CSCI-GA 3033

Instructor: Joan Bruna

Office: 60 Fifth ave, 612

Office hours: Fridays 9:30-11:00am

Email: [email protected]

Lecture: 2pm-3:40pm, Wed, 194 Mercer St Room 204

TA: Lei Chen

Office hours (OH): Mon 1:00-2:00pm

OH link: https://nyu.zoom.us/j/96760955584

Email: [email protected]

CampusWire: https://campuswire.com/p/G117229D6 (code: 1250)

Recitation (Rt): 11:15am-12:05pm, Friday

Rt link: https://nyu.zoom.us/j/97008504131

Course Description

In this graduate-level course, we will explore selected mathematical aspects of neural networks, addressing their ability to extract useful information in high-dimensions when trained with gradient-descent methods.

Part I: Feature learning in neural networks: linear and non-linear approximation with shallow neural networks. single- and multi-index models. Quantitative guarantees of (S)GD. Computational lower bounds. Connections to related high-dimensional inference problems. Open problems.
Part II: Generative modeling. Langevin Dynamics and Functional Inequalities. Beyond log-concavity. Score-based diffusion, stochastic interpolants and probability flows. Connections with Stochastic Control and Renormalization Groups. Quantitative guarantees using Neural Network Ansatze. Open problems.

Enrollment

Prerequisite(s): solid foundations in linear algebra, analysis, probability and statistics.

Recommended Preparation: Notions of measure concentration, high-dimensional probability, statistical mechanics and harmonic analysis will be helpful, but not strictly required.

Final Project

Instructions for Final Project (Updated on April 17)

Bibliography

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Schedule

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<aside> 📌 This course schedule provides a thorough list of weekly topics, readings, assignments, and exams. Click All to switch to week, exam, or calendar view.

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Grading

Breakdown

Participation: 25% Proposal : 25% Final Project: 50%

Scale

A 90%-100% B 80%-89% C 70%-79% D 60%-69% F < 60%