3 papers
stat.ML2026
Preconditioned One-Step Generative Modeling for Bayesian Inverse Problems in Function Spaces
Zilan Cheng, Li-Lian Wang, Zhongjian Wang
We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime. Based on one-step generative transport, the method learns an amortized neural op…
math.NA2026
Explicit Construction of Approximate Kolmogorov Superpositions with C2 Smoothness
Lunji Song, Zilan Cheng, Juan Diego Toscano +1
We explicitly construct an approximate version of the Kolmogorov superpositions, which is composed of C2-inner and outer functions, and can approximate an arbitrary alpha Holder co…
cs.LG2024
KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics
Juan Diego Toscano, Li-Lian Wang, George Em Karniadakis
Inspired by the Kolmogorov-Arnold representation theorem and Kurkova's principle of using approximate representations, we propose the Kurkova-Kolmogorov-Arnold Network (KKAN), a ne…