34 citations · 212 across the 40 of their papers we have counts for
5 papers · 1 filter
On the Dimension-Free Approximation of Deep Neural Networks for Symmetric Korobov Functions
Yulong Lu, Tong Mao, Jinchao Xu +1
Deep neural networks have been widely used as universal approximators for functions with inherent physical structures, including permutation symmetry. In this paper, we construct s…
Improving Data Fidelity via Diffusion Model-based Correction and Super-Resolution
Wuzhe Xu, Yulong Lu, Sifan Wang +1
We propose a unified diffusion model-based correction and super-resolution method to enhance the fidelity and resolution of diverse low-quality data through a two-step pipeline. Fi…
Convergence of Time-Averaged Mean Field Gradient Descent Dynamics for Continuous Multi-Player Zero-Sum Games
Yulong Lu, Pierre Monmarché
The approximation of mixed Nash equilibria (MNE) for zero-sum games with mean-field interacting players has recently raised much interest in machine learning. In this paper we prop…
Diffusion-based Models for Unpaired Super-resolution in Fluid Dynamics
Wuzhe Xu, Yulong Lu, Lian Shen +2
High-fidelity, high-resolution numerical simulations are crucial for studying complex multiscale phenomena in fluid dynamics, such as turbulent flows and ocean waves. However, dire…
In-Context Learning of Linear Dynamical Systems with Transformers: Approximation Bounds and Depth-Separation
Frank Cole, Yuxuan Zhao, Yulong Lu +1
This paper investigates approximation-theoretic aspects of the in-context learning capability of the transformers in representing a family of noisy linear dynamical systems. Our fi…