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ABSTRACT: When numbers are added in the usual way, ‘carries’ appear along the way. It is natural to ask ‘how do the carries go’? How many are typical; if we just had a carry is it more or less likely that we have a following carry? It turns out that this is very close to the question ‘how many times should a deck of cards be shuffled to mix it up’ (!). I will explain the connection in a talk aimed at a non specialist audience.
DATE: Wednesday, November 27, 2019
VENUE: Amphithéâtre (S1-151) Pavillon Jean-Coutu
2940, chemin de Polytechnique, Montréal H3T 1J4
5:00 pm : speeches for the 50th anniversary of the CRM
5:30 pm : lecture by Persi Diaconis
Persi Diaconis is an American mathematician born in 1945. His interest for magic tricks made him leave school early on, but his fascination for mathematics and, in particular, probability theory brought him back there. He obtained his doctorate from Harvard University and he is now the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University. He received twice a MacArthur Fellowship and was awarded the Rollo Davidson Prize and the Van Wijngaarden Award. He was elected to the American National Academy of Sciences and is Fellow of the American Mathematical Society. He is recognized for his mathematical results on games of chance and gambling: How many shuffle does it take to make a deck of cards random? Are a coin tail and head really equiprobable? The website youtube offers several of his pedagogical presentations.
Lundi 16 avril / Monday, April 16 11:30 – 12:30 Université de Montréal, Pavillon André-Aisenstadt, salle / room 1360
Conférence inaugurale / Opening keynote lecture Deep Learning for AI
Yoshua Bengio (Université de Montréal)
There has been rather impressive progress recently with brain-inspired statistical learning algorithms based on the idea of learning multiple levels of representation, also known as neural networks or deep learning. They shine in artificial intelligence tasks involving perception and generation of sensory data like images or sounds and to some extent in understanding and generating natural language. We have proposed new generative models which lead to training frameworks very different from the traditional maximum likelihood framework, and borrowing from game theory. Theoretical understanding of the success of deep learning is work in progress but relies on representation aspects as well as optimization aspects, which interact. At the heart is the ability of these learning mechanisms to capitalize on the compositional nature of the underlying data distributions, meaning that some functions can be represented exponentially more efficiently with deep distributed networks compared to approaches like standard non-parametric methods which lack both depth and distributed representations. On the optimization side, we now have evidence that local minima (due to the highly non-convex nature of the training objective) may not be as much of a problem as thought a few years ago, and that training with variants of stochastic gradient descent actually helps to quickly find better-generalizing solutions. Finally, new interesting questions and answers are arising regarding learning theory for deep networks, why even very large networks do not necessarily overfit and how the representation-forming structure of these networks may give rise to better error bounds which do not absolutely depend on the iid data hypothesis.