{"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/learning-provablely-improves-the-convergence","title":"Learning Provably Improves the Convergence of Gradient Descent","arxiv_id":"2501.18092","date":"2025-01-30","proceeding":null,"authors":["Qingyu Song","Wei Lin","Hong Xu"],"abstract":"Learn to Optimize (L2O) trains deep neural network based solvers for optimization, achieving success in accelerating convex problems and improving non-convex solutions. However, L2O lacks rigorous theoretical backing for its own training convergence, as existing analyses often use unrealistic assumptions -- a gap this work highlights empirically. We bridge this gap by proving the training convergence of L2O models that learn Gradient Descent (GD) hyperparameters for quadratic programming, leveraging the Neural Tangent Kernel (NTK) theory. We propose a deterministic initialization strategy to support our theoretical results and promote stable training over extended optimization horizons by mitigating gradient explosion. Our L2O framework demonstrates over 50\\% better optimality against GD and superior robustness over state-of-the-art L2O methods on synthetic datasets.","url_abs":"https://arxiv.org/abs/2501.18092v4","url_pdf":"https://arxiv.org/pdf/2501.18092v4.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":[],"tasks":[],"methods":[{"method_slug":"align","method_name":"ALIGN"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2501.18092","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2501.18092"}},"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":"deterministic:regex_extraction","url":"https://github.com/NetX-lab/MathL2OProof-Official","reach":null}],"summary":{"ran_draft_wrong":1},"by_repo_kind":{"found_in_text":{"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":0,"samples":[{"code_sha256_prefix":"6eeb77dd307deac7","entry":"unroll_BP","repo":"NetX-lab/MathL2OProof-Official","repo_kind":"found_in_text","path":"main_train_anlys.py","file_url":"https://github.com/NetX-lab/MathL2OProof-Official/blob/HEAD/main_train_anlys.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"6eeb77dd307deac7"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}