Monday, May 23, 2022

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2022-05-30 / 16:30 ~ 17:30
IBS-KAIST 세미나 - 이산수학: Learning Symmetric Rules with SATNet 인쇄
by 양홍석(KAIST)
SATNet is a differentiable constraint solver with a custom backpropagation algorithm, which can be used as a layer in a deep-learning system. It is a promising proposal for bridging deep learning and logical reasoning. In fact, SATNet has been successfully applied to learn, among others, the rules of a complex logical puzzle, such as Sudoku, just from input and output pairs where inputs are given as images. In this paper, we show how to improve the learning of SATNet by exploiting symmetries in the target rules of a given but unknown logical puzzle or more generally a logical formula. We present SymSATNet, a variant of SATNet that translates the given symmetries of the target rules to a condition on the parameters of SATNet and requires that the parameters should have a particular parametric form that guarantees the condition. The requirement dramatically reduces the number of parameters to learn for the rules with enough symmetries, and makes the parameter learning of SymSATNet much easier than that of SATNet. We also describe a technique for automatically discovering symmetries of the target rules from examples. Our experiments with Sudoku and Rubik’s cube show the substantial improvement of SymSATNet over the baseline SATNet. This is joint work with Sangho Lim and Eungyeol Oh.
2022-05-27 / 15:30 ~ 16:30
학과 세미나/콜로퀴엄 - 확률론: 인쇄
by 진우영()
The law of iterated logarithm (LIL) is a crowning achievement in classical probability theory that gives the sharp upper bound for the magnitude of fluctuations of a random walk. If each step has mean zero and variance one, then the upper bound (in certain sense) is given by \sqrt{2n\log\log n}, hence the name “iterated logarithm.” Despite being considered the “third fundamental limit theorem in probability” by some probabilists after the law of large numbers and the central limit theorem, its proof is not so accessible to non-experts. For instance, most textbooks either only consider special cases or use sophisticated machineries in their proofs. The purpose of this talk is to provide a relatively simple and elementary proof of the so-called Hartman—Wintner LIL. The idea is to generalize a proof of the central limit theorem (CLT), which will be also presented, to obtain a result on the rate of convergence in the CLT. First principles in probability (e.g. the second Borel—Cantelli lemma) are the only technical prerequisites.
2022-05-24 / 15:30 ~ 16:30
학과 세미나/콜로퀴엄 - 박사논문심사: 타원과 쌍곡선형 특이 극한을 통한 반응-확산 방정식의 파동 전파 인쇄
by 박현준(KAIST)
심사위원장 : 김용정, 심사위원 : 강문진, 김재경, 임미경, 안인경(고려대학교)
2022-05-24 / 14:30 ~ 15:30
학과 세미나/콜로퀴엄 - 박사논문심사: 불균질 확산 방정식으로의 수렴 및 반응-확산 방정식에서 파동 전파 인쇄
by 김호연(KAIST)
심사위원장 : 김용정, 심사위원 : 강문진, 김재경, 임미경, 안인경(고려대학교)
2022-05-25 / 16:00 ~ 17:00
IBS-KAIST 세미나 - IBS-KAIST 세미나: 인쇄
by ()
We shall give an explicit estimate of the lower bound of the Bergman kernel associated to a positive line bundle. In the compact Riemann surface case, our result can be seen as an explicit version of Tian’s partial C0-estimate.
2022-05-25 / 17:00 ~ 18:15
SAARC 세미나 - SAARC 세미나: 인쇄
by 김영헌(브리티시컬럼비아 대학)

2022-05-23 / 16:00 ~ 17:00
학과 세미나/콜로퀴엄 - PDE 세미나: 인쇄
by ()
This talk is concerned with the bifurcation and stability of the compresible Taylor vortex. Consider the compressible Navier-Stokes equations in a domain between two concentric infinite cylinders. If the outer cylinder is at rest and the inner one rotates with sufficiently small angular velocity, a laminar flow, called the Couette flow, is stable. When the angular velocity of the inner cylinder increases, beyond a certain value of the angular velocity, the Couette flow becomes unstable and a vortex pattern, called the Taylor vortex, bifurcates and is observed stably. This phenomena is mathematically formulated as a bifurcation and stability problem. In this talk, the compressible Taylor vortex is shown to bifurcate near the criticality for the incompressible problem when the Mach number is sufficiently small. The localized stability of the compressible Taylor vortex is considered under sufficiently small axisymmetric perturbations; and it is shown that the large time behavior of solutions around the Taylor vortex is described by solutions of a system of diffusion equations.
2022-05-26 / 16:00 ~ 17:30
학과 세미나/콜로퀴엄 - 박사논문심사: 깁스 그리고 가우시안 측도들의 해밀토니안 편미분 방정식들의 흐름에 따른 운송 성질들 인쇄
by 성기훈(KAIST)
심사위원장 : 권순식, 심사위원 : 배명진, 남경식, Yoshio Tsutsumi(Kyoto University), Mamoru Okamoto(Osaka University)
2022-05-23 / 16:30 ~ 18:00
학과 세미나/콜로퀴엄 - 계산수학 세미나: 인쇄
by 최민석()
Despite of great progress over the last decades in simulating complex problems with the numerical discretization of (stochastic) partial differential equations (PDEs), solving high-dimensional problems governed by parameterized PDEs remains challenging. Machine learning has emerged as a promising alternative in scientific computing community by enforcing the physical laws. We review some of machine learning approaches and present a novel algorithm based on variational inference to solve (stochastic) systems. Numerical examples are provided to illustrate the proposed algorithm.
2022-05-26 / 14:30 ~ 15:45
SAARC 세미나 - SAARC 세미나: 인쇄
by 김영헌(브리티시컬럼비아 대학)

