{
  "abstract": "Scaling laws and hyperparameter tuning remain central challenges in training large-scale models, particularly under differential privacy (DP), where optimization is further complicated by noise injection and per-sample gradient clipping. While Maximal Update Parametrization ($μ$P) allows for zero-shot hyperparameter transfer in standard training, we show that it fails under DP constraints due to the distinct spectral properties of high-dimensional noise versus low-rank gradients. In this work, we introduce DP-$μ$P, a theoretically grounded framework that extends $μ$P to the privacy-preserving setting. By analyzing the interaction between gradient clipping, noise injection, and feature learning, we derive a Signal-to-Noise Ratio (SNR) condition that governs layer-wise learning rate scaling. Combining this with our proposed spectral scaling formulation, we provide specific scaling rules for DP-SGD, DP-Adam, and DP-Muon optimizers. Empirically, we demonstrate that DP-$μ$P enables effective zero-shot transfer of learning rates across model widths on diverse architectures (MLP, ViT, GPT-2), matching or exceeding the performance of individually tuned baselines while significantly reducing computational costs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22976",
  "author_total": 3,
  "authors": [
    {
      "name": "Tianze Wang"
    },
    {
      "name": "Zhiqi Bu"
    },
    {
      "name": "Linjun Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0dtg434dkbb8m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22976",
  "fulltext_url": null,
  "id": "0dtg434dkbb8m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22976",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CR"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Privacy-Preserving Technologies in Data"
    ]
  ],
  "openalex": "W7222915157",
  "pdf_url": "https://arxiv.org/pdf/2610.22976",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0dtg434dkbb8m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:13Z",
      "native_id": "2610.22976",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22976"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Towards Hyperparameter Transfer for Differentially Private Optimization",
  "title_text": "Towards Hyperparameter Transfer for Differentially Private Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:13Z",
  "url": "https://research.draconitic.com/paper/0dtg434dkbb8m",
  "venue": "arXiv",
  "versions": []
}