欢迎大家参与11月17日（星期二）的午餐会。报告时间是12:15-13:00，午餐于12:00开始提供。
应用数学青年讨论班(午餐会)--Sharp Sobolev Approximation by Linearized Shallow Networks with Analytic Activations
报告人: 李佳（北京大学）
时间: 2026-11-17 12:15-13:00
地点: 智华楼-四元厅-225
摘要：Shallow neural networks with fixed inner parameters are linear in their output coefficients, reducing training to a convex optimization problem. This makes them attractive for numerical approximation and scientific computing. A natural question is whether fixing the inner parameters compromises their approximation power. Recent work by Liu, Mao, and Xu shows that optimal Sobolev approximation rates can still be achieved for ReLU^k activations.
Motivated by this work, we investigate linearized shallow networks with real-analytic activations on the sphere and general bounded domains. Under suitable assumptions, we prove that suitably distributed inner parameters can be fixed independently of the target function, while still achieving optimal Sobolev approximation rates. For analytic targets, sub-exponential convergence rates can be obtained. Our results cover a broad class of real-analytic activations, including tanh, the logistic sigmoid, arctan, and certain rational functions.
报告人简介：李佳，北京大学数学科学学院2025级博士生，导师是吴朔男老师，主要研究兴趣是偏微分方程数值解与神经网络逼近理论。
