6 papers
Fractional Parabolic Partial Differential Equations in Anisotropic Spectral Barron Spaces: Regularity and Neural Approximation
Jae-Hwan Choi, Hyojae Lim, Jinsol Seo +2
We study fractional parabolic initial-value problems with lower-order drift and potential terms in anisotropic spectral Barron spaces, defined by weighted space--time Fourier …
Lean-GAP: A Dataset of Formalized Graduate Algebra Problems
Seewoo Lee, Byung-Hak Hwang, Hyojae Lim +10
We present Lean-GAP (Lean-Graduate Agebra Problems), 430 formalized graduate-level algebra problems from the textbook Abstract Algebra by Dummit and Foote. We develop a scalable pi…
Provable wavelet-based neural approximation
Youngmi Hur, Hyojae Lim, Mikyoung Lim
In this paper, we develop a wavelet-based theoretical framework for analyzing the universal approximation capabilities of neural networks over a wide range of activation functions.…
Simplifying Formal Proof-Generating Models with ChatGPT and Basic Searching Techniques
Sangjun Han, Taeil Hur, Youngmi Hur +3
The challenge of formal proof generation has a rich history, but with modern techniques, we may finally be at the stage of making actual progress in real-life mathematical problems…
New Tight Wavelet Frame Constructions Sharing Responsibility
Youngmi Hur, Hyojae Lim
Tight wavelet frames (TWFs) in \(L^2(\mathbb{R}^n)\) are versatile, and are practically useful due to their perfect reconstruction property. Nevertheless, existing TWF construction…
Wavelet series expansion in Hardy spaces with approximate duals
Youngmi Hur, Hyojae Lim
In this paper, we provide sufficient conditions for the functions and to be the approximate duals in the Hardy space for all . Based on these co…