4 papers
When Rough Data Helps: A Phase Transition in Convergence Rates for Kernel Recovery in Integral Operators
Jihong Wang, Fei Lu, Yue Yu
Learning kernels in operators from data is a fundamental task that arises in nonlocal continuum mechanics, operator learning, and interacting particle systems. A central question i…
Learning Lévy density via adaptive RKHS regression with bi-level optimization
Luxuan Yang, Fei Lu, Ting Gao +2
We propose a nonparametric method to learn the Lévy density from probability density data governed by a nonlocal Fokker-Planck equation. We recast the problem as identifying the k…
Transformer learns the cross-task prior and regularization for in-context learning
Fei Lu, Yue Yu
Transformers have shown a remarkable ability for in-context learning (ICL), making predictions based on contextual examples. However, while theoretical analyses have explored this…
Robust First and Second-Order Differentiation for Regularized Optimal Transport
Xingjie Li, Fei Lu, Molei Tao +1
Applications such as unbalanced and fully shuffled regression can be approached by optimizing regularized optimal transport (OT) distances, such as the entropic OT and Sinkhorn dis…