Speaker |
Kevin H. Huang |
|---|---|
Affiliation |
University College London |
Date |
Friday, 21 March 2025 |
Time |
12:00-13:00 |
Location |
UCL Centre for Artificial Intelligence, 1st Floor, 90 High Holborn, London WC1V 6BH |
Link |
https://ucl.zoom.us/j/99748820264 |
Event series |
Jump Trading/ELLIS CSML Seminar Series |
Abstract |
Incorporating group symmetries has been a cornerstone of success in many AI-for-science applications. Diagonal groups of isometries, which describe the invariance under a simultaneous movement of multiple objects, arise naturally in many-body quantum problems. Despite their importance, they receive relatively little attention in state-of-the-art variational Monte Carlo (VMC) neural network solvers for the many-electron Schrödinger equation. We study different ways of incorporating diagonal invariance in neural network ansatze trained via VMC, and consider specifically data augmentation, group averaging and canonicalization. We show that, contrary to standard ML setups, in-training symmetrization for VMC destabilizes training and can lead to worse performance. Our theoretical and numerical results indicate that this unexpected behavior may arise from a computationalstatistical tradeoff that is unique to VMC, and not found in standard ML analyses of symmetrization. Meanwhile, we demonstrate that post hoc averaging is less sensitive to such tradeoffs and emerges as a simple, flexible and effective method for improving neural network solvers. https://arxiv.org/abs/2502.05318 |
Biography |
Kevin is a final year PhD student at the Gatsby Computational Neuroscience Unit at UCL, advised by Peter Orbanz and Morgane Austern from the Department of Statistics at Harvard University. He studies the mathematical behaviours of large stochastic systems that emerge in machine learning, scientific and statistical applications, and how they motivate algorithms for estimation, prediction and uncertainty quantification. He is particularly interested in settings where data are high-dimensional and/or exhibit special geometric and correlation structures. |