{"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-second-order-methods-for-non-convex","title":"Online Second Order Methods for Non-Convex Stochastic Optimizations","arxiv_id":"1803.09383","date":"2018-03-26","proceeding":null,"authors":["Xi-Lin Li"],"abstract":"This paper proposes a family of online second order methods for possibly\nnon-convex stochastic optimizations based on the theory of preconditioned\nstochastic gradient descent (PSGD), which can be regarded as an enhance\nstochastic Newton method with the ability to handle gradient noise and\nnon-convexity simultaneously. We have improved the implementations of the\noriginal PSGD in several ways, e.g., new forms of preconditioners, more\naccurate Hessian vector product calculations, and better numerical stability\nwith vanishing or ill-conditioned Hessian, etc.. We also have unrevealed the\nrelationship between feature normalization and PSGD with Kronecker product\npreconditioners, which explains the excellent performance of Kronecker product\npreconditioners in deep neural network learning. A software package\n(https://github.com/lixilinx/psgd_tf) implemented in Tensorflow is provided to\ncompare variations of stochastic gradient descent (SGD) and PSGD with five\ndifferent preconditioners on a wide range of benchmark problems with commonly\nused neural network architectures, e.g., convolutional and recurrent neural\nnetworks. Experimental results clearly demonstrate the advantages of PSGD in\nterms of generalization performance and convergence speed.","url_abs":"http://arxiv.org/abs/1803.09383v3","url_pdf":"http://arxiv.org/pdf/1803.09383v3.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-second-order-methods-for-non-convex","repo_url":"https://github.com/lixilinx/psgd_tf","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}}],"tasks":[{"task_slug":"second-order-methods","task_name":"Second-order methods"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1803.09383","atlas_url":"https://app.syntology.ai/?focus=1803.09383","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}