Friday, November 24, 2023

2023-11-28 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 대수기하학:

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2023-12-01 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 응용 및 계산수학 세미나:

by 권도현(서울시립대학교 수학과)

The study of gradient flows has been extensive in the fields of partial differential equations, optimization, and machine learning. In this talk, we aim to explore the relationship between gradient flows and their discretized formulations, known as De Giorgi's minimizing movements, in various spaces. Our discussion begins with examining the backward Euler method in Euclidean space, and mean curvature flow in the space of sets. Then, we investigate gradient flows in the space of probability measures equipped with the distance arising in the Monge-Kantorovich optimal transport problem. Subsequently, we provide a theoretical understanding of score-based generative models, demonstrating their convergence in the Wasserstein distance.

2023-11-27 / 10:00 ~ 11:00

학과 세미나/콜로퀴엄 - 박사논문심사: 무한 너비 신경망의 두터운 꼬리 분포와 노드간 의존성

by 이호일(KAIST)

2023-11-28 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Towards a high-dimensional Dirac’s theorem

by 이현우(KAIST & IBS 극단조합및확률그룹)

Dirac's theorem determines the sharp minimum degree threshold for graphs to contain perfect matchings and Hamiltonian cycles. There have been various attempts to generalize this theorem to hypergraphs with larger uniformity by considering hypergraph matchings and Hamiltonian cycles. We consider another natural generalization of the perfect matchings, Steiner triple systems. As a Steiner triple system can be viewed as a partition of pairs of vertices, it is a natural high-dimensional analogue of a perfect matching in graphs. We prove that for sufficiently large integer $n$ with $n \equiv 1 \text{ or } 3 \pmod{6},$ any $n$-vertex $3$-uniform hypergraph $H$ with minimum codegree at least $\left(\frac{3 + \sqrt{57}}{12} + o(1) \right)n = (0.879... + o(1))n$ contains a Steiner triple system. In fact, we prove a stronger statement by considering transversal Steiner triple systems in a collection of hypergraphs. We conjecture that the number $\frac{3 + \sqrt{57}}{12}$ can be replaced with $\frac{3}{4}$ which would provide an asymptotically tight high-dimensional generalization of Dirac's theorem.

2023-11-30 / 11:50 ~ 12:40

대학원생 세미나 - 대학원생 세미나: Data Topology and Geometry-dependent Bounds on ReLU Network Widths

by 이상민(Dept. of Mathematical Sciences, KAIST)

While deep neural networks (DNNs) have been widely used in numerous applications over the past few decades, their underlying theoretical mechanisms remain incompletely understood. In this presentation, we propose a geometrical and topological approach to understand how deep ReLU networks work on classification tasks. Specifically, we provide lower and upper bounds of neural network widths based on the geometrical and topological features of the given data manifold. We also prove that irrespective of whether the mean square error (MSE) loss or binary cross entropy (BCE) loss is employed, the loss landscape has no local minimum.

2023-11-30 / 14:30 ~ 15:45

학과 세미나/콜로퀴엄 - 기타:

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(information) "Introduction to Oriented Matroids" Series Thursdays 14:30-15:45

Events for the 취소된 행사 포함