{
  "abstract": "Adaptive optimizers such as Adam are standard for training Transformers, but storing gradient first and second moments incurs substantial memory overhead. We introduce PowerStep, a memory-efficient optimizer that achieves coordinate-wise adaptivity without storing second-moment statistics. Motivated by $\\ell_p$-norm steepest descent, PowerStep applies a signed-power transform directly to one momentum buffer. We establish a finite-horizon stationarity bound for exact, unregularized updates, with an $O(1/\\sqrt{T})$ term and a noise-dependent residual. Experiments on Transformers from 124M to 235B parameters show competitive validation quality while halving $\\texttt{fp32}$ optimizer-state memory relative to AdamW. Combined with uniform $\\texttt{int8}$ quantization, PowerStep remains numerically stable and reduces optimizer-state memory by $\\sim8\\times$ compared to $\\texttt{fp32}$ AdamW. PowerStep thus provides a simple, memory-efficient alternative for large-scale training.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.10335",
  "author_total": 4,
  "authors": [
    {
      "name": "Yao Lu"
    },
    {
      "name": "Dengdong Fan"
    },
    {
      "name": "Shixun Zhang"
    },
    {
      "name": "Yonghong Tian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8xvzg4t6phjms.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.10335",
  "fulltext_url": null,
  "id": "8xvzg4t6phjms",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.10335",
  "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.AI"
    ],
    [
      "arxiv",
      "cs.CL"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7160930927",
  "pdf_url": "https://arxiv.org/pdf/2605.10335",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8xvzg4t6phjms.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2605.10335",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.10335"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "PowerStep: Memory-Efficient Adaptive Optimization via $\\ell_p$-Norm Steepest Descent",
  "title_text": "PowerStep: Memory-Efficient Adaptive Optimization via ℓ_p-Norm Steepest Descent",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/8xvzg4t6phjms",
  "venue": "arXiv",
  "versions": []
}