Georgia Institute of Technology College of Sciences

Our topic is around the Dynamics and noise in optimization algorithms. And our research is based on the Gradient Descent algorithm and extends the algorithm by certain variations, as we called Linearized Bregman and Iterative Shrinkage Thresholding Algorithm. We will examine the choice of different variations and mimic what in real world works best for each algorithm. Yeah, so stay tuned, and we will be talking more in our presentation! 

Deep learning has achieved great success in recent years. One aspect overlooked by traditional deep-learning methods is uncertainty modeling, which can be very important in certain applications such as medical image classification and reinforcement learning. A standard way for uncertainty modeling is by adopting Bayesian inference. In this talk, I will share some of our recent work on scalable Bayesian inference by sampling, called optimal-transport sampling, motivated from the optimal-transport theory. Our framework formulates Bayesian sampling as optimizing a set of particles, overcoming some intrinsic issues of standard Bayesian sampling algorithms such as sampling efficiency and algorithm scalability. I will also describe how our sampling framework be applied to uncertainty and repulsive attention modeling in state-of-the-art natural-language-processing models.

https://bluejeans.com/197711728

The three-dimensional Poincare conjecture shows that any closed three-manifold other than the three-sphere has non-trivial fundamental group. A natural question is how to measure the non-triviality of such a group, and conjecturally this can be concretely realized by a non-trivial representation to SU(2). We will show that the fundamental groups of three-manifolds with incompressible tori admit non-trivial SU(2) representations. This is joint work with Juanita Pinzon-Caicedo and Raphael Zentner.

The speaker will hold online office hours from 3:15-4:15 pm for interested graduate students and postdocs.

 This is a gentle introduction to the classical Oseledets' Multiplicative Ergodic Theorem (MET), which can be viewed as either a dynamical version of the Jordan normal form of a matrix, or a matrix version of the pointwise ergodic theorem (which itself can be viewed as a generalization of the strong law of large numbers).  We will also sketch Raghunathan's proof of the MET and discuss how the MET can be applied to smooth ergodic theory.