Speaker: 王立联教授，南洋理工大学

Inviter: 于海军(AMSS,研究员), 翟佳羽(上海科技大学), 廖奇峰(上海科技大学)

Title: Kolmogorov Superpositions: Construction, Approximation and Neural Networks

Language: Chinese

Time & Venue: 2026.10.26 14:00-15:00 腾讯会议：602-613-835

Abstract: The Kolmogorov Superposition Theorem (KST, 1957), offers a mathematically elegant framework for expressing any high-dimensional continuous function as a superposition of lower-or one-dimensional continuous functions. This foundational theorem has recently gained renewed interest, particularly in neural networks. However, a major challenge remains: the one-dimensional functions resulting from all constructions are highly non-smooth. In this talk, we present a novel approximate version of Kolmogorov superpositions involving C2 inner functions and piecewise C2 outer functions and show its applications in neural network approximations. This talk will be based on joint works with L. Song (Lanzhou University), Z. Chen & Z. Wang (NTU), and J. Toscane & G. Karniadakis (Brown University).