Colloque CRM – Simone Brugiapaglia

The Mathematical Foundations of Deep Learning: From Rating Impossibility to Practical Existence Theorems

Simone Brugiapaglia (Concordia University)

Résumé

Deep learning is having a profound impact on industry and scientific research. Yet, while this paradigm continues to show impressive performance in a wide variety of applications, its mathematical foundations are far from being well established. In this talk, I will present recent developments in this area by illustrating two case studies. First, motivated by applications in cognitive science, I will present “rating impossibility » theorems. They identify frameworks where deep learning is provably unable to generalize outside the training set for the seemingly simple task of learning identity effects, i.e. classifying whether pairs of objects are identical or not. Second, motivated by applications in scientific computing, I will illustrate “practical existence » theorems. They combine universal approximation results for deep neural networks with compressed sensing and high-dimensional polynomial approximation theory. As a result, they yield sufficient conditions on the network architecture, the training strategy, and the number of samples able to guarantee accurate approximation of smooth functions of many variables. Time permitting, I will also discuss work in progress and open questions.

http://crm.umontreal.ca/quebec-mathematical-sciences-colloquium/408 

LIEU / PLACE
CRM, Salle / Room 5340, Pavillon André Aisenstadt
Une réception suivra au salon Maurice-Labbé (salle 6245)
A reception will follow in the Maurice-Labbé lounge (room 6245)

ZOOM
https://us06web.zoom.us/j/84226701306?pwd=UEZ5NVpZaUlldW5qNU8vZzIvbEJXQT09
ID: 842 2670 1306 / CODE: 692788

ORGANISATEURS / ORGANIZERS
Erica Moodie (McGill University)
Giovanni Rosso (Concordia University)
Alina Stancu (Concordia University)
Hugh R. Thomas (Université du Québec à Montréal)
Guy Wolf (Université de Montréal)