유튜브 스트리밍 예정입니다.

1. 일시: 2024년 10월 30일(수), 14:00-16:00

2. 장소: 판교 테크노밸리 산업수학혁신센터 세미나실

   • 경기 성남시 수정구 대왕판교로 815, 기업지원허브 231호 국가수리과학연구소
   • 무료주차는 2시간 지원됩니다.

3. 발표자: 신선영 교수(포항공대)

4. 주요내용: Clustered hidden Markov models

We consider cases where a hidden Markov model (HMM) has so many distinct states that its state space needs a simpler structure. A novel framework we develop, named the clustered hidden Markov model (CHMM), decomposes the state space into sets of clustered states, by adding a hidden process to the HMM. The CHMM consists of two hidden processes and an observable process, where the first hidden process is a Markov process with clustered state representations and the second hidden process has the original state space. The second hidden process is second-order dependent on the first hidden process; that is, the current state of the second hidden process is dependent on the current and previous states of the first hidden process. The CHMM is a new approach to designing the structure of the hidden states while maintaining the information in the HMM. We derive two hidden Markov submodels from the CHMM. The first hidden process and the observable process of the CHMM form a hidden Markov model with additional dependencies while the second hidden process and the observable process of the CHMM form a classical hidden Markov model. A novel finding is that the hidden states corresponding to a clustered state share the same transition probabilities, which are represented as the identical transition matrix rows of the second hidden Markov model. The identical row structure of the transition matrix motivates us to consider the penalization method for learning the CHMM, simultaneously recovering the clustered state space. The penalized estimation maximizes the likelihood regularized by group smooth clipped absolute deviation (SCAD) penalty to all pairwise differences of the transition matrix rows. We establish the asymptotic properties of the penalized estimator. Simulation studies support the outperformance of our proposed method. Its application to protein structure sequence data demonstrates that the CHMM simplifies the classification of protein segments, and consequently improves interpretability.

유튜브 스트리밍 예정입니다.

1. 일시: 2024년 10월 29일(화), 10:30-12:30

2. 장소: 판교 테크노밸리 산업수학혁신센터 세미나실

   • 경기 성남시 수정구 대왕판교로 815, 기업지원허브 231호 국가수리과학연구소
   • 무료주차는 2시간 지원됩니다.

3. 발표자: 김혜현 교수(경희대학교)

4. 주요내용: Partitioned neural networks for partial differential equations

In this talk, I will give a brief introduction to neural network approximation to partial differential equations (PDEs). To deal with error and performance issues in the neural network approximation, partitioned neural networks (PNNs) can be used as a solution surrogate. PNNs are formed based on the partition of the problem domain and each network in PNNs approximates the PDE solution in each small subdomain. The use of PNNs allows more flexible local network and hyperparameter settings, and more efficient parameter training by parallel computation. In the second part of my talk, I will present iterative algorithms for PNNs, that can utilize the partitioned network structure for the parallel computation. Numerical results will be presented for test examples to show the performance and scalability of the proposed iterative algorithms.

1. 일시: 2024년 8월 29일(목), 14:30-17:30

2. 장소: 판교 테크노밸리 산업수학혁신센터 세미나실

   • 경기 성남시 수정구 대왕판교로 815, 기업지원허브 231호 국가수리과학연구소
   • 무료주차는 2시간 지원됩니다.

3. 14:30-16:00

   • 발표자: 서효원 교수(국립군산대학교)
   • 주제: Multi-agent system on a sphere
   • 초록: As technology advances, multi-agent systems operating throughout the entire Earth’s surface have become feasible. We are concerned with a multi-agent system, which contains centripetal force, inter-particle bonding force, and velocity-alignment operator. In particular, we employ a regularized rotation operator to overcome the singularity problem at antipodal points. In this talk, we introduce several control laws for given tasks, such as target tracking or formation. Using these control laws, we observe the asymptotic behavior of agents: complete or practical synchronization. Our numerical simulations show that it is applicable to reality. The presented results come from a series of work with S.-H. Choi and D. Kwon.

