{"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/when-does-differentially-private-learning-not","title":"When Does Differentially Private Learning Not Suffer in High Dimensions?","arxiv_id":"2207.00160","date":"2022-07-01","proceeding":null,"authors":["Xuechen Li","Daogao Liu","Tatsunori Hashimoto","Huseyin A. Inan","Janardhan Kulkarni","Yin Tat Lee","Abhradeep Guha Thakurta"],"abstract":"Large pretrained models can be privately fine-tuned to achieve performance approaching that of non-private models. A common theme in these results is the surprising observation that high-dimensional models can achieve favorable privacy-utility trade-offs. This seemingly contradicts known results on the model-size dependence of differentially private convex learning and raises the following research question: When does the performance of differentially private learning not degrade with increasing model size? We identify that the magnitudes of gradients projected onto subspaces is a key factor that determines performance. To precisely characterize this for private convex learning, we introduce a condition on the objective that we term \\emph{restricted Lipschitz continuity} and derive improved bounds for the excess empirical and population risks that are dimension-independent under additional conditions. We empirically show that in private fine-tuning of large language models, gradients obtained during fine-tuning are mostly controlled by a few principal components. This behavior is similar to conditions under which we obtain dimension-independent bounds in convex settings. Our theoretical and empirical results together provide a possible explanation for recent successes in large-scale private fine-tuning. Code to reproduce our results can be found at \\url{https://github.com/lxuechen/private-transformers/tree/main/examples/classification/spectral_analysis}.","url_abs":"https://arxiv.org/abs/2207.00160v4","url_pdf":"https://arxiv.org/pdf/2207.00160v4.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":"when-does-differentially-private-learning-not","repo_url":"https://github.com/lxuechen/private-transformers","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2207.00160","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}