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Summary

Name Hyemin Gu
Research interest generative modeling, dynamical transport, gradient flows, particle transport, Wasserstein proximal regularization, entropic regularization
Languages English, Korean
Contact hgu@umass.edu

Education

  • 2020 - Present
    PhD candidate in Mathematics
    University of Massachusetts Amherst, MA, US
    • Specializing in Mathematical machine learning
    • Advised by Markos Katsoulakis
  • 2018 - 2020
    MSc in Mathematics
    Ewha Womans University, Seoul, Republic of Korea
    • Thesis "Convolutional Neural Network for 2D Flow Estimation Problem"
    • Specializing in Numerical analysis
    • Advised by June-Yub Lee
  • 2014 - 2018
    BSc in Mathematics
    Ewha Womans University, Seoul, Republic of Korea
    • Second major in Computational Science and its thesis "Low cost training of a classification Neural Network with respect to Weight Selection"
    • Minor in Statistics
    • Dean’s list 5 semesters

Academic Interests

  • dynamical transport, gradient flows, particle transport
  • Wasserstein proximal regularization, entropic regularization
  • generative modeling

Conferences

  • 2023
    Poster presentation
    Optimal Transport in Data Science, ICERM, Brown university
    • H. Gu et al., Lipschitz Regularized Gradient Flows and Latent Generative Particles
  • 2018
    Poster presentation
    Joint Mathematics Meetings, Mathematical Association of America
    • H. Gu, Training a 2 layer Neural Network using SVD-generated weights
  • 2017
    Poster presentation
    Joint Mathematics Meetings, Mathematical Association of America
    • J. Park et al., Necessary and sufficient conditions for shortest vectors in lattices of dimension 2 and 3

Projects

  • Lipschitz regularized generative particles algorithm
    • Implementation of a particle transportation algorithm through gradient flows associated with Lipschitz regularized f-divergences.
    • A generative model alternative to GANs in low training data regimes.
    • Mathematical interpretation of applying spectral normalization on neural network discriminators as a particle transportation speed regularization.
  • Wasserstein-1/Wasserstein-2 proximal generative flow
    • Formulated and implemented a generative model with continuous-time adversarial flow architecture for learning distributions that are supported on low-dimensional manifolds.
    • Our formulation is analyzed via Mean Field Game theory and ensures good properties of the learned flow such as uniqueness of solution and optimal (linear) paths.

Training

  • 2018
    Industrial Mathematics Academy
    National Institute for Mathematical Sciences, South Korea
    • Presented a final result of a group project for solving industrial problem
    • Proposed a Convolutional Neural Network for classifying infected individual from images
    • Coordinated team efforts for the group project
    • Attended tutorials on Python data analysis and Keras, lectures on matrix based data analysis, linear programming theory and practice
  • 2017
    Industrial Mathematics Academy
    National Institute for Mathematical Sciences, South Korea
    • Proposed a model for assessing safe driving scores from Onboard diagnostic data based on Poisson process
    • Attended tutorials on basics to neural networks

Teaching Experience

  • 2021
    Graduate teaching assistant
    University of Massachusetts - Amherst, Amherst, MA, US
    • (MATH532H) Nonlinear dynamics and chaos with applications; graded assignments and conducted tutorial sessions for Python ODE solving
    • (MATH545) Linear algebra for applied mathematics; graded assignments, conducted discussion sessions and arranged offie hours
    • (MATH235) Linear algebra, (MATH545) Linear algebra for applied mathematics; graded assignments
  • 2018 - 2019
    Graduate teaching assistant
    Ewha Womans University, Seoul, Korea
    • Numerical differential equations (numerics for ODE/PDE, Monte-Carlo, optimization); graded assignments and arranged office hours
    • Finite mathematics and programming (Matlab programming, mathematical logic, combinatorics); graded assignments and arranged office hours
    • Calculus 2 (multivariate calculus); graded assignments and arranged office hours
    • Numerical analysis (linear system solving, power method, numerical integration/differentiation); graded assignments and arranged office hours

Work Experience

  • 2020
    Statistics specialist
    Ewha Womans University Seoul Hospital, Seoul, Korea
    • Developed a pipeline for acquiring, analyzing, and visualizing gene expression data from open repositories using R; authored a tutorial book on the process
    • Conducted training sessions on statistical analysis using R for colleagues

Leadership

  • 2022 - Present
    Department seminar organizer
    Department of Mathematics and Statistics, University of Massachusetts Amherst, MA, USA
    • Invited speakers among faculties in the department for introducing their research interests to early career graduate students and hosted talks
    • Participated in regular Graduate Student Advisory Committees meetings, reported the progress, and discussed future directions

Honors and Awards

  • 2024
    Mathematics and statistics department in University of Massachusetts Amherst
    • Anne and Peter Costa Graduate Prize in Applied Mathematics