4. 16:00 – 17:30

   • 발표자: 최선호 교수(경희대학교)
   • 주제: MULTI-AGENT SYSTEMS USING BEARING ANGLES AND ANCHOR POINTS
   • 초록: We propose a bearing-based control law for double-integrator multi-agent systems. The objective is that each agent converges towards a predefined point. Since bearing angles alone cannot determine a unique formation, at least three anchor points are required. The leader agents are those converging towards these anchor points. These leader agents have access to the location information of the anchor points, their own location information, and the bearing angles of surrounding agents. We assume that all other agents can only collect bearing angle information from neighboring agents. Like most bearing-based models, our model includes singularities, preventing the use of LaSalle’s invariance principle. To overcome this, we introduce a new energy functional. Using this energy functional and Barbalat’s lemma, we prove that all global solutions of this equation converge to the specified formation.

현장 강의만 진행될 예정입니다.

1. 일시: 2024년 8월 26일(월), 14:00-16:00

2. 장소: 판교 테크노밸리 산업수학혁신센터 세미나실

   • 경기 성남시 수정구 대왕판교로 815, 기업지원허브 231호 국가수리과학연구소
   • 무료주차는 2시간 지원됩니다.

3. 발표자: 김미란 교수(한양대학교)

4. 주요내용: Homomorphic encryption

Homomorphic encryption is an encryption method to allow arbitrary computation on encrypted data without decryption. It has emerged as one of the promising solutions to address privacy and security issues in outsourcing computation on sensitive data. In this talk, I will introduce recent development and progress on homomorphic encryption. In particular, I will introduce a homomorphic encryption cryptosystem that enables approximate computation over encryption, which has shown remarkable performance in artificial intelligence. I will then summarize the state-of-art benchmarks of the encryption systems in real-world applications such as machine learning and biomedical study.

유튜브 스트리밍 예정입니다.

1. 일시: 2024년 8월 21일(수), 10:30-12:30

2. 장소: 판교 테크노밸리 산업수학혁신센터 세미나실

   • 경기 성남시 수정구 대왕판교로 815, 기업지원허브 231호 국가수리과학연구소
   • 무료주차는 2시간 지원됩니다.

3. 발표자: 박예찬 박사(고등과학원)

4. 주요내용: Understanding and Acceleration of Grokking Phenomena in Learning Arithmetic Operations via Kolmogorov-Arnold Representation

We propose novel methodologies aimed at accelerating the grokking phenomenon, which refers to the rapid increment of test accuracy after a long period of overfitting as reported in~\cite{power2022grokking}. Focusing on the grokking phenomenon that arises in learning arithmetic binary operations via the transformer model, we begin with a discussion on data augmentation in the case of commutative binary operations. To further accelerate, we elucidate arithmetic operations through the lens of the Kolmogorov-Arnold (KA) representation theorem, revealing its correspondence to the transformer architecture: embedding, decoder block, and classifier. Observing the shared structure between KA representations associated with binary operations, we suggest various transfer learning mechanisms that expedite grokking. This interpretation is substantiated through a series of rigorous experiments. In addition, our approach is successful in learning two nonstandard arithmetic tasks: composition of operations and a system of equations. Furthermore, we reveal that the model is capable of learning arithmetic operations using a limited number of tokens under embedding transfer, which is supported by a set of experiments as well.

유튜브 스트리밍 예정입니다.

1. 일시: 2024년 7월 8일(월), 15:00-17:00

2. 장소: 판교 테크노밸리 산업수학혁신센터 세미나실

   • 경기 성남시 수정구 대왕판교로 815, 기업지원허브 231호 국가수리과학연구소
   • 무료주차는 2시간 지원됩니다.

3. 발표자: 김형지 교수(Trinity University)

4. 주요내용: Forecasting Agricultural Futures Contracts with Econometric Factors and Stochastic Differential Equations

In this talk, we will begin by exploring the fundamentals of probabilistic modeling using stochastic differential equations (SDEs). We will then examine how SDEs, in conjunction with econometric models, can be employed to forecast the prices of futures contracts for agricultural commodities, such as corn. Our approach models price fluctuations in these contracts using an autoregressive moving average (ARMA) model with Fourier terms, integrated with stochastic processes to capture the Samuelson effect. To achieve this, we introduce an additional volatility term that varies with time-to-execution, which is explained through the Ornstein-Uhlenbeck (OU) process, also known as the mean-reversion process. As we delve into more advanced topics, we will discuss quantitative functional inequalities for specific classes of SDEs with degenerate noise, known as hypoelliptic SDEs. These include the reverse log-Sobolev inequality and Wang-type Harnack inequality, which provide deeper insights into the solutions of SDEs.