2022-05-24 / 16:00 ~ 17:15
SAARC 세미나 - SAARC 세미나: 인쇄
by 김영헌(브리티시컬럼비아 대학)

2022-05-23 / 16:30 ~ 17:30
IBS-KAIST 세미나 - 이산수학: The precise diameter of reconfiguration graphs 인쇄
by Stijn Cambie(IBS 극단 조합 및 확률 그룹)

2022-05-27 / 10:00 ~ 11:00
SAARC 세미나 - SAARC 세미나: OptiDICE for Offline Reinforcement Learning 인쇄
by 김기응(한국과학기술원 AI대학원)
Offline reinforcement learning (RL) refers to the problem setting where the agent aims to optimize the policy solely from the pre-collected data without further environment interactions. In offline RL, the distributional shift becomes the primary source of difficulty, which arises from the deviation of the target policy being optimized from the behavior policy used for data collection. This typically causes overestimation of action values, which poses severe problems for model-free algorithms that use bootstrapping. To mitigate the problem, prior offline RL algorithms often used sophisticated techniques that encourage underestimation of action values, which introduces an additional set of hyperparameters that need to be tuned properly. In this talk, I present OptiDICE, an offline RL algorithm that prevents overestimation in a more principled way. OptiDICE directly estimates the stationary distribution corrections of the optimal policy and does not rely on policy-gradients, unlike previous offline RL algorithms. Using an extensive set of benchmark datasets for offline RL, OptiDICE is shown to perform competitively with the state-of-the-art methods. This is a joint work with Jongmin Lee (UC Berkeley), Wonseok Jeon (Qualcomm), Byung-Jun Lee (Korea U.), and Joelle Pineau (MILA)
2022-05-26 / 12:00 ~ 12:25
대학원생 세미나 - 대학원생 세미나: Spectrum of sparse random graphs and related problems 인쇄
by 이재훈(KAIST)
Around early 2010, there was a huge success in understanding the spectrum of large random matrices, in other words, large random graphs. It was only for large but dense random graphs at first. However, as random matrix theory has been developed, there is some progress in sparse cases. In this short talk, I will review a series of results for spectral statistics of sparse random graphs and explain their implications.
2022-05-26 / 12:25 ~ 12:50
대학원생 세미나 - 대학원생 세미나: Deriving Stationary distributions from an underlying graph structure 인쇄
by 홍혁표(KAIST)
Randomness of biochemical reactions is inherent in various biological systems, from DNA to organs and the human body. These stochastic dynamics are frequently modeled using a continuous-time Markov chain (CTMC). Its long-term behavior is described by a stationary distribution, corresponding to its deterministic counterpart called a steady state. Stationary distribution can be derived analytically only in limited systems such as linear or finite-state systems. In this talk, I will introduce a recent result by Anderson, Craciun, and Kurtz deriving stationary distribution from the underlying graph structure of a reaction network and how we can extend it. For those who are first told the word 'Mathematical Biology,' I will briefly introduce mathematical biology before going into the detailed topic.
2022-05-26 / 16:15 ~ 17:15
학과 세미나/콜로퀴엄 - 콜로퀴엄: 인쇄
by ()
Inside living cells, chemical reactions form a large web of networks and they are responsible for physiological functions. Understanding the behavior of complex reaction networks is a challenging and interesting task. In this talk, I would like to illustrate how the methods of algebraic topology can shed light on the properties of chemical reaction systems. In particular, we discuss the following two problems: (1) response of reaction systems to external perturbations and (2) simplification of complex reaction networks without altering the behavior of the system.
2022-05-25 / 17:00 ~ 18:00
IBS-KAIST 세미나 - 수리생물학: 인쇄
by ()
I will discuss the development, analysis and applications of multi-resolution methods for spatio-temporal modelling of intracellular processes, which use (detailed) Brownian dynamics or molecular dynamics simulations in localized regions of particular interest (in which accuracy and microscopic details are important) and a (less-detailed) coarser model in other regions in which accuracy may be traded for simulation efficiency. I will discuss the error analysis and convergence properties of the developed multi-resolution methods, their software implementation and applications of these multiscale methodologies to modelling of intracellular calcium dynamics, actin dynamics and DNA dynamics. I will also discuss the development of multiscale methods which couple molecular dynamics and coarser stochastic models in the same dynamic simulation.
2022-05-25 / 16:30 ~ 16:55
IBS-KAIST 세미나 - 수리생물학: 인쇄
by ()
I will introduce mathematical and computational methods for spatio-temporal modelling in molecular and cell biology, including all-atom and coarse-grained molecular dynamics (MD), Brownian dynamics (BD), stochastic reaction-diffusion models and macroscopic mean-field equations. Microscopic (BD, MD) models are based on the simulation of trajectories of individual molecules and their localized interactions (for example, reactions). Mesoscopic (lattice-based) stochastic reaction-diffusion approaches divide the computational domain into a finite number of compartments and simulate the time evolution of the numbers of molecules in each compartment, while macroscopic models are often written in terms of mean-field reaction-diffusion partial differential equations for spatially varying concentrations.
Events for the 취소된 행사 포함 모두인쇄
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