{"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/adapting-newton-s-method-to-neural-networks","title":"Adapting Newton's Method to Neural Networks through a Summary of Higher-Order Derivatives","arxiv_id":"2312.03885","date":"2023-12-06","proceeding":null,"authors":["Pierre Wolinski"],"abstract":"When training large models, such as neural networks, the full derivatives of order 2 and beyond are usually inaccessible, due to their computational cost. This is why, among the second-order optimization methods, it is very common to bypass the computation of the Hessian by using first-order information, such as the gradient of the parameters (e.g., quasi-Newton methods) or the activations (e.g., K-FAC). In this paper, we focus on the exact and explicit computation of projections of the Hessian and higher-order derivatives on well-chosen subspaces, which are relevant for optimization. Namely, for a given partition of the set of parameters, it is possible to compute tensors which can be seen as \"higher-order derivatives according to the partition\", at a reasonable cost as long as the number of subsets of the partition remains small. Then, we propose an optimization method exploiting these tensors at order 2 and 3 with several interesting properties, including: it outputs a learning rate per subset of parameters, which can be used for hyperparameter tuning; it takes into account long-range interactions between the layers of the trained neural network, which is usually not the case in similar methods (e.g., K-FAC); the trajectory of the optimization is invariant under affine layer-wise reparameterization. Code available at https://github.com/p-wol/GroupedNewton/ .","url_abs":"https://arxiv.org/abs/2312.03885v3","url_pdf":"https://arxiv.org/pdf/2312.03885v3.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":"adapting-newton-s-method-to-neural-networks","repo_url":"https://github.com/p-wol/GroupedNewton","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"second-order-methods","task_name":"Second-order methods"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}