Discovering the Future
Mathematical Foundations of Deep Learning
A 2-week intensive course by Prof. Arnak Dalalyan.
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General Information
About the course

The course is conducted by Arnak Dalalyan, Professor of Statistics at ENSAE Paris. It is organized within the ADVANCE STEM Research grant program in which Prof. Dalalyan is an international Principal Investigator of the research project named “Statistical analysis of machine learning algorithms (SAM-lab)”.

The course is free of charge and aims to present statistical aspects of deep learning. The course is composed of 6 (blackboard/whiteboard) lectures of 1.5 hours. The tentative plan of the lectures is as follows:

  • Lecture 1: A quick overview of mathematical and statistical challenges related to deep learning
  • Lecture 2: Generalization in statistical learning
  • Lecture 3: Implicit regularization
  • Lecture 4: Benign overfitting
  • Lecture 5: Efficient optimization
  • Lecture 6: Generalization in the linear regime

The main references for the course are the recent papers:

Deep learning: a statistical viewpoint by Peter L. Bartlett, Andrea Montanari, Alexander Rakhlin

A Selective Overview of Deep Learning Jianqing Fan, Cong Ma, Yiqiao Zhong

Learning outcomes
  1. Mathematical definition of Neural Networks and Deep Learning

  2. Risk bounds in classification

  3. Mathematical tools for proving risk bounds

  4. Recent approaches to tackle the main challenges of Deep Learning

Target Audience

The main target audience for this course are Master and PhD students, as well as researchers in Mathematics, Computer Science, Physics and Engineering. Most of the lectures might also be interesting for the last-year bachelor students. The pace of progress will be tailored to the audience.

  • Good knowledge of linear algebra

  • Probability theory and analysis

  • Some notions of optimization and mathematical statistics.

Course Duration: August 16 - 27

Days: Monday, Wednesday, Friday

Hours: 17:00 - 18:45 (with a 15 minutes break)

Venue: FAST Creative Campus (Mergelyan Institute, 3 Hakob Hakobyan str.)

Language: Armenian(if necessary, the lecturer can translate some parts)

Registration: Click here to register by August 13

Short bio

Arnak Dalalyan is a Professor of Statistics at ENSAE, Institut Polytechnique de Paris, and the Director of the Center of Research in Economics and Statistics (CREST). In 1999, Prof. Dalalyan received an M.Sc. from the Paris 6 University and in 2001, earned a PhD from the University of Le Mans. He defended his habilitation in 2007 at the Paris 6 University. Prof. Dalalyan's research focuses on high-dimensional statistics, statistical machine learning, nonparametric function estimation, and computer vision. He serves currently as Associate Editor for several statistical journals including the Annals of Statistics, Bernoulli, Electronic Journal of Statistics and Journal of Machine Learning Research.