My research is partially supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. RS-2023-00252516 and No. RS-2024-00408003) and the POSCO Science Fellowship of POSCO TJ Park Foundation. I consider myself very fortunate to have worked with the collaborators on the various exciting projects we've undertaken together.
2025
Area-Preserving Anisotropic Mean Curvature Flow in Two Dimensions (with Eric Kim), Calculus of Variations and Partial Differential Equations. 64, 27, 2025. [arXiv]
2024
Maximum Entropy Inverse Reinforcement Learning of Diffusion Models with Energy-Based Models (with Sangwoong Yoon, Himchan Hwang, Yung-Kyun Noh, and Frank C Park), Advances in Neural Information Processing Systems 37 (NeurIPS 2024, Oral) [arXiv] [Media]
On the Complexity of First-Order Methods in Stochastic Bilevel Optimization (with Jeongyeol Kwon and Hanbaek Lyu), The 41st International Conference on Machine Learning (ICML 2024) [arXiv]
Memorization Capacity for Additive Fine-Tuning with Small ReLu Networks (with Jy-yong Sohn, Seoyeon An, Kangwook Lee), The 40th Conference on Uncertainty in Artificial Intelligence (UAI 2024) [arXiv] [Openreview]
On Penalty Methods for Nonconvex Bilevel Optimization and First-Order Stochastic Approximation (with Jeongyeol Kwon, Stephen Wright, and Robert Nowak), The Twelfth International Conference on Learning Representations, (ICLR 2024, Spotlight) [arXiv]
The Regularity with Respect to Domains of the Additive Eigenvalues of Superquadratic Hamilton-Jacobi Equation and Related Vanishing Discount Problems (with Farid Bozorgnia and Son N.T. Tu), Journal of Differential Equations, 402: 518-553, 2024 [arXiv]
Cucker-Smale Type Flocking Models on a Sphere (with Sun-Ho Choi and Hyowon Seo), Journal of Mathematical Physics, 65 (4): 042701, 2024 [arXiv]
Target Tracking Systems on a Sphere With Topographic Information (with Sun-Ho Choi, Hyowon Seo, and Soyeong Jeong), IEEE Transactions on Cybernetics, 54(5): 2901-2913, 2024
2023
Complexity of Block Coordinate Descent With Proximal Regularization and Applications to Wasserstein Cp-Dictionary Learning (with Hanbaek Lyu), The 40th International Conference on Machine Learning (ICML 2023) [arXiv]
A Fully First-Order Method for Stochastic Bilevel Optimization (with Jeongyeol Kwon, Stephen Wright, and Robert Nowak), The 40th International Conference on Machine Learning (ICML 2023, Oral) [arXiv]
Multi-Agent System for Target Tracking on a Sphere and Its Asymptotic Behavior (with Sun-Ho Choi and Hyowon Seo), Communications in Nonlinear Science and Numerical Simulation, 117, 106967, 2023 [arXiv]
2022
Level-Set Forced Mean Curvature Flow With the Neumann Boundary Condition (with Jiwoong Jang, Hiroyoshi Mitake, and Hung Vinh Tran), Journal de Mathématiques Pures et Appliquées, 168:143-167, 2022 [arXiv] [Video] [Slides]
On Volume-Preserving Crystalline Mean Curvature Flow (with Inwon Kim and Norbert Požár). Mathematische Annalen, 384(1), 1-42, 2022 [arXiv] [Slides 2021 version] [Slides 2023 version]
Score-Based Generative Modeling Secretly Minimizes the Wasserstein Distance (with Kangwook Lee and Ying Fan), Advances in Neural Information Processing Systems 35 (NeurIPS 2022) [arXiv] [Short Video] [Long Video (Korean)]
2021
Degenerate Nonlinear Parabolic Equations With Discontinuous Diffusion Coefficients (with Alpár Richárd Mészáros), Journal of the London Mathematical Society, 104(2), 688-746, 2021 [arXiv] [Slides]
2020
Volume Preserving Mean Curvature Flow for Star-Shaped Sets (with Inwon Kim). Calculus of Variations and Partial Differential Equations, 59(2), 2020 [arXiv] [Slides]
On Mean Curvature Flow with Forcing (with Inwon Kim). Communications in Partial Differential Equations. 45(5):414-455, 2020 [arXiv]
2018
Dispersal Toward Food: A Study of a Singular Limit of an Allen-Cahn Equation (with Danielle Hilhorst, Yong Jung Kim, and Thanh Nam Nguyen). Journal of Mathematical Biology, 76(3):531-565, 2018
Preprints
Training Wasserstein GANs Without Gradient Penalties (with Guido Montúfar, Yeoneung Kim, and Insoon Yang) [Slides] [Video1] [Video2]
Flocking Formation and Stabilizer of Boosted Cooperative Control on a Sphere (with Sun-Ho Choi and Hyowon Seo)
Uniform Position Alignment Estimate of Spherical Flocking Model With Inter-Particle Bonding Forces (with Sun-Ho Choi and Hyowon Seo)
Thesis
Mean Curvature Flows with Forcing and Degenerate Nonlinear Parabolic Equations. Dissertation, UCLA, 2020