arXiv Machine Learning By Philipp Grohs, Davide Nobile

Is Variational Monte Carlo Robust? Sharp Moment Thresholds and Heavy-tailed Stochastic Optimization

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arXiv:2606. 26009v1 Announce Type: new Abstract: Variational Monte Carlo (VMC) is a central algorithm in electronic structure theory and has gained renewed importance through modern neural-network ans\"atze such as FermiNet.

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arXiv Machine Learning
Jun 15

Direct/adaptive-mixture phase-gradient learning for neural-network quantum states with complex phase structure

arXiv:2606. 13912v1 Announce Type: cross Abstract: Neural-network quantum states (NQS) are a leading variational tool for quantum many-body physics, yet their optimization is fragile whenever the ground state carries a non-trivial sign or complex phase structure, a situation generic to gauge fields, broken time-reversal symmetry, and fermionic statistics.

By Yi-Ran Xue, Rui Wang, Baigeng Wang, Chenan Wei
arXiv Machine Learning
Sep 14

Almost Sure Convergence Analysis of Stochastic Gradient Methods with Clipping and Additive Noise

The paper proves that stochastic gradient descent with gradient clipping and additive Gaussian noise (SGD‑CN) converges almost surely under smoothness and bounded noise assumptions, given standard decaying step sizes. The analysis extends to momentum variants such as the stochastic heavy ball and Nesterov's accelerated gradient, showing that careful energy constructions yield similar guarantees. These results provide stronger theoretical foundations for understanding the pathwise behaviour of clipped stochastic gradient methods in both convex and nonconvex regimes.

By Amartya Mukherjee, Jun Liu