# 학과 세미나 및 콜로퀴엄

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산업경영학동(E2) Room 2216
응용 및 계산수학 세미나
길이만 (성균관대)
A New Direction of Probability Model Based Machine Learning

산업경영학동(E2) Room 2216

응용 및 계산수학 세미나

This talk presents new methods of solving machine learning problems using probability models. For classification problems, the classifier referred to as the class probability output network (CPON) which can provide accurate posterior probabilities for the soft classification decision, is proposed. In this model, the uncertainty of decision is defined using the accuracy of estimation. The deep structure of CPON is also presented to obtain the best classification performance for the given data. Applications of CPON models are also addressed.

(Online participation) Zoom Link: https://kaist.zoom.us/j/87516570701

(Online participation) Zoom Link: https://kaist.zoom.us/j/87516570701

While deep learning has many remarkable success stories, finding a satisfactory mathematical explanation on why it is so effective is still considered an open challenge. One recent promising direction for this challenge is to analyse the mathematical properties of neural networks in the limit where the widths of hidden layers of the networks go to infinity. Researchers were able to prove highly-nontrivial properties of such infinitely-wide neural networks, such as the gradient-based training achieving the zero training error (so that it finds a global optimum), and the typical random initialisation of those infinitely-wide networks making them so called Gaussian processes, which are well-studied random objects in machine learning, statistics, and probability theory. These theoretical findings also led to new algorithms based on so-called kernels, which sometimes outperform existing kernel-based algorithms.
The purpose of this talk is to explain these recent theoretical results on infinitely wide neural networks. If time permits, I will briefly describe my work in this domain, which aims at developing a new neural-network architecture that has multiple nice theoretical properties in the infinite-width limit. This work is jointly pursued with Fadhel Ayed, Francois Caron, Paul Jung, Hoil Lee, and Juho Lee.

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Zoom (https://kaist.zoom.us/j/89977002928)
응용 및 계산수학 세미나
Guannan Zhang (Oak Ridge National Lab)
A Nonlocal Gradient for High-Dimensional Black-Box Optimization in Scientific Applications

Zoom (https://kaist.zoom.us/j/89977002928)

응용 및 계산수학 세미나

In this talk, we consider the problem of minimizing multi-modal loss functions with a large number of local optima. Since the local gradient points to the direction of the steepest slope in an infinitesimal neighborhood, an optimizer guided by the local gradient is often trapped in a local minimum. To address this issue, we develop a novel nonlocal gradient to skip small local minima by capturing major structures of the loss's landscape in black-box optimization. The nonlocal gradient is defined by a directional Gaussian smoothing (DGS) approach. The key idea is to conducts 1D long-range exploration with a large smoothing radius along orthogonal directions, each of which defines a nonlocal directional derivative as a 1D integral. Such long-range exploration enables the nonlocal gradient to skip small local minima. We use the Gauss-Hermite quadrature rule to approximate the d 1D integrals to obtain an accurate estimator. We also provide theoretical analysis on the convergence of the method on nonconvex landscape. In this work, we investigate the scenario where the objective function is composed of a convex function, perturbed by a highly oscillating, deterministic noise. We provide a convergence theory under which the iterates converge to a tightened neighborhood of the solution, whose size is characterized by the noise frequency. Furthermore, if the noise level decays to zero when approaching global minimum, we prove that the DGS optimization converges to the exact global minimum with linear rates, similarly to standard gradient-based method in optimizing convex functions. We complement our theoretical analysis with numerical experiments to illustrate the performance of this approach.

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산업경영학동(E2) Room 2216
응용 및 계산수학 세미나
정재훈 (포항공대 (POSTECH) 수학과)
Topological data analysis of time-series data

산업경영학동(E2) Room 2216

응용 및 계산수학 세미나

Time-series data analysis is found in various applications that deal
with sequential data over the given interval of, e.g. time. In this talk, we
discuss time-series data analysis based on topological data analysis (TDA). The commonly used TDA method for time-series data analysis utilizes the embedding techniques such as sliding window embedding. With sliding window embedding the given data points are translated into the point cloud in the embedding space and the method of persistent homology is applied to the obtained point cloud. In this talk, we first show some examples of time-series data analysis with TDA. The first example is from music data for which the dynamic processes in time is summarized by low dimensional representation based on persistence homology. The
second is the example of the gravitational wave detection problem and we will discuss how we concatenate the real signal and topological features. Then we will introduce our recent work of exact and fast multi-parameter persistent homology (EMPH) theory. The EMPH method is based on the Fourier transform of the data and the exact persistent barcodes. The EMPH is highly advantageous for time-series data analysis in that its computational complexity is as low as O(N log N) and it provides various topological inferences almost in no time. The presented works are in collaboration with Mai Lan Tran, Chris Bresten and Keunsu Kim.

