Friday, April 30, 2021

2021-05-06 / 13:00 ~ 14:00

by ()

Introduction: In this lecture series, we'll discuss algebro-geometric study on fundamental problems concerning tensors via higher secant varieties. We start by recalling definition of tensors, basic properties and small examples and proceed to discussion on tensor rank, decomposition, and X-rank for any nondegenerate variety $X$ in a projective space. Higher secant varieties of Segre (resp. Veronese) embeddings will be regarded as a natural parameter space of general (resp. symmetric) tensors in the lectures. We also review known results on dimensions of secants of Segre and Veronese, and consider various techniques to provide equations on the secants. In the end, we'll finish the lectures by introducing some open problems related to the theme such as syzygy structures and singularities of higher secant varieties.

2021-05-07 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 대수기하학: Introduction to infinity-categories VI

by 조창연(QSMS Seoul National University)

This is part VI of the lectures on infinity-categories. I'll keep talking about the simplicial nerve construction in contrast to the ordinary nerve functor. To finish off this whole series, some overview of the theory of infinity-categories will be given, including how similar and different it is to the ordinary category theory.

2021-04-30 / 10:00 ~ 12:00

학과 세미나/콜로퀴엄 - SAARC 세미나:

by 김용대()

Deep generative models have received much attention recently since they can generate very realistic synthetic images. There are two regimes for the estimation of deep generaitve models. One is generative adversarial network (GAN) and the other is variational auto encoder (VAE), Even though GAN is known to generate more clean synthetic images, it suffers from numerical instability and mode collapsing problems. VAE is an useful alternative to GAN and an important advantage of VAE is that the representational learning (i.e. learning latent variables) is possible. In this talk, I explain my recent studies about VAE. The first topic is computation. Typically, the estimation of VAE is done by maximizing the ELBO – an upper bound of the marginal likelihood. However, it is known that ELBO is inferior to the maximum likelihood estimator. I propose an efficient EM algorithm for VAE which directly finds the maximizer of the likelihood (the maximum likelihood estimator, MLE). The second topic is theory. I explain how the MLE of VAE behaves asymptotically. I derive a convergence rate which depends on the noise level as well as the complexity of a deep architecture. A surprising observation is that the convergence rate of the MLE becomes slower when the noise level is too low. A new technique to modify the MLE when the noise level is small is proposed and is shown to outperform the original MLE by analyzing real data.

2021-04-30 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 수리생물학:

by ()

Oscillatory signals are ubiquitously observed in many different intracellular systems such as immune systems and DNA repair processes. While we know how oscillatory signals are created, we do not fully understand what a critical role they play to regulate signal pathway systems in cells. Recently by using a stochastic nucleosome system, we found that a special signal (NFkB signal) in an immune cell can enhance the variability of the immune response to inflammatory stimulations when the signal is oscillatory. Hence in this talk, we discuss the roles of oscillatory and non-oscillatory NFkB signals in an inflammatory system of immune cells as the main example for revealing the role of oscillatory signals. And then we will talk about how this finding can be generalized for other intra- or extra-cellular systems to study why cells use oscillations.

2021-05-07 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 대수기하학: Motivic homotopy theory of logarithmic schemes I

by Doosung Park(University of Zürich, Switzerland)

Morel and Voevodsky constructed the A^1-motivic homotopy category SH(k). One purpose of motivic homotopy theory is to incorporate various cohomology theories into a single framework so that one can discuss relations between cohomology theories more efficiently. However, there are still lots of non A^1-invariant cohomology theories, e.g. Hodge cohomology and topological cyclic homology. There is no way to represent these in SH(k). In the first talk, I will explain the construction of logDM^{eff}(k) for a perfect field k, which is strictly larger than Voevodsky's triangulated categories of motives DM^{eff}(k) because Hodge cohomology is representable in logDM^{eff}(k). This work is joint with Federico Binda and Paul Arne Østvær.

2021-05-07 / 10:30 ~ 12:00

학과 세미나/콜로퀴엄 - SAARC 세미나:

by ()

The standard machine learning paradigm optimizing average-case performance performs poorly under distributional shift. For example, image classifiers have low accuracy on underrepresented demographic groups, and their performance degrades significantly on domains that are different from what the model was trained on. We develop and analyze a distributionally robust stochastic optimization (DRO) framework over shifts in the data-generating distribution. Our procedure efficiently optimizes the worst-case performance, and guarantees a uniform level of performance over subpopulations. We characterize the trade-off between distributional robustness and sample complexity, and prove that our procedure achieves this optimal trade-off. Empirically, our procedure improves tail performance, and maintains good performance on subpopulations even over time.

2021-05-06 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄: Sublinear expander and embeddings sparse graphs

by 홍 리우(워릭 대학교)

A notion of sublinear expander has played a central role in the resolutions of a couple of long-standing conjectures in embedding problems in graph theory, including e.g. the odd cycle problem of Erdos and Hajnal that the harmonic sum of odd cycle length in a graph diverges with its chromatic number. I will survey some of these developments.

Events for the 취소된 행사 포함