Summer Graduate School

<p>Artificial image generation by flow-based generative models starting from noise</p>

The last decades have witnessed tremendous success of deep learning tools and concepts in virtually all aspects of science and engineering. Modern generative models have demonstrated unprecedented performance in generation of artificial images, audios, texts, and find growing applications in scientific domains. While much of these developments have been enabled by the availability of huge data sets and the increase in computational power, breakthroughs in analysis and algorithm design also play a crucial role to advance the capabilities of deep learning. This is a fast growing area of research that offers many opportunities for mathematics, ranging from gaining a better theoretical understanding of the inner workings of deep learning tools, through improving existing algorithms in this context, to leveraging deep learning to solve long-standing challenges in applied and computational mathematics once thought intractable because of the curses of dimensionality.

The overarching goal of this summer school is to expose students to the latest developments in the mathematics of generative models. Our ultimate goal is to teach them how to conduct research in this exciting area in machine learning and use their knowledge to make contributions to applied mathematics using these new tools.

School Structure

There will be two lectures each day, each followed by an accompanying collaborative sessions. 

Prerequisites

(undergraduate level) Calculus; Linear Algebra; Probability; Ordinary Differential Equations; Numerical Analysis

Basic knowledge on stochastic differential equations will be useful, though not required.

We also list some useful books / review articles for those who want to get more prepared (not required for the course):

Introduction to Machine Learning:
Learning Theory from First Principles by Francis Bach (prepublication PDF)

Introduction to Stochastic Modeling and Analysis:
Applied Stochastic Analysis (Graduate Studies in Mathematics) by Weinan E, Tiejun Li and Eric Vanden-Eijnden

Introduction to Numerical Solutions to SDEs:
An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations, SIAM Review, Vol. 43, No. 3, pp. 525–546, by Desmond J. Higham

Application Procedure

For eligibility and how to apply, see the Summer Graduate Schools homepage.