유튜브 스트리밍 예정입니다.

1. 일시: 2024년 7월 4일(목), 14:00-16:00

2. 장소: 판교 테크노밸리 산업수학혁신센터 세미나실

   • 경기 성남시 수정구 대왕판교로 815, 기업지원허브 231호 국가수리과학연구소
   • 무료주차는 2시간 지원됩니다.

3. 발표자: 이재용 교수 (중앙대학교)

4. 주요내용: Two approaches using Deep Learning to solve partial differential equations

Many differential equations and partial differential equations (PDEs) are being studied to model physical phenomena in nature with mathematical expressions. Recently, new numerical approaches using machine learning and deep learning have been actively studied. There are two mainstream deep learning approaches to approximate solutions to the PDEs, i.e., using neural networks directly to parametrize the solution to the PDE and learning operators from the parameters of the PDEs to their solutions. As the first direction, Physics-Informed Neural Network was introduced in (Raissi, Perdikaris, and Karniadakis 2019), which learns the neural network parameters to minimize the PDE residuals in the least-squares sense. On the other side, operator learning using neural networks has been studied to approximate a PDE solution operator, which is nonlinear and complex in general. In this talk, I will introduce these two ways to approximate the solution of PDE and my research related to them.

유튜브 스트리밍 예정입니다.

1. 일시: 2024년 7월 3일(수), 10:30-12:30

2. 장소: 판교 테크노밸리 산업수학혁신센터 세미나실

   • 경기 성남시 수정구 대왕판교로 815, 기업지원허브 231호 국가수리과학연구소
   • 무료주차는 2시간 지원됩니다.

3. 발표자: 이성윤 교수(한양대학교)

4. 주요내용: How Large Models Learn?

For years, large models (trained with deep learning algorithms) have been able to “survive” in the competitive and wild “nature”. But how? How could large models have been “selected” by practitioners? Is it because of the architecture of the neural networks or the gradient-based optimization? In this talk, we try to answer these questions.

유튜브 스트리밍 예정입니다.

We present a maximum entropy inverse reinforcement learning (IRL) approach for improving the sample quality of diffusion generative models, especially when the number of generation time steps is small. As IRL trains a policy using the reward function learned from expert demonstrations, we train (or fine-tune) a diffusion model using the log probability density estimated from training data. Since we employ an energy-based model (EBM) to represent the log density, our approach boils down to the joint training of a diffusion model and an EBM. Our IRL formulation, named Generalized Contrastive Divergence (GCD), is a minimax problem that reaches equilibrium when both models converge to the data distribution. The entropy maximization plays a key role in GCD, facilitating the exploration of the diffusion model and ensuring the convergence of the EBM. We also propose Diffusion by Dynamic Programming (DiDP), a novel RL approach for diffusion models, as a subroutine in GCD. DiDP makes the diffusion model update in GCD efficient by transforming the original problem into an optimal control formulation where value functions replace back-propagation in time. Our empirical studies show that diffusion models fine-tuned using GCD and DiDP can generate high-quality samples with fewer steps. Additionally, GCD-DiDP enables the training of an EBM without MCMC, stabilizing EBM training dynamics and enhancing outlier detection performance.

유튜브 스트리밍 예정입니다.

정보 이론의 주요 관심사 중 하나는 통신 과정에서 오류가 발생할 확률을 최소화하는 것이다. 예를 들어 PCR 검사 결과 음성일 경우 0으로 코드화하고 양성일 경우 1로 코드화한다고 하였을 때, 이 중요한 정보가 통신 상황에서 오류가 발생하여 0이 1로 잘못 전달되거나 1이 0으로 잘못 전달되는 경우가 발생할 수 있다. 만약 오류 발생 확률이 10%라면 적절한 방법을 동원하여 오류 발생 확률을 3% 혹은 1% 등으로 줄이기 위해 노력하는 것이 자연스럽다. 강연 전반부의 목표는 주어진 자원의 어느 정도를 오류 정정에 사용하는 것이 가장 효율적일지를 다루는 샤논 채널 코딩 정리의 의미를 이해하는 것이다. 그리고 강연 후반부의 목표는 최근 큰 주목을 받고 있는 양자 정보 이론 분야에서 2000년대 초반 확립된 코딩 정리의 의미를 파악하고, 이와 관련한 수학적 난제를 소개하는 것이다.

유튜브 스트리밍 예정입니다.