2026 Fall
The seminar of this semester is organized by Zihao Li and He Wang, and co-organized by the graduate student union in the School of Mathematical Sciences at Fudan. This section is partially sponsored by Shanghai Key Laboratory for Contemporary Applied Mathematics.
2026-09-17 16:10:00 - 17:00:00 @ Rm 1801, Guanghua East Tower
[poster]
- Title:
Optimization of Neural Network Wavefunctions in Variational Monte Carlo
- Speaker: Yuyang Wang (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
- Advisor: Xin Liu (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
Abstract: Click to expand
Variational Monte Carlo (VMC) with neural network wavefunctions is a powerful approach to ground-state calculations, but its performance depends critically on wavefunction optimization. In this talk, we will introduce VMC and focus on geometry-aware optimization methods for neural network wavefunctions, in particular stochastic reconfiguration (SR) and its variants. Among them, SPRING, inspired by the randomized Kaczmarz method, has shown strong empirical performance but is sensitive to the choice of a momentum-like parameter $\mu$. We analyze this sensitivity and reveal a qualitative difference between $\mu<1$ and $\mu=1$. For $0\leq\mu<1$, we establish first-order convergence under weak moment assumptions allowing heavy-tailed Monte Carlo noise; for $\mu=1$, we construct counterexamples showing divergence through accumulation along kernel-related directions. Motivated by these results, we propose PRIME-SR, an adaptive SR method that adjusts the momentum parameter based on spectral information and subspace overlap. Numerical experiments show that PRIME-SR achieves performance comparable to well-tuned SPRING while substantially improving robustness in neural wavefunction optimization.
Past Presentations
2026-09-10 16:10:00 - 17:00:00 @ Rm 1801, Guanghua East Tower
[poster]
- Title:
Accelerated Gradient Descent by Concatenation of Stepsize Schedules
- Speaker: Zehao Zhang (Fudan University)
- Advisor: Rujun Jiang (Fudan University)
Abstract: Click to expand
This work considers stepsize schedules for gradient descent on smooth convex objectives. We extend the existing literature and propose a unified technique for constructing stepsizes with analytic bounds for an arbitrary number of iterations. This technique constructs new stepsize schedules by concatenating two stepsize schedules with fewer steps. Using this approach, we introduce two new families of stepsize schedules, achieving a convergence rate of $O(n^{-\log_2{(\sqrt 2+1)}})$ with state-of-the-art constants for the objective value and gradient norm of the last iterate, respectively. Furthermore, our analytically derived stepsize schedules either match or surpass the existing best numerically computed stepsize schedules.
