2024-04-18-battash24a.md

title	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Revisiting the Noise Model of Stochastic Gradient Descent	The effectiveness of stochastic gradient descent (SGD) in neural network optimization is significantly influenced by stochastic gradient noise (SGN). Following the central limit theorem, SGN was initially described as Gaussian, but recently Simsekli et al (2019) demonstrated that the $S\alpha S$ Lévy distribution provides a better fit for the SGN. This assertion was purportedly debunked and rebounded to the Gaussian noise model that had been previously proposed. This study provides robust, comprehensive empirical evidence that SGN is heavy-tailed and is better represented by the $S\alpha S$ distribution. Our experiments include several datasets and multiple models, both discriminative and generative. Furthermore, we argue that different network parameters preserve distinct SGN properties. We develop a novel framework based on a Lévy-driven stochastic differential equation (SDE), where one-dimensional Lévy processes describe each parameter. This leads to a more accurate characterization of the dynamics of SGD around local minima. We use our framework to study SGD properties near local minima; these include the mean escape time and preferable exit directions.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	battash24a	0	Revisiting the Noise Model of Stochastic Gradient Descent	4780	4788	4780-4788	4780	false	Battash, Barak and Wolf, Lior and Lindenbaum, Ofir	given family Barak Battash given family Lior Wolf given family Ofir Lindenbaum	2024-04-18		Proceedings of The 27th International Conference on Artificial Intelligence and Statistics	238	inproceedings	date-parts 2024 4 18	https://proceedings.mlr.press/v238/battash24a/battash24a.pdf