From the 1 of 5 linked papers with an AI index.
5 papers
Neural Network Approximation of Solutions to Fractional Parabolic Partial Differential Equations
Jae-Hwan Choi, Hyojae Lim, Jinsol Seo +2
The paper develops a dimension‑efficient neural network approximation theory for solutions of fractional parabolic PDEs, introducing anisotropic spectral Barron spaces and proving…
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…
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…
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…