Tuesday, October 3, 2023

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2023-10-06 / 16:00 ~ 17:00
학과 세미나/콜로퀴엄 - 대수기하학: 인쇄
by ()

2023-10-05 / 11:00 ~ 12:00
학과 세미나/콜로퀴엄 - 계산수학 세미나: 인쇄
by 이명수()
In this talk, we discuss the Neural Tangent Kernel. The NTK is closely related to the dynamics of the neural network during training via the Gradient Flow(or Gradient Descent). But, since the NTK is random at initialization and varies during training, it is quite delicate to understand the dynamics of the neural network. In relation to this issue, we introduce an interesting result: in the infinite-width limit, the NTK converge to a deterministic kernel at initialization and remains constant during training. We provide a brief proof of the result for the simplest case.
2023-10-04 / 10:00 ~ 11:15
학과 세미나/콜로퀴엄 - 계산수학 세미나: 인쇄
by 이명수()
In this talk, we discuss the Neural Tangent Kernel. The NTK is closely related to the dynamics of the neural network during training via the Gradient Flow(or Gradient Descent). But, since the NTK is random at initialization and varies during training, it is quite delicate to understand the dynamics of the neural network. In relation to this issue, we introduce an interesting result: in the infinite-width limit, the NTK converge to a deterministic kernel at initialization and remains constant during training. We provide a brief proof of the result for the simplest case.
2023-10-06 / 11:00 ~ 12:00
학과 세미나/콜로퀴엄 - 응용 및 계산수학 세미나: 생성형 AI 기반 제품 설계 및 디자인 인쇄
by 강남우(KAIST)
"어떻게 하면 더 좋은 제품을 더 빠르게 개발할 수 있을까?"라는 문제는 모든 제조업이 안고 있는 숙제입니다. 최근 DX를 통해 많은 데이터들이 디지털화되고, AI의 급격한 발전을 통해 제품개발프로세스를 혁신하려는 시도가 일어나고 있습니다. 과거의 시뮬레이션 기반 설계에서 AI 기반 설계로의 패러다임 전환을 통해 제품개발 기간을 단축함과 동시에 제품의 품질을 향상시킬 수 있습니다. 본 세미나는 딥러닝을 통해 제품 설계안을 생성/탐색/예측/최적화/추천할 수 있는 생성형 AI 기반의 설계 프로세스(Deep Generative Design)를 소개하고, 모빌리티를 비롯한 제조 산업에 적용된 다양한 사례들을 소개합니다.
2023-10-10 / 16:30 ~ 17:30
IBS-KAIST 세미나 - 이산수학: Effective bounds for induced size-Ramsey numbers of cycles 인쇄
by Domagoj Bradač(ETH Zürich)
The k-color induced size-Ramsey number of a graph H is the smallest number of edges a (host) graph G can have such that for any k-coloring of its edges, there exists a monochromatic copy of H which is an induced subgraph of G. In 1995, in their seminal paper, Haxell, Kohayakawa and Łuczak showed that for cycles these numbers are linear for any constant number of colours, i.e., for some C=C(k), there is a graph with at most Cn edges whose any k-edge-coloring contains a monochromatic induced cycle of length n. The value of C comes from the use of the sparse regularity lemma and has a tower-type dependence on k. In this work, we obtain nearly optimal bounds for the required value of C. Joint work with Nemanja Draganić and Benny Sudakov.
2023-10-05 / 11:50 ~ 12:40
대학원생 세미나 - 대학원생 세미나: Online Learning in Markov Settings 인쇄
by 김영종(Dept. of Mathematical Sciences, KAIST)
In this talk, I will explain the setting of online convex optimization and the definition of regret and constraint violation. I then will introduce various algorithms and their theoretical guarantees under various assumptions. The connection with some topics in machine learning such as stochastic gradient descent, multi-armed bandit, and reinforcement learning will also be briefly discussed.
2023-10-05 / 14:30 ~ 15:45
학과 세미나/콜로퀴엄 - 기타: 인쇄
by ()
(information) "Introduction to Oriented Matroids" Series Thursdays 14:30-15:45
2023-10-10 / 16:00 ~ 17:00
SAARC 세미나 - SAARC 세미나: Colloquium: Quantum-Classical Correspondence from an Analytic Point of View 인쇄
by 홍영훈(중앙대학교 수학과)
In physics, Bohr’s correspondence principle asserts that the theory of quantum mechanics can be reduced to that of classical mechanics in the limit of large quantum numbers. This rather vague statement can be formulated explicitly in various ways. In this talk, focusing on an analytic point of view, we discuss the correspondence between basic inequalities and that between measures. Then, as an application, we present the convergence from quantum to kinetic white dwarfs.
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