{"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/sorsa-singular-values-and-orthonormal","title":"SORSA: Singular Values and Orthonormal Regularized Singular Vectors Adaptation of Large Language Models","arxiv_id":"2409.00055","date":"2024-08-21","proceeding":null,"authors":["Yang Cao"],"abstract":"In this paper, we propose Singular Values and Orthonormal Regularized Singular Vectors Adaptation, or SORSA, a novel PEFT method. Each SORSA adapter consists of two main parts: trainable principal singular weights $W_p = U_p \\text{diag}(S_p) V^\\top_p$, and frozen residual weights $W_r = U_r \\text{diag}(S_r) V^\\top_r$. These parts are initialized by performing singular value decomposition (SVD) on pre-trained weights. Moreover, we implement and analyze an orthonormal regularizer, which we prove could decrease the condition number of $W_p$ and make the optimization more efficient. SORSA adapters could be merged during inference, thus eliminating any inference latency. We also introduce a method to analyze the variation of the parameters by performing SVD and discuss and analyze SORSA's superiority in minimizing the alteration in the SVD aspect. After all, SORSA shows a faster convergence than LoRA and PiSSA in our experiments. On the GSM-8K benchmark, Llama 2 7B adapted using SORSA achieved 56.03% accuracy, surpassing LoRA (42.30%), AdaLoRA (47.30%), Full FT (49.05%), and PiSSA (53.07%). On the MATH benchmark, SORSA achieved 10.36% accuracy, outperforming LoRA (5.50%), AdaLoRA (6.48%), Full FT (7.22%), and PiSSA (7.44%). We conclude that SORSA offers a new perspective on parameter-efficient fine-tuning, demonstrating remarkable performance.","url_abs":"https://arxiv.org/abs/2409.00055v5","url_pdf":"https://arxiv.org/pdf/2409.00055v5.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":"sorsa-singular-values-and-orthonormal","repo_url":"https://github.com/Gunale0926/SORSA","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[{"task_slug":null,"task_name":"8k"},{"task_slug":"gsm8k","task_name":"GSM8K"},{"task_slug":"math","task_name":"Math"},{"task_slug":"parameter-efficient-fine-tuning","task_name":"parameter-efficient fine-tuning"}],"methods":[{"method_slug":"sorsa","method_name":"SORSA"}],"datasets_introduced":[],"methods_introduced":[{"slug":"sorsa","name":"SORSA","full_name":"Singular Values and Orthonormal Regularized Singular Vectors Adaptation"}],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2409.00055","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2409.00055"}},"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. 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