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
Contact: p.sharma@nyu.edu

Schedule

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

#	Date	Topic
1	Sept 14	Framing the Course. LLMs as scientific objects; generalization as the organizing question.
2	Sept 21	Architecture I. The transformer from scratch — attention, residuals, layer norm; inductive biases and what they imply for generalization.
3	Sept 28	Architecture II. Hyperparameter choices and ablations; depth vs. width; attention alternatives and mixtures of experts.
4	Oct 5	Optimization & Training Dynamics. Adam, SGD, Muon; learning rate schedules; batch size effects; grokking, double descent, the Edge of Stability.
—	Oct 12	Fall Break — no class
5	Oct 14 (Legislative Monday)	Generalization Theory. Classical bias–variance vs. the modern regime; benign overfitting; what networks memorize vs. generalize.
6	Oct 19	Scaling Laws. Kaplan vs. Chinchilla; compute-optimal training; when scaling loss translates into capabilities — and when it does not.
7	Oct 26	Data I. From raw data to a pre-training corpus; filtering, deduplication, quality signals; data quantity vs. quality.
8	Nov 2	Data II. Repetition and memorization; domain diversity and mixing; synthetic data and its generalization limits.
9	Nov 9	Geometry & Representations. Invariances and symmetries; the linear representation hypothesis; probing as an empirical tool.
10	Nov 16	In-Context Learning & Prompting. ICL as generalization from context; what the prompt contributes; chain-of-thought empirically; prompt sensitivity as a failure mode.
11	Nov 23	Emergent Capabilities. Emergence as a generalization phenomenon; the metric problem; smooth vs. sharp transitions; compositional generalization failures.
12	Nov 30	Alignment & Fine-Tuning. SFT and what changes in the weights; RLHF and RL for reasoning; shortcut learning and sycophancy; the superficial alignment hypothesis.
13	Dec 7	Evaluation. Benchmark contamination; designing evaluations that measure generalization; LLM-as-judge; the moving target problem.
14	Dec 14	Project Presentations & Open Problems. What we still do not understand; student project presentations; frontiers.