstrations.
9	Nov 9	Reasoning.	Chain-of-thought. DeepSeek-R1. Agentic RL.
10	Nov 16	Evaluation.	HELM. Emergence mirage? Red-teaming.
11	Nov 23	Reinforcement Learning.	Role of RL beyond SFT? RLxForgetting. Dr.GRPO.
12	Nov 30	Alignment	InstructGPT. J-Space. Pacing the frontier.
13	Dec 7	Interpretability. Guest lecture by John Hewitt.
14	Dec 14	Project Presentations & Open Problems. What we still do not understand; student project presentations.