(Online participation) Zoom Link: https://kaist.zoom.us/j/87516570701

(Online participation) Zoom Link: https://kaist.zoom.us/j/87516570701

Tree decompositions are a powerful tool in both structural
graph theory and graph algorithms. Many hard problems become tractable if
the input graph is known to have a tree decomposition of bounded
“width”. Exhibiting a particular kind of a tree decomposition is also
a useful way to describe the structure of a graph.
Tree decompositions have traditionally been used in the context of
forbidden graph minors; bringing them into the realm of forbidden
induced subgraphs has until recently remained out of reach. Over the last
couple of years we have made significant progress in this direction, exploring
both the classical notion of bounded tree-width, and concepts of more
structural flavor. This talk will survey some of these ideas and
results.

We present a framework of predictive modeling of unknown system from measurement data. The method is designed to discover/approximate the unknown evolution operator, i.e., flow map, behind the data. Deep neural network (DNN) is employed to construct such an approximation. Once an accurate DNN model for the evolution operator is constructed, it serves as a predictive model for the unknown system and enables us to conduct system
analysis. We demonstrate that flow map learning (FML) approach is applicable for modeling a wide class of problems, including dynamical systems, systems with missing variables and hidden parameters, as well as partial differential equations (PDEs).

KAI-X Distinguished Lecture Series

KAI-X Distinguished Lecture Series

Collective cell movement is critical to the emergent properties of many multicellular systems including microbial self-organization in biofilms, wound healing, and cancer metastasis. However, even the best-studied systems lack a complete picture of how diverse physical and chemical cues act upon individual cells to ensure coordinated multicellular behavior. Myxococcus xanthus is a model bacteria famous for its coordinated multicellular behavior resulting in dynamic patterns formation. For example, when starving millions of cells coordinate their movement to organize into fruiting bodies – aggregates containing tens of thousands of bacteria. Relating these complex self-organization patterns to the behavior of individual cells is a complex-reverse engineering problem that cannot be solved solely by experimental research. In collaboration with experimental colleagues, we use a combination of quantitative microscopy, image processing, agent-based modeling, and kinetic theory PDEs to uncover the mechanisms of emergent collective behaviors.

Professor of Bioengineering & BioSciences, Associate Chair of Bioengineering, Rice U

Professor of Bioengineering & BioSciences, Associate Chair of Bioengineering, Rice U

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창의학습관(E11) Room 210
기타
Moon-Jin Kang (Department of Mathematical Sciences)
Well-Posedness of Compressible Euler System, and Its Applications

창의학습관(E11) Room 210

기타

Compressible Euler system (CE) is a well-known PDE model that was formulated in the 19th century for dynamics of compressible fluid. The most important feature of CE is the finite-time breakdown of smooth solutions, especially, the formation of shock wave as severe singularity. Therefore, a fundamental question (since Riemann 1858) is on what happens after a shock occurs. This is the problem on well-posedness (that is, existence, uniqueness, stability) of CE in a suitable class of solutions. We will discuss on the well-posedness problem, and its generalization for applications to other PDE models arising in various contexts such as magnetohydrodynamics, tumor angiogenesis, vehicular traffic flow, etc.

첫수융합포럼 The First Wednesday Multidisciplinary Forum, May 2023 with School of Business and Technology Management ZOOM Link: https://kaist.zoom.us/j/84028206160?pwd=VzNPRGxSR2hRcnJTNk4rMHQ4Z1hiQT09

첫수융합포럼 The First Wednesday Multidisciplinary Forum, May 2023 with School of Business and Technology Management ZOOM Link: https://kaist.zoom.us/j/84028206160?pwd=VzNPRGxSR2hRcnJTNk4rMHQ4Z1hiQT09