Thursday, April 1, 2021

2021-04-07 / 12:00 ~ 13:00

학과 세미나/콜로퀴엄 - 기타: (첫수융합포럼) 곡면 상의 위상적 동역학계와 그 응용

by 백형렬(KAIST 수리과학과)

Thurston classified mappings from a given surface to itself. By iterating the surface mappings, one can view this as a dynamical system. Most of those surface mappings are so-called pseudo-Anosov. We briefly explain how we should understand these pseudo-Anosov maps and their physical meaning.

2021-04-07 / 12:00 ~ 13:00

학과 세미나/콜로퀴엄 - 기타: (첫수융합포럼) 액정물질 기반 위상학적 결함구조의 상전이

by 윤동기(KAIST 화학과)

Topological defect structure is one of the most interesting topics in natural sciences. Especially, the topological defect transition was highlighted by Nobel prize in 2016. But this topic is hard to understand and realize in the practical condition because the size and time-scale are huge in cosmos or so tiny in skyrmion system. So, we proposed to use liquid crystal (LC) materials to directly show this interesting topic, phase transition of topological defect.

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

학과 세미나/콜로퀴엄 - SAARC 세미나:

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.

2021-04-01 / 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.

2021-04-02 / 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.

2021-04-08 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄: Reduction of stochastic systems via resolvent equations

by 서인석(서울대학교)

In this talk, we consider stochastic systems with several stable sets. Typical examples are low-temperature physical systems and stochastic optimization algorithms. The macroscopic description of such systems is usually carried out via a so-called model reduction. We explain a necessary and sufficient condition for model reduction in terms of solutions of certain form of partial differential equations.

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