Shenzhen University School of Mathematical Sciences
Liyuan Scholars Colloquium Session 167
Title: Momentum Stability and Adaptive Control in Stochastic Reconfiguration
Speaker: Professor Xin Liu (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
Time: 10:00–11:00, May 14, 2026
Location: Room 4, Huixing Building, Yuehai Campus, Shenzhen University
Abstract: Variational Monte Carlo (VMC) combined with expressive neural network wavefunctions has become a powerful route to high-accuracy ground-state calculations, yet its practical success hinges on efficient and stable wavefunction optimization. While stochastic reconfiguration (SR) provides a geometry-aware preconditioner motivated by imaginary-time evolution, its Kaczmarzinspired variant, subsampled projected-increment natural gradient descent (SPRING), achieves state-of-the-art empirical performance. However, the effectiveness of SPRING is highly sensitive to the choice of a momentum-like parameter μ. The origin of this sensitivity and the instability observed at μ = 1 have remained unclear. In this work, we clarify the distinct mechanisms governing the regimes μ < 1 and μ = 1. We establish convergence guarantees for 0 ≤ μ < 1 under mild assumptions, and construct counterexamples showing that μ = 1 can induce divergence via uncontrolled growth along kernel-related directions when the step-size is not summable. Motivated by this theoretical insight and extensive numerical experiments, we further propose a tuning-free adaptive strategy for selecting μ based on spectral flatness and subspace overlap. This approach achieves performance comparable to optimally tuned SPRING, while significantly improving robustness in VMC optimization.
Speaker Profile: Xin Liu is a researcher and doctoral advisor at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and serves as Deputy Director of the Institute of Computational Mathematics and Engineering. His primary research interests include manifold optimization, distributed optimization, and their applications in materials computation, big data analysis, and machine learning.Xin Liu received funding from the National Natural Science Foundation of China’s Excellent Young Scientists Fund in 2016, the Distinguished Young Scientists Fund in 2021, and the Ministry of Science and Technology’s Key Special Project in 2023. In 2024, he received the Xiao Shutie Applied Mathematics Award from the Chinese Society for Industrial and Applied Mathematics. He currently serves on the editorial boards of domestic and international journals such as MPC, JCM, and APJOR; as a Young Editorial Board Member for Science in China: Mathematics (Chinese and English editions); and as Associate Editor of Computational Mathematics. He also holds the following positions: President of the Chinese Academy of Sciences Youth Innovation Promotion Association; Secretary-General of the Chinese Society for Industrial and Applied Mathematics; Standing Council Member of the Chinese Operations Research Society; and Standing Council Member of the Computational Mathematics Branch of the Chinese Mathematical Society.
All faculty and students are welcome!
School of Mathematical Sciences
May 8, 2026
