Friday, March 26, 2021

2021-04-01 / 10:30 ~ 12:00

by 이진엽()

Bose-Einstein condensation (BEC) is one of the most famous phenomena, which cannot be explained by classical mechanics. Here, we discuss the time evolution of BEC in the mean-field limit. First, we review quantum mechanics briefly, and we understand the problem in a mathematically rigorous way. Then, we taste the idea of proof by using coherent state and the Fock space. Finally, some recent developments will be provided.

2021-04-02 / 10:00 ~ 12:00

학과 세미나/콜로퀴엄 - SAARC 세미나:

by 윤철희()

Overparametrized neural networks have infinitely many solutions that achieve zero training loss, but gradient-based optimization methods succeed in finding solutions that generalize well. It is conjectured that the optimization algorithm and the network architecture induce an implicit bias towards favorable solutions, and understanding such a bias has become a popular topic. We study the implicit bias of gradient flow (i.e., gradient descent with infinitesimal step size) applied on linear neural network training. We consider separable classification and underdetermined linear regression problems where there exist many solutions that achieve zero training error, and characterize how the network architecture and initialization affects the final solution found by gradient flow. Our results apply to a general tensor formulation of neural networks that includes linear fully-connected networks and linear convolutional networks as special cases, while removing convergence assumptions required by prior research. We also provide experiments that corroborate our theoretical analysis.

2021-03-26 / 10:00 ~ 12:00

학과 세미나/콜로퀴엄 - SAARC 세미나:

by 김경훈(고려대학교)

Many types of diffusion equations have been used to describe diverse natural phenomena. The classical heat equation describes the heat propagation in homogeneous media, and the heat equation with fractional time derivative describes anomalous diffusion, especially sub-diffusion, caused by particle sticking and trapping effects. On the other hand, space-fractional diffusion equations are related to diffusion of particles with long range jumps. In this talk, I will introduce the following: 1. Elementary notion of stochastic parabolic equations 2. Stochastic processes with jumps and their related PDEs and Stochastic PDEs 3. Some regularity results of PDEs and Stochastic PDEs with non-local operators

2021-04-01 / 13:00 ~ 14:30

학과 세미나/콜로퀴엄 - 대수기하학:

by 한강진()

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.

2021-03-26 / 14:00 ~ 15:30

학과 세미나/콜로퀴엄 - 대수기하학:

by 한강진()

2021-04-02 / 16:00 ~ 17:00

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

by 조창연(QSMS Seoul National University)

This is part II of the lecture series in infinity-categories. I'll continue to talk about higher categories and some difficulty in defining them. In the end, a few models for infinity-categories will be introduced very roughly.

2021-04-01 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄: WGAN with an Infinitely Wide Generator Has No Spurious Stationary Points

by 류경석(서울대학교)

Generative adversarial networks (GAN) are a widely used class of deep generative models, but their minimax training dynamics are not understood very well. In this work, we show that GANs with a 2-layer infinite-width generator and a 2-layer finite-width discriminator trained with stochastic gradient ascent-descent have no spurious stationary points. We then show that when the width of the generator is finite but wide, there are no spurious stationary points within a ball whose radius becomes arbitrarily large (to cover the entire parameter space) as the width goes to infinity.

Events for the 취소된 행사 포함