UAI 2024poster2 citations
Gradient descent in matrix factorization: Understanding large initialization
Hengchao Chen, Xin Chen, Mohamad Elmasri, Qiang Sun
Abstract
Gradient Descent (GD) has been proven effective in solving various matrix factorization problems. However, its optimization behavior with large initial values remains less understood. To address this gap, this paper presents a novel theoretical framework for examining the convergence trajectory of GD with a large initialization. The framework is grounded in signal-to-noise ratio concepts and inductive arguments. The results uncover an implicit incremental learning phenomenon in GD and offer a deeper understanding of its performance in large initialization scenarios.
BibTeX
@InProceedings{pmlr-v244-chen24a,
title = {Gradient descent in matrix factorization: Understanding large initialization},
author = {Chen, Hengchao and Chen, Xin and Elmasri, Mohamad and Sun, Qiang},
booktitle = {Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence},
pages = {619--647},
year = {2024},
editor = {Kiyavash, Negar and Mooij, Joris M.},
volume = {244},
series = {Proceedings of Machine Learning Research},
month = {15--19 Jul},
publisher = {PMLR},
pdf = {https://raw.githubusercontent.com/mlresearch/v244/main/assets/chen24a/chen24a.pdf},
url = {https://proceedings.mlr.press/v244/chen24a.html},
abstract = {Gradient Descent (GD) has been proven effective in solving various matrix factorization problems. However, its optimization behavior with large initial values remains less understood. To address this gap, this paper presents a novel theoretical framework for examining the convergence trajectory of GD with a large initialization. The framework is grounded in signal-to-noise ratio concepts and inductive arguments. The results uncover an implicit incremental learning phenomenon in GD and offer a deeper understanding of its performance in large initialization scenarios.}
}