{"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/structured-inverse-free-natural-gradient","title":"Structured Inverse-Free Natural Gradient: Memory-Efficient & Numerically-Stable KFAC","arxiv_id":"2312.05705","date":"2023-12-09","proceeding":null,"authors":["Wu Lin","Felix Dangel","Runa Eschenhagen","Kirill Neklyudov","Agustinus Kristiadi","Richard E. Turner","Alireza Makhzani"],"abstract":"Second-order methods such as KFAC can be useful for neural net training. However, they are often memory-inefficient since their preconditioning Kronecker factors are dense, and numerically unstable in low precision as they require matrix inversion or decomposition. These limitations render such methods unpopular for modern mixed-precision training. We address them by (i) formulating an inverse-free KFAC update and (ii) imposing structures in the Kronecker factors, resulting in structured inverse-free natural gradient descent (SINGD). On modern neural networks, we show that SINGD is memory-efficient and numerically robust, in contrast to KFAC, and often outperforms AdamW even in half precision. Our work closes a gap between first- and second-order methods in modern low-precision training.","url_abs":"https://arxiv.org/abs/2312.05705v4","url_pdf":"https://arxiv.org/pdf/2312.05705v4.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":"structured-inverse-free-natural-gradient","repo_url":"https://github.com/f-dangel/singd","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"structured-inverse-free-natural-gradient","repo_url":"https://github.com/f-dangel/sirfshampoo","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"second-order-methods","task_name":"Second-order methods"}],"methods":[{"method_slug":"adamw","method_name":"AdamW"},{"method_slug":"natural-gradient-descent","method_name":"Natural Gradient Descent"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2312.05705","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2312.05705"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/f-dangel/sirfshampoo","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/f-dangel/singd","reach":{"status":"ok"}}],"summary":{"ran":1},"by_repo_kind":{"official":{"samples":1,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":1,"samples":[{"code_sha256_prefix":"72c09c1400c34913","entry":"linear_process_input","repo":"f-dangel/singd","repo_kind":"official","path":"singd/optim/utils.py","file_url":"https://github.com/f-dangel/singd/blob/HEAD/singd/optim/utils.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"72c09c1400c34913"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}