arXiv subjects

Minyoung Jeong

Publications and source records attributed to Minyoung Jeong.

4 recordsLinked to original sources

arXiv2026

Non-conical classical solutions to the one-phase free boundary problem with an isolated singularity

Several examples of one-homogeneous classical solutions to the one-phase free boundary problem with an isolated free boundary singularity are known. Adapting the approach of Caffarelli, Hardt, and Simon for minimal surfaces, we construct non-conical classical solutions with an isolated free boundary singularity by perturbing a one-homogeneous solution $U$. Moreover, if $U$ is strictly stable (respectively, non-degenerate), then any solution sufficiently close to $U$ is also strictly stable (respectively, non-degenerate).

math.AP↗

arXiv2026

Regularity of Weak Solutions near Singular Minimizing Cones for the One-Phase Free Boundary Problem

Alt and Caffarelli proved an Allard-type $ε$-regularity theorem near the flat one-homogeneous minimizer of the one-phase free boundary problem. A natural follow-up question is whether an analogous regularity result holds near singular minimizing cones. In this paper, we prove such an $ε$-regularity theorem near a strongly integrable one-phase minimizing cone with an isolated singularity. More precisely, we show that, after a suitable translation and rotation, the free boundary of any non-degenerate weak solution sufficiently close to the cone is graphical over the free boundary of a leaf of the De Silva--Jerison--Shahgholian foliation. This result is analogous to recent $ε$-regularity theorems in minimal surface theory by Edelen and by Edelen--Spolaor; our proof adapts the strategy of Edelen to the one-phase setting.

math.AP↗

arXiv2021

What Changes Can Large-scale Language Models Bring? Intensive Study on HyperCLOVA: Billions-scale Korean Generative Pretrained Transformers

GPT-3 shows remarkable in-context learning ability of large-scale language models (LMs) trained on hundreds of billion scale data. Here we address some remaining issues less reported by the GPT-3 paper, such as a non-English LM, the performances of different sized models, and the effect of recently introduced prompt optimization on in-context learning. To achieve this, we introduce HyperCLOVA, a Korean variant of 82B GPT-3 trained on a Korean-centric corpus of 560B tokens. Enhanced by our Korean-specific tokenization, HyperCLOVA with our training configuration shows state-of-the-art in-context zero-shot and few-shot learning performances on various downstream tasks in Korean. Also, we show the performance benefits of prompt-based learning and demonstrate how it can be integrated into the prompt engineering pipeline. Then we discuss the possibility of materializing the No Code AI paradigm by providing AI prototyping capabilities to non-experts of ML by introducing HyperCLOVA studio, an interactive prompt engineering interface. Lastly, we demonstrate the potential of our methods with three successful in-house applications.

cs.CL↗

arXiv2020

CareCall: a Call-Based Active Monitoring Dialog Agent for Managing COVID-19 Pandemic

Tracking suspected cases of COVID-19 is crucial to suppressing the spread of COVID-19 pandemic. Active monitoring and proactive inspection are indispensable to mitigate COVID-19 spread, though these require considerable social and economic expense. To address this issue, we introduce CareCall, a call-based dialog agent which is deployed for active monitoring in Korea and Japan. We describe our system with a case study with statistics to show how the system works. Finally, we discuss a simple idea which uses CareCall to support proactive inspection.

cs.HC↗