Monday, April 29, 2024

2024-05-03 / 14:00 ~ 15:00

by 허은우()

Link prediction (LP), inferring the connectivity between nodes, is a significant research area in graph data, where a link represents essential information on relationships between nodes. Although graph neural network (GNN)-based models have achieved high performance in LP, understanding why they perform well is challenging because most comprise complex neural networks. We employ persistent homology (PH), a topological data analysis method that helps analyze the topological information of graphs, to explain the reasons for the high performance. We propose a novel method that employs PH for LP (PHLP) focusing on how the presence or absence of target links influences the overall topology. The PHLP utilizes the angle hop subgraph and new node labeling called degree double radius node labeling (Degree DRNL), distinguishing the information of graphs better than DRNL. Using only a classifier, PHLP performs similarly to state-of-the-art (SOTA) models on most benchmark datasets. Incorporating the outputs calculated using PHLP into the existing GNN-based SOTA models improves performance across all benchmark datasets. To the best of our knowledge, PHLP is the first method of applying PH to LP without GNNs. The proposed approach, employing PH while not relying on neural networks, enables the identification of crucial factors for improving performance. https://arxiv.org/abs/2404.15225

2024-05-03 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 계산수학 세미나: Multi-stage Neural Networks: Function Approximator of Machine Precision

by Yongji Wang(Stanford Univerisity)

Deep learning techniques are increasingly applied to scientific problems, where the precision of networks is crucial. Despite being deemed as universal function approximators, neural networks, in practice, struggle to reduce the prediction errors below O(10−5) even with large network size and extended training iterations. To address this issue, we developed the multi-stage neural networks that divides the training process into different stages, with each stage using a new network that is optimized to fit the residue from the previous stage. Across successive stages, the residue magnitudes decreases substantially and follows an inverse power-law relationship with the residue frequencies. The multi-stage neural networks effectively mitigate the spectral biases associated with regular neural networks, enabling them to capture the high frequency feature of target functions. We demonstrate that the prediction error from the multi-stage training for both regression problems and physics-informed neural networks can nearly reach the machine-precision O(10−16) of double-floating point within a finite number of iterations. Such levels of accuracy are rarely attainable using single neural networks alone.

2024-05-03 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - 계산수학 세미나: Rapid Convergence of Unadjusted Langevin Algorithm

by 최우진(카이스트)

최신 논문 리뷰: Rapid Convergence of Unadjusted Langevin Algorithm (Vempala et al) and Score-Based Generative Models(Song et al)

2024-05-03 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - 기타: Introduction to étale cohomology 4

by 이제학(KAIST)

This is an introductory reading seminar presented by a senior undergraduate student, Jaehak Lee, who is studying the subject.

2024-05-03 / 16:00 ~ 17:30

학과 세미나/콜로퀴엄 - 대수기하학:

by 황준묵(IBS-CCG)

I tell a personal story of how a mathematician working in complex algebraic geometry had come to discover the relevance of Cartan geometry, a subject in differential geometry, in an old problem in algebraic geometry, the problem of deformations of Grassmannians as projective manifolds, which originated from the work of Kodaira and Spencer. In my joint work with Ngaiming Mok, we used the theory of minimal rational curves to study such deformations and it reduced the question to a problem in Cartan geometry.

2024-04-30 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Towards the half-integral Erdős-Pósa property for even dicycles

by Maximilian Gorsky(TU Berlin)

A family $\mathcal F$ of (di)graphs is said to have the half- or quarter-integral Erdős-Pósa property if, for any integer $k$ and any (di)graph $G$, there either exist $k$ copies of graphs in $\mathcal F$ within $G$ such that any vertex of $G$ is contained in at most 2, respectively at most 4, of these copies, or there exists a vertex set $A$ of size at most $f(k)$ such that $G - A$ contains no copies of graphs in $\mathcal F$. Very recently we showed that even dicycles have the quarter-integral Erdős-Pósa property [STOC'24] via the proof of a structure theorem for digraphs without large packings of even dicycles. In this talk we discuss our current effort to improve this approach towards the half-integral Erdős-Pósa property, which would be best possible, as even dicycles do not have the integral Erdős-Pósa property. Complementing the talk given by Sebastian Wiederrecht in this seminar regarding our initial result, we also shine a light on some of the particulars of the embedding we use in lieu of flatness and how this helps us to move even dicycles through the digraph. In the process of this, we highlight the parts of the proof that initially caused the result to be quarter-integral. (This is joint work with Ken-ichi Kawarabayashi, Stephan Kreutzer, and Sebastian Wiederrecht.)

2024-05-02 / 11:50 ~ 12:40

대학원생 세미나 - 대학원생 세미나: The Hardy type inequality on the bounded domain with mean zero condition

by 전은찬(KAIST)

This talk aims to consider the attainability of the Hardy-type inequality in the bounded smooth domain with average-zero type constraint. Since the criteria of the attainability depends to the concentration-compactness type arguments, we will briefly introduce the results for some classical Hardy-type inequalities and the concentration-compactness arguments. Subsequently, we propose new function spaces that well define the new inequalities. Finally, we will discuss the attainability of the optimal constant of the inequality in the general smooth domain.

2024-05-01 / 16:00 ~ 17:00

SAARC 세미나 - SAARC 세미나:

by 한범석(성신여자대학교)

In this talk, we will introduce support properties of solutions to nonlinear stochastic reaction-diffusion equations driven by random noise ˙W : ∂tu = aijuxixj + biuxi + cu + ξσ(u) ˙W , (ω, t, x) ∈ Ω × R+ × Rd; u(0, ·) = u0, where aij , bi, c and ξ are bounded and random coefficients. The noise ˙W is spacetime white noise or spatially homogeneous colored noise satisfying reinforced Dalang’s condition. We present examples of conditions on σ(u) that guarantee the compact support property of the solution. In addition, we suggest potential generalization of these conditions. This is joint work with Kunwoo Kim and Jaeyun Yi.

2024-05-03 / 11:00 ~ 12:00

IBS-KAIST 세미나 - 수리생물학:

by ()

2024-05-02 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄: 한국수학 70년

by 금종해()

Events for the 취소된 행사 포함