{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/online-learning-and-information-exponents-on","title":"Online Learning and Information Exponents: On The Importance of Batch size, and Time/Complexity Tradeoffs","arxiv_id":"2406.02157","date":"2024-06-04","proceeding":null,"authors":["Luca Arnaboldi","Yatin Dandi","Florent Krzakala","Bruno Loureiro","Luca Pesce","Ludovic Stephan"],"abstract":"We study the impact of the batch size $n_b$ on the iteration time $T$ of training two-layer neural networks with one-pass stochastic gradient descent (SGD) on multi-index target functions of isotropic covariates. We characterize the optimal batch size minimizing the iteration time as a function of the hardness of the target, as characterized by the information exponents. We show that performing gradient updates with large batches $n_b \\lesssim d^{\\frac{\\ell}{2}}$ minimizes the training time without changing the total sample complexity, where $\\ell$ is the information exponent of the target to be learned \\citep{arous2021online} and $d$ is the input dimension. However, larger batch sizes than $n_b \\gg d^{\\frac{\\ell}{2}}$ are detrimental for improving the time complexity of SGD. We provably overcome this fundamental limitation via a different training protocol, \\textit{Correlation loss SGD}, which suppresses the auto-correlation terms in the loss function. We show that one can track the training progress by a system of low-dimensional ordinary differential equations (ODEs). Finally, we validate our theoretical results with numerical experiments.","url_abs":"https://arxiv.org/abs/2406.02157v1","url_pdf":"https://arxiv.org/pdf/2406.02157v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"online-learning-and-information-exponents-on","repo_url":"https://github.com/IdePHICS/batch-size-time-complexity-tradeoffs","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[{"method_slug":"sgd","method_name":"SGD"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2406.02157